Quantum Pair Generation in Nonlinear Metasurfaces with Mixed and Pure Photon Polarizations

Jiho Noh, José Tomás Santiago-Cruz, Vitaliy Sultanov, Chloe F. Doiron, Sylvain D. Gennaro, Maria Chekhova, Igal Brener

Metasurfaces are highly effective at manipulating classical light in the linear regime; however, effectively controlling the polarization of nonclassical light generated from nonlinear resonant metasurfaces remains a challenge. Here, we present a solution by achieving polarization engineering of frequency-nondegenerate biphotons emitted via spontaneous parametric down-conversion in GaAs metasurfaces, utilizing quasi-bound states in the continuum (qBIC) resonances to enhance biphoton generation. Through comprehensive polarization tomography, we demonstrate that the emitted photons’ polarization directly reflects the qBIC mode’s far-field properties. Furthermore, we show that both the type of qBIC mode and the symmetry of the meta-atoms can be tailored to control each single-photon polarization state, and that the subsequent two-photon polarization states are nearly separable, offering potential applications in the heralded generation of single photons with adjustable polarization. This work provides a significant step toward utilizing metasurfaces to generate quantum light and engineer their polarization, a critical aspect for future quantum technologies.

High-harmonic generation by a bright squeezed vacuum

Andrei Rasputnyi, Zhaopin Chen, Michael Birk, Oren Cohen, Ido Kaminer, Michael Krüger, Denis Seletskiy, Maria Chekhova, Francesco Tani

High-harmonic generation has been driving the development of attosecond science and sources. More recently, high-harmonic generation in solids has been adopted by other communities as a method to study material properties. However, so far high-harmonic generation has only been driven by classical light, despite theoretical proposals to do so with quantum states of light. Here we observe non-perturbative high-harmonic generation in solids driven by a macroscopic quantum state of light, a bright squeezed vacuum, which we generate in a single spatiotemporal mode. The process driven by a bright squeezed vacuum is considerably more efficient in the generation of high harmonics than classical light of the same mean intensity. Due to its broad photon-number distribution, covering states from 0 to 2 × 10 13 photons per pulse, and strong subcycle electric field fluctuations, a bright squeezed vacuum gives access to free carrier dynamics within a much broader range of peak intensities than accessible with classical light.

Advances in quantum imaging

Hugo Defienne, Warwick P. Bowen, Maria Chekhova, Gabriela Barreto Lemos, Dan Oron, Sven Ramelow, Nicolas Treps, Daniele Faccio

Modern imaging technologies are widely based on classical principles of light or electromagnetic wave propagation. They can be remarkably sophisticated, with recent successes ranging from single-molecule microscopy to imaging far-distant galaxies. However, new imaging technologies based on quantum principles are gradually emerging. They can either surpass classical approaches or provide novel imaging capabilities that would not otherwise be possible. Here we provide an overview of the most recently developed quantum imaging systems, highlighting the nonclassical properties of sources, such as bright squeezed light, entangled photons and single-photon emitters that enable their functionality. We outline potential upcoming trends and the associated challenges, all driven by a central enquiry, which is to understand whether quantum light can make visible the invisible.

Fourier-transform infrared spectroscopy with undetected photons from high-gain spontaneous parametric down-conversion

Kazuki Hashimoto, Dmitri B. Horoshko, Mikhail I. Kolobov, Yoad Michael, Ziv Gefen, Maria Chekhova

Fourier-transform infrared spectroscopy (FTIR) is an indispensable analytical method that allows label-free identification of substances via fundamental molecular vibrations. However, traditional FTIR spectrometers require mid-infrared (MIR) elements, including low-efficiency MIR photodetectors. SU(1,1) interferometry has previously enabled FTIR with undetected MIR photons via spontaneous parametric down-conversion in the low-parametric-gain regime, where the number of photons per mode is much less than one and sensitive photodetectors are needed. In this work, we develop a high-parametric-gain SU(1,1) interferometer for MIR-range FTIR with undetected photons. Using our method, we demonstrate three major advantages: a high photon number at the interferometer output, a considerably lower photon number at the sample, and improved interference contrast. In addition, we broaden the spectral range of the interferometer by aperiodic poling in the gain medium. Exploiting the broadband SU(1,1) interferometer, we measure and evaluate the MIR absorption spectra of polymers in the 3-μm region.

Roadmap on photonic metasurfaces

Sebastian A. Schulz, Rupert. F. Oulton, Mitchell Kenney, Andrea Alù, Isabelle Staude, Ayesheh Bashiri, Zlata Fedorova, Radoslaw Kolkowski, A. Femius Koenderink, et al.

Here we present a roadmap on Photonic metasurfaces. This document consists of a number of perspective articles on different applications, challenge areas or technologies underlying photonic metasurfaces. Each perspective will introduce the topic, present a state of the art as well as give an insight into the future direction of the subfield.

Tunable entangled photon-pair generation in a liquid crystal

Vitaliy Sultanov, Aljaž Kavčič, Emmanouil Kokkinakis, Nerea Sebastián, Maria Chekhova, Matjaž Humar

Liquid crystals, with their ability to self-assemble, strong response to an electric field and integrability into complex systems, are key materials in light-beam manipulation1. The recently discovered ferroelectric nematic liquid crystals2,3 also have considerable second-order optical nonlinearity, making them a potential material for nonlinear optics4,5. Their use as sources of quantum light could considerably extend the boundaries of photonic quantum technologies6. However, spontaneous parametric down-conversion, the basic source of entangled photons7, heralded single photons8 and squeezed light9, has so far not been observed in liquid crystals—or in any liquids or organic materials. Here we implement spontaneous parametric down-conversion in a ferroelectric nematic liquid crystal and demonstrate electric-field tunable broadband generation of entangled photons, with an efficiency comparable to that of the best nonlinear crystals. The emission rate and polarization state of photon pairs is markedly varied by applying a few volts or twisting the molecular orientation along the sample. A liquid-crystal source enables a special type of quasi-phase matching10, which is based on the molecular twist structure and is therefore reconfigurable for the desired spectral and polarization properties of photon pairs. Such sources promise to outperform standard nonlinear optical materials in terms of functionality, brightness and the tunability of the generated quantum state. The concepts developed here can be extended to complex topological structures, macroscopic devices and multi-pixel tunable quantum light sources.

Multiphoton electron emission with non-classical light

Jonas Heimerl, Alexander Mikhaylov, Stefan Meier, Henrick Höllerer, Ido Kaminer, Maria Chekhova, Peter Hommelhoff

Photon number distributions of classical and non-classical light sources have been studied extensively, yet their impact on photoemission processes is largely unexplored. In this article, we present measurements of electron number distributions from metal needle tips illuminated with ultrashort light pulses with various photon quantum statistics. By varying the photon statistics of the exciting light field between classical (Poissonian) and quantum (super-Poissonian), we demonstrate that the measured electron distributions are changed substantially. Using single-mode bright squeezed vacuum light, we measure extreme statistics events with up to 65 electrons from one light pulse at a mean of 0.27 electrons per pulse—the likelihood for such an event equals 10−128 with Poissonian statistics. By changing the number of modes of the exciting bright squeezed vacuum, we can tailor the electron number distribution on demand. Most importantly, our results demonstrate that the photon statistics is imprinted from the driving light to the emitted electrons, opening the door to new sensor devices and to strong-field optics with quantum light and electrons.

Quantitative analysis of the intensity distribution of optical rogue waves

Éva Rácz, Kirill Spasibko, Mathieu Manceau, László Ruppert, Maria Chekhova, Radim Filip

The field of optical rogue waves is a rapidly expanding topic with a focus on explaining their emergence. To complement this research, instead of providing a microscopic model that generates extreme events, we concentrate on a general quantitative description of the observed behavior. We explore two complementary top-down approaches to estimating the exponent describing the power-law decaying distribution of optical rogue waves observed in supercontinuum generated in a single-mode fiber in the normal-dispersion regime by applying a highly fluctuating pump. The two distinct approaches provide consistent results, outperforming the standard Hill estimator. Further analysis of the distributions reveals the breakdown of power-law behavior due to pump depletion and detector saturation. Either of our methods is adaptable to analyze extreme-intensity events from arbitrary experimental data.

Broadband Spectroscopy and Interferometry with Undetected Photons at Strong Parametric Amplification

Kazuki Hashimoto, Dmitri B. Horoshko, Maria Chekhova

Nonlinear interferometry with entangled photons allows for characterizing a sample without detecting the photons interacting with it. This method enables highly sensitive optical sensing in the wavelength regions where efficient detectors are still under development. Recently, nonlinear interferometry has been applied to interferometric measurement techniques with broadband light sources, such as Fourier-transform infrared spectroscopy and infrared optical coherence tomography. However, they have been demonstrated with photon pairs produced through spontaneous parametric down-conversion (SPDC) at a low parametric gain, where the average number of photons per mode is much smaller than one. The regime of high-gain SPDC offers several important advantages, such as the amplification of light after its interaction with the sample and a large number of photons per mode at the interferometer output. This work presents broadband spectroscopy and high-resolution optical coherence tomography with undetected photons generated via high-gain SPDC in an aperiodically poled lithium niobate crystal. To prove the principle, reflective Fourier-transform near-infrared spectroscopy with a spectral bandwidth of 17 THz and optical coherence tomography with an axial resolution of 11 µm are demonstrated.<br>

Temporally Distilled High-Dimensional Biphotonic States from Thin Sources

Vitaliy Sultanov, Maria Chekhova

Generation of entangled photons through spontaneous parametric down-conversion (SPDC) from micro- and nanoscale sources offers unprecedented freedom in quantum state engineering, including the ability to generate two-photon states with high-dimensional hyperentanglement. However, as the source of SPDC gets smaller, the role of photoluminescence increases, which leads to the contamination of two-photon states with a thermal background. Here we propose and implement a solution to this problem: by using pulsed SPDC and time distillation, we increase the purity and the heralding efficiency of the photon pairs. In the experiment, we increased the purity of the two-photon states generated in a 7 μm film of lithium niobate from 0.002 to 0.99. With the higher purity we were able to observe and characterize different polarization states of photon pairs generated simultaneously due to relaxed phase matching. In particular, we showed the presence of orthogonally polarized photons that are potentially usable for the generation of polarization entanglement.

Wigner function tomography via optical parametric amplification

Mahmoud Kalash, Maria V. Chekhova

Wigner function tomography is indispensable for characterizing quantum states, but its commonly used version, balanced homodyne detection, suffers from several weaknesses. First, it requires efficient detection, which is critical for measuring fragile non-Gaussian states, especially bright ones. Second, it needs a local oscillator, tailored to match the spatiotemporal properties of the state under test, and fails for multimode and broadband states. Here we propose Wigner function tomography based on optical parametric amplification followed by direct detection. The method is immune to detection inefficiency and loss, and suitable for broadband, spatially and temporally multimode quantum states. To prove the principle, we experimentally reconstruct the Wigner function of squeezed vacuum occupying a single mode of a strongly multimode state. We obtain a squeezing of −7.5±0.4dB and purity of 0.91(+0.09−0.08) despite more than 97% loss caused mainly by filtering. Theoretically, we also consider the reconstruction of a squeezed single photon—a bright non-Gaussian state. Due to multimode parametric amplification, the method allows for simultaneous tomography of multiple modes. This makes it a powerful tool for optical quantum information processing.

Collectively Enhanced Giant Circular Dichroism of Germanium Nanohelix Square Lattice Arrays

Günter Ellrott, Paul Beck, Vitaliy Sultanov, Sergej Rothau, Norbert Lindlein, Maria Chekhova, Vojislav Kristic

Circular dichroism is a unique chiroptical signature of the chirality of a system and is a prevalent way to characterize and distinguish systems on a fundamental level and for their technological applicability. Thus, engineering and maximizing the chiroptical response of a single chiral object or a metasurface composed of chiral entities is a formidable task. Current efforts strongly focus on individual metallic nanostructures and their periodic ensembles to harvest on (resonant) plasmonic properties and interactions. This route, however, waives the advantages of high-refractive-index nanoscale materials embracing low dissipative losses at optical wavelengths and electromagnetic fields penetrating and propagating in such materials. Herein, a strong circular dichroism is demonstrated in square lattices of nanohelices made of the high-refractive-index semiconductor germanium, with dissymmetry factors outperforming metal-based ensembles. The observation of a much higher dissymmetry emerges for illumination with spatially coherent light, in comparison to spatially incoherent light. High dissymmetry is attributed to cooperative coupling between single helices, resulting from the combination of dielectric resonances of both the individual helical building blocks and the highly ordered lattice.

Tunable fiber source of entangled UV-C and infrared photons

Santiago López-Huidrobro, Noureddin Mohammad, Maria V. Chekhova, Nicolas Y. Joly

Pairs of entangled photons—biphotons—are indispensable in quantum applications. However, some important spectral ranges, like the ultraviolet, have been inaccessible to them so far. Here, we use four-wave mixing in a xenon-filled single-ring photonic crystal fiber to generate biphotons with one of the photons in the ultraviolet and its entangled partner in the infrared spectral range. We tune the biphotons in frequency by varying the gas pressure inside the fiber and thus tailoring the fiber dispersion landscape. The ultraviolet photons are tunable from 271 nm to 231 nm and their entangled partners, from 764 nm to 1500 nm, respectively. Tunability up to 192 THz is achieved by adjusting the gas pressure by only 0.68 bar. At 1.43 bar, the photons of a pair are separated by more than 2 octaves. The access to ultraviolet wavelengths opens the possibility for spectroscopy and sensing with undetected photons in this spectral range.

Nonlinear Interferometry for Quantum-Enhanced Measurements of Multiphoton Absorption

Shahram Panahiyan, Carlos Sánchez Muñoz, Maria V. Chekhova, Frank Schlawin

Multiphoton absorption is of vital importance in many spectroscopic, microscopic, or lithographic applications. However, given that it is an inherently weak process, the detection of multiphoton absorption signals typically requires large field intensities, hindering its applicability in many practical situations. In this Letter, we show that placing a multiphoton absorbent inside an imbalanced nonlinear interferometer can enhance the precision of multiphoton cross section estimation with respect to strategies based on photon-number measurements using coherent or even squeezed light directly transmitted through the medium. In particular, the power scaling of the sensitivity with photon flux can be increased by 1 order compared with transmission measurements of the sample with coherent light, such that the measurement precision at any given intensity can be greatly enhanced. Furthermore, we show that this enhanced measurement precision is robust against experimental imperfections leading to photon losses, which usually tend to degrade the detection sensitivity. We trace the origin of this enhancement to an optimal degree of squeezing which has to be generated in a nonlinear SU(1,1) interferometer.

Crystal superlattices for versatile and sensitive quantum spectroscopy

Zi S. D. Toa, Maria V. Chekhova, Leonid A. Krivitsky, Anna V. Paterova

Nonlinear interferometers with quantum correlated photons have been demonstrated to improve optical characterization and metrology. These interferometers can be used in gas spectroscopy, which is of particular interest for monitoring greenhouse gas emissions, breath analysis and industrial applications. Here, we show that gas spectroscopy can be further enhanced via the deployment of crystal superlattices. This is a cascaded arrangement of nonlinear crystals forming interferometers, allowing the sensitivity to scale with the number of nonlinear elements. In particular, the enhanced sensitivity is observed via the maximum intensity of interference fringes that scales with low concentration of infrared absorbers, while for high concentration the sensitivity is better in interferometric visibility measurements. Thus, a superlattice acts as a versatile gas sensor since it can operate by measuring different observables, which are relevant to practical applications. We believe that our approach offers a compelling path towards further enhancements for quantum metrology and imaging using nonlinear interferometers with correlated photons.

Photon pairs bi-directionally emitted from a resonant metasurface

Changjin Son, Vitaliy Sultanov, Tomas Santiago-Cruz, Aravind P. Anthur, Haizhong Zhang, Ramon Paniagua-Dominguez, Leonid Krivitsky, Arseniy I. Kuznetsov, Maria V. Chekhova

Metasurfaces are artificially structured surfaces able to control the properties of light at subwavelength scales. While, initially, they have been proposed as means to control classical optical fields, they are now emerging as nanoscale sources of quantum light, in particular of entangled photons with versatile properties. Geometric resonances in metasurfaces have been recently used to engineer the frequency spectrum of entangled photons, but the emission directivity was so far less studied. Here, we generate photon pairs via spontaneous parametric down conversion from a metasurface supporting a quasi-bound state in the continuum (BIC) leading to remarkable emission directivities. The pair generation rate is enhanced 67 times compared to the case of an unpatterned film of the same thickness and material. At the wavelength of the quasi-BIC resonance, photons are mostly emitted backwards, while their partners, spectrally detuned by only 8 nm, are emitted forwards. This behavior demonstrates fine spectral splitting of entangled photons and their bi-directional emission, never before observed in nanoscale sources. We expect this work to be a starting point for the efficient demultiplexing of photons in nanoscale quantum optics.

Two-photon-absorption measurements in the presence of single-photon losses

Sharam Panahiyan, Carlos Sánchez Muñoz, Maria V. Chekhova, Frank Schlawin

We discuss how two-photon absorption (TPA) of squeezed and coherent states of light can be detected in measurements of the transmitted light fields. Such measurements typically suffer from competing loss mechanisms such as experimental imperfections (i.e., imperfect photodetectors) and other linear scattering losses inside the sample itself, which can lead to incorrect assessments of the two-photon-absorption cross section. We evaluate the sensitivity with which TPA can be detected and find that at sufficiently large photon numbers TPA sensitivity of squeezed vacua or squeezed coherent states can become independent of linear losses that occur after the TPA event has taken place. In particular, this happens for measurements of the photon number or of the antisqueezed field quadrature, where large fluctuations counteract and exactly cancel the degradation caused by single-photon losses.

Analysis of the signal measured in spectral-domain optical coherence tomography based on nonlinear interferometers

Arturo Rojas-Santana, Gerard J. Machado, Maria V. Chekhova, Dorilian Lopez-Mago, Juan P. Torres

We analyze and compare the output signals obtained in three different configurations of optical coherence tomography (OCT). After appropriate processing, these signals are used to retrieve an image of the sample under investigation. One of the configurations considered is the common choice in most OCT applications and is based on the use of a Michelson interferometer. For brevity, here we refer to it as standard OCT. The other two configurations are two types of optical coherence tomography based on the use of so-called nonlinear interferometers, interferometers that contain optical parametric amplifiers inside. The goal is to highlight the differences and similarities between the output signals measured in standard OCT and in these two OCT schemes, with the aim of evaluating if retrieval of information about the sample can be better done in one case over the others. We consider schemes where the optical sectioning of the sample is obtained by measuring the output signal spectrum (spectral or Fourier-domain OCT), since it shows better performance in terms of speed and sensitivity than the counterpart time-domain OCT.

Resonant metasurfaces for generating complex quantum states

Tomas Santiago-Cruz, Sylvain D. Gennaro, Oleg Mitrofanov, Sadhvikas Addamane, John Reno, Igal Brener, Maria V. Chekhova

Quantum state engineering, the cornerstone of quantum photonic technologies, mainly relies on spontaneous parametric downconversion and four-wave mixing, where one or two pump photons spontaneously decay into a photon pair. Both of these nonlinear effects require momentum conservation for the participating photons, which strongly limits the versatility of the resulting quantum states. Nonlinear metasurfaces have subwavelength thickness and allow the relaxation of this constraint; when combined with resonances, they greatly expand the possibilities of quantum state engineering. Here, we generated entangled photons via spontaneous parametric downconversion in semiconductor metasurfaces with high–quality factor, quasi-bound state in the continuum resonances. By enhancing the quantum vacuum field, our metasurfaces boost the emission of nondegenerate entangled photons within multiple narrow resonance bands and over a wide spectral range. A single resonance or several resonances in the same sample, pumped at multiple wavelengths, can generate multifrequency quantum states, including cluster states. These features reveal metasurfaces as versatile sources of complex states for quantum information.

Classical model of spontaneous parametric down-conversion

Girish Kulkarni, Jeremy Rioux, Boris Braverman, Maria V. Chekhova, Robert W. Boyd

We model spontaneous parametric down-conversion (SPDC) as classical difference frequency generation (DFG) of the pump field and a hypothetical stochastic “vacuum” seed field. We analytically show that the second-order spatiotemporal correlations of the field generated from the DFG process replicate those of the signal field from SPDC. Specifically, for low gain, the model is consistent with the quantum calculation of the signal photon’s reduced density matrix; and for high gain, the model’s predictions are in good agreement with our experimental measurements of the far-field intensity profile, orbital angular momentum spectrum, and wavelength spectrum of the SPDC field for increasing pump strengths. We further theoretically show that the model successfully captures second-order SU(1,1) interference and induced coherence effects in both gain regimes. Intriguingly, the model also correctly predicts the linear scaling of the interference visibility with object transmittance in the low-gain regime—a feature that is often regarded as a quintessential signature of the nonclassicality of induced coherence. Our model may not only lead to fundamental insights into the classical-quantum divide in the context of SPDC and induced coherence, but can also be a useful theoretical tool for numerous experiments and applications based on SPDC.

Metasurfaces for quantum technologies

Kai Wang, Maria V. Chekhova, Yuri S. Kivshar

Subwavelength planar structures can generate, reshape, and entangle photons in a compact and stable device.

Flat-optics generation of broadband photon pairs with tunable polarization entanglement

Vitaliy Sultanov, José Tomás Santiago-Cruz, Maria V. Chekhova

The concept of “flat optics” is quickly conquering different fields of photonics, but its implementation in quantum optics is still in its infancy. In particular, polarization entanglement, strongly required in quantum photonics, is so far not realized on “flat” platforms. Meanwhile, relaxed phase matching of “flat” nonlinear optical sources enables enormous freedom in tailoring their polarization properties. Here we use this freedom to generate photon pairs with tunable polarization entanglement via spontaneous parametric downconversion (SPDC) in a 400 nm GaP film. By changing the pump polarization, we tune the polarization state of photon pairs from maximally entangled to almost disentangled, which is impossible in a single bulk SPDC source. Polarization entanglement, together with the broadband frequency spectrum, results in an ultranarrow (12 fs) Hong–Ou–Mandel effect and promises extensions to hyperentanglement.

Cascaded frequency up-conversion of bright squeezed vacuum: spectral and correlation properties

Andrei V. Rasputnyi, Denis A. Kopylov, Tatiana V. Murzina, Maria V. Chekhova

High-gain parametric down-conversion (PDC) is inevitably accompanied by cascaded up-conversion (CUpC) of PDC radiation in a nonlinear crystal even if CUpC is nonphase matched. Here we study experimentally and theoretically the spectral properties of broadband phase-matched and nonphase-matched CUpC radiation in a beta barium borate (BBO) crystal. Our calculations of the normalized second- order correlation function predict the super-bunching of CUpC radiation.

Bright squeezed vacuum for two-photon spectroscopy: simultaneously high resolution in time and frequency, space and wavevector

Paula Cutipa, Maria V. Chekhova

Entangled photons offer two advantages for two-photon absorption spectroscopy. One of them, the linear scaling of two-photon absorption rate with the input photon flux, is valid only at very low photon fluxes and is therefore impractical. The other is the overcoming of the classical constraints for simultaneous resolution in time–frequency and in space–wavevector. Here we consider bright squeezed vacuum (BSV) as an alternative to entangled photons. The efficiency increase it offers in comparison with coherent light is modest, but it does not depend on the photon flux. Moreover, and this is what we show in this work, BSV also provides simultaneously high resolution in time and frequency, and in space and wavevector. In our experiment, we measure the widths of the second-order correlation functions in space, time, frequency, and angle and demonstrate the violation of the constraint given by the Fourier transformation, in the case of photon pairs, known as the Mancini criterion of entanglement.

Fiber-based biphoton source with ultrabroad frequency tunability

Santiago López-Huidrobro, Markus Lippl, Nicolas Joly, Maria Chekhova

Tunable biphotons are highly important for a wide range of quantum applications. For some applications, especially interesting are cases where two photons of a pair are far apart in frequency. Here, we report a tunable biphoton source based on a xenon-filled hollow-core photonic crystal fiber. Tunability is achieved by adjusting the pressure of the gas inside the fiber. This allows us to tailor the dispersion landscape of the fiber, overcoming the principal limitations of solid-core fiber-based biphoton sources. We report a maximum tunability of 120 THz for a pressure range of 4 bar with a continuous shift of 30 THz/bar. At 21 bar, the photons of a pair are separated by more than one octave. Despite the large separation, both photons have large bandwidths. At 17 bar, they form a very broad (110 THz) band around the frequency of the pump.

Overcoming detection loss and noise in squeezing-based optical sensing

Gaetano Frascella, Sascha Agne, Farid Ya. Khalili, Maria V. Chekhova

Among the known resources of quantum metrology, one of the most practical and efficient is squeezing. Squeezed states of atoms and light improve the sensing of the phase, magnetic field, polarization, mechanical displacement. They promise to considerably increase signal-to-noise ratio in imaging and spectroscopy, and are already used in real-life gravitational-wave detectors. But despite being more robust than other states, they are still very fragile, which narrows the scope of their application. In particular, squeezed states are useless in measurements where the detection is inefficient or the noise is high. Here, we experimentally demonstrate a remedy against loss and noise: strong noiseless amplification before detection. This way, we achieve loss-tolerant operation of an interferometer fed with squeezed and coherent light. With only 50% detection efficiency and with noise exceeding the level of squeezed light more than 50 times, we overcome the shot-noise limit by 6 dB. Sub-shot-noise phase sensitivity survives up to 87% loss. Application of this technique to other types of optical sensing and imaging promises a full use of quantum resources in these fields.

Photon Pairs from Resonant Metasurfaces

Tomas Santiago-Cruz, Anna Fedotova, Vitaliy Sultanov, Maximilian A. Weissflog, Dennis Arslan, Mohammadreza Younesi, Thomas Pertsch, Isabelle Staude, Frank Setzpfandt, et al.

All-dielectric optical metasurfaces are a workhorse in nano-optics, because of both their ability to manipulate light in different degrees of freedom and their excellent performance at light frequency conversion. Here, we demonstrate first-time generation of photon pairs via spontaneous parametric-down conversion in lithium niobate quantum optical metasurfaces with electric and magnetic Mie-like resonances at various wavelengths. By engineering the quantum optical metasurface, we tailor the photon-pair spectrum in a controlled way. Within a narrow bandwidth around the resonance, the rate of pair production is enhanced up to 2 orders of magnitude, compared to an unpatterned film of the same thickness and material. These results enable flat-optics sources of entangled photons—a new promising platform for quantum optics experiments.

Multimode optical parametric amplification in the phase-sensitive regime

Gaetano Frascella, R. V. Zakharov, O. V. Tikhonova, Maria V. Chekhova

Phase-sensitive optical parametric amplification of squeezed states helps to overcome detection loss and noise and thus increases the robustness of sub-shot-noise sensing. Because such techniques, e.g., imaging and spectroscopy, operate with multimode light, multimode amplification is required. Here we find the optimal methods for multimode phase-sensitive amplification and verify them in an experiment where a pumped second-order nonlinear crystal is seeded with a Gaussian coherent beam. Phase-sensitive amplification is obtained by tightly focusing the seed into the crystal, rather than seeding with close-to-plane waves. This suggests that phase-sensitive amplification of sub-shot-noise images should be performed in the near field. A similar recipe can be formulated for the time and frequency, which makes this work relevant for quantum-enhanced spectroscopy.

Polarization of Light: In Classical, Quantum, and Nonlinear Optics

Maria V. Chekhova, Peter Banzer

This book starts with the description of polarization in classical optics, including also a chapter on crystal optics, which is necessary to understand the use of nonlinear crystals. In addition, spatially non-uniform polarization states are introduced and described. Further, the role of polarization in nonlinear optics is discussed. The final chapters are devoted to the description and applications of polarization in quantum optics and quantum technologies.

Special Topic: Quantum sensing with correlated light sources

Alex S. Clark, Maria V. Chekhova, Jonathan C F Matthews, John G. Rarity, Rupert F. Oulton

Entangled photons from subwavelength nonlinear films

Tomas Santiago-Cruz, Vitaliy Sultanov, Haizhong Zhang, Leonid A. Krivitsky, Maria V. Chekhova

Miniaturized entangled photon sources, in particular based on subwavelength metasurfaces, are highly demanded for the development of integrated quantum photonics. Here, as a first step towards the development of quantum optical metasurfaces (QOMs), we demonstrate generation of entangled photons via spontaneous parametric down-conversion (SPDC) from subwavelength films. We achieve photon pair generation with a high coincidence-to-accidental ratio in lithium niobate and gallium phosphide nanofilms. By implementing the fiber spectroscopy of SPDC in nanofilms, we measure a spectrum with a bandwidth of 500 nm, limited only by the overall detection efficiency. The spectrum reveals vacuum field enhancement due to a Fabry–Perot resonance inside the nonlinear films. It also suggests a strategy for observing SPDC from QOM. Our experiments lay the groundwork for future development of flat SPDC sources, including QOM.

Broadening the high sensitivity range of squeezing-assisted interferometers by means of two-channel detection

Gaurav Shukla, Dariya Salykina, Gaetano Frascella, Devendra Kumar Mishra, Maria V. Chekhova, Farit Khalili

For a squeezing-enhanced linear (so-called SU(2)) interferometer, we theoretically investigate the possibility to broaden the phase range of sub-shot-noise sensitivity. We show that this goal can be achieved by implementing detection in both output ports, with the optimal combination of the detectors outputs. With this modification, the interferometer has the phase sensitivity independent of the interferometer operation point and, similar to the standard dark port regime, is not affected by the laser technical (excess) noise. Provided that each detector is preceded by a phase-sensitive amplifier, this sensitivity could be also tolerant to the detection loss.

Reconstructing two-dimensional spatial modes for classical and quantum light

Valentin A. Averchenko, Gaetano Frascella, Mahmoud Kalash, Andrea Cavanna, Maria V. Chekhova

We propose a method for finding two-dimensional spatial modes of thermal field through a direct measurement of the field intensity and an offline analysis of its spatial fluctuations. Using this method, in a simple and efficient way we reconstruct the modes of a multimode fiber and the spatial Schmidt modes of squeezed vacuum generated via high-gain parametric down-conversion. The reconstructed shapes agree with the theoretical results.

Optical coherence tomography with a nonlinear interferometer in the high parametric gain regime

Gerard J. Machado, Gaetano Frascella, Juan P. Torres, Maria V. Chekhova

We demonstrate optical coherence tomography based on an SU(1,1) nonlinear interferometer with high-gain parametric downconversion. For imaging and sensing applications, this scheme promises to outperform previous experiments working at low parametric gain, since higher photon fluxes provide lower integration times for obtaining high-quality images. In this way, one can avoid using single-photon detectors or CCD cameras with very high sensitivities, and standard spectrometers can be used instead. Other advantages are higher sensitivity to small loss and amplification before detection so that the detected light power considerably exceeds the probing one.

Pump depletion in parametric down-conversion with low pump energies

Jefferson Flórez, Jeff S. Lundeen, M. V. Chekhova

We report the efficient generation of high-gain parametric down-conversion, including pump depletion, with pump powers as low as 100 μW (energies 0.1 μJ/pulse) and conver- sion efficiencies up to 33%. In our simple configuration, the pump beam is tightly focused into a bulk periodically poled lithium niobate crystal placed in free space. We also observe a change in the photon number statistics for both the pump and down-converted beams as the pump power increases to reach the depleted pump regime. The experimental results are a clear signature of the interplay between the pump and the down-converted beams in highly efficient parametric down-conversion sources

Direct measurement of the coupled spatiotemporal coherence of parametric down-conversion under negative group-velocity dispersion

Paula Cutipa, Kirill Spasibko, Maria Chekhova

We present a direct measurement of the spatiotemporal coherence of parametric down-conversion in the range of negative group-velocity dispersion. In this case, the frequency-angular spectra are ring-shaped, and temporal coherence is coupled to spatial coherence. Correspondingly, the lack of coherence due to spatial displacement can be compensated for with the introduction of time delay. We show a simple technique, based on a modified Mach– Zehnder interferometer, which allows us to measure time coherence and near-field space coherence simultaneously, with complete control over both variables. This technique is also suitable for the measurement of second-order coher- ence, where the main applications are related to two-photon spectroscopy.

Spectral properties of second, third and fourth harmonics generation from broadband multimode bright squeezed vacuum

Denis A Kopylov, Andrei V Rasputnyi, Tatiana V Murzina, Maria V. Chekhova

We study theoretically the spectra of second, third and fourth harmonics from multimode bright squeezed vacuum obtained by type-I broadband high-gain parametric down conversion. The different contributions to the spectra of harmonics are analyzed. A new method for the measurement of second-order correlation function g(2)(0) of parametric down conversion radiation is suggested.

Progress toward third-order parametric down-conversion in optical fibers

A. Cavanna, J. Hammer, C. Okoth, E. Ortiz-Ricardo, H. Cruz-Ramirez, K. Garay-Palmett, A. B. U’Ren, M. Frosz, X. Jiang, et al.

Optical fibers have been considered an optimal platform for third-order parametric down-conversion since they can potentially overcome the weak third-order nonlinearity by their long interaction length. Here we present, in the first part, a theoretical derivation for the conversion rate both in the case of spontaneous generation and in the presence of a seed beam. Then we review three types of optical fibers and we examine their properties in terms of conversion efficiency and practical feasibility.

Properties of bright squeezed vacuum at increasing brightness

P. R. Sharapova, Gaetano Frascella, A. M. Perez, O. V. Tikhonova, S. Lemieux, R. W. Boyd, Gerd Leuchs, M. V. Chekhova

A bright squeezed vacuum (BSV) is a nonclassical macroscopic state of light, which is generated through high-gain parametric down-conversion or four-wave mixing. Although the BSV is an important tool in quantum optics and has a lot of applications, its theoretical description is still not complete. In particular, the existing description in terms of Schmidt modes with gain-independent shapes fails to explain the spectral broadening observed in the experiment as the mean number of photons increases. Meanwhile, the semiclassical description accounting for the broadening does not allow us to decouple the intermodal photon-number correlations. In this work, we present a new generalized theoretical approach to describe the spatial properties of a multimode BSV. In the multimode case, one has to take into account the complicated interplay between all involved modes: each plane-wave mode interacts with all other modes, which complicates the problem significantly. The developed approach is based on exchanging the (k, t ) and (ω, z) representations and solving a system of integrodifferential equations. Our approach predicts correctly the dynamics of the Schmidt modes and the broadening of the angular distribution with the increase in the BSV mean photon number due to a stronger pumping. Moreover, the model correctly describes various properties of a widely used experimental configuration with two crystals and an air gap between them, namely, an SU(1,1) interferometer. In particular, it predicts the narrowing of the intensity distribution, the reduction and shift of the side lobes, and the decline in the interference visibility as the mean photon number increases due to stronger pumping. The presented experimental results confirm the validity of the new approach. The model can be easily extended to the case of the frequency spectrum, frequency Schmidt modes, and other experimental configurations.

Broadly tunable photon-pair generation in a suspended-core fiber

Jonas Hammer, Maria V. Chekhova, Daniel Häupl, Riccardo Pennetta, Nicolas Y. Joly

Nowadays fiber biphoton sources are nearly as popular as crystal-based ones. They offer a single spatial mode and easy integrability into optical networks. However, fiber sources lack the broad tunability of crystals, which do not require a tunable pump. Here, we report a broadly tunable biphoton source based on a suspended core fiber. This is achieved by introducing pressurized gas into the fibers hollow channels, changing the step index. The mechanism circumvents the need for a tunable pump laser, making this a broadly tunable fiber biphoton source with a convenient tuning mechanism, comparable to crystals. We report a continuous shift of 0.30 THz/bar of the sidebands, using up to 25 bar of argon.

Idealized Einstein-Podolsky-Rosen states from non–phase-matched parametric down-conversion

Cameron Okoth, E. Kovlakov, F. Bönsel, Andrea Cavanna, S. Straupe, S. P. Kulik, Maria Chekhova

The most common source of entangled photons is spontaneous parametric down-conversion (SPDC). The degree of energy and momentum entanglement in SPDC is determined by the nonlinear interaction volume. By reducing the length of a highly nonlinear material, we relax the longitudinal phase-matching condition and reach record levels of transverse momentum entanglement. The degree of entanglement is estimated using both correlation measurements and stimulated emission tomography in wave-vector space. The high entanglement of the state in wave-vector space can be used to massively increase the quantum information capacity of photons, but more interestingly the equivalent state measured in position space is correlated over distances far less than the photon wavelength. This property promises to improve the resolution of many quantum imaging techniques beyond the current state of the art.

Microscale Generation of Entangled Photons without Momentum Conservation

Cameron Okoth, Andrea Cavanna, Tomas Santiago-Cruz, Maria Chekhova

We report, for the first time, the observation of spontaneous parametric down-conversion (SPDC) free of phase matching (momentum conservation).We alleviate the need to conserve momentum by exploiting the<br>position-momentum uncertainty relation and using a planar geometry source, a 6 μm thick layer of lithium niobate. Nonphase-matched SPDC opens up a new platform on which to investigate fundamental quantum<br>effects but it also has practical applications. The ultrasmall thickness leads to a frequency spectrum an order of magnitude broader than that of phase-matched SPDC. The strong two-photon correlations are still<br>preserved due to energy conservation. This results in ultrashort temporal correlation widths and huge frequency entanglement. The studies we make here can be considered as the initial steps into the emerging field of nonlinear quantum optics on the microscale and nanoscale.

Detection-device-independent verification of nonclassical light

M Bohmann, L Qi, W Vogel, Maria Chekhova

The efficient certification of nonclassical effects of light forms the basis for applications in optical quantum technologies. We derive general correlation conditions for the verification of nonclassical light based on multiplexed detection. The obtained nonclassicality criteria are valid for imperfectly balanced multiplexing scenarios with on-off detectors and do not require any knowledge about the detector system. In this sense, they are fully independent of the detector system. In our experiment, we study light emitted by clusters of single-photon emitters, whose photon number may exceed the number of detection channels. Even under such conditions, our criteria certify nonclassicality with high statistical significance.

Feasibility of quantum key distribution with macroscopically bright coherent light

Olena Kovalenko, Kirill Spasibko, M. V. Chekhova, Vladyslav C. Usenko, Radim Filip

We address feasibility of continuous-variable quantum key distribution using bright multimode coherent states of light and homodyne detection. We experimentally verify the possibility to properly select signal modes by matching them with the local oscillator and this way to decrease the quadrature noise concerned with unmatched bright modes. We apply the results to theoretically predict the performance of continuous-variable quantum key distribution scheme using multimode coherent states in scenarios where modulation is applied either to all the modes or only to the matched ones, and confirm that the protocol is feasible at high overall brightness. Our results open the pathway towards full-scale implementation of quantum key distribution using bright light, thus bringing quantum communication closer to classical optics.

Experimental reconstruction of spatial Schmidt modes for a wide-field SU(1,1) interferometer

Gaetano Frascella, Roman V Zakharov, Olga V Tikhonova, Maria Chekhova

We study the spatial mode content at the output of a wide-field SU(1, 1) interferometer, i.e. a nonlinear interferometer comprising two coherently-pumped spatially-multimode optical parametric amplifiers placed in sequence with a focusing element in between. This device is expected to provide a phase sensitivity below the shot-noise limit for multiple modes over<br>a broad angular range. To reconstruct the spatial modes and their weights, we implement<br>a simple method based on the acquisition of only intensity distributions. The eigenmode decomposition of the field is obtained through the measurement of the covariance of intensities at different spatial points. We investigate both the radial and azimuthal (orbital angular momentum) modes and show that their total number is large enough to enable applications of the interferometer in spatially-resolved phase measurements.

Nonlinear Mach–Zehnder interferometer with ultrabroadband squeezed light

D. B. Horoshko, M. I. Kolobov, F. Gumpert, I. Shand, F. König, M. V. Chekhova

We study both theoretically and experimentally the interference pattern in a nonlinear Mach–Zehnder interferometer formed by two aperiodically-poled crystals, where broadband squeezed light is generated by both crystals via parametric down-conversion with a common quasi- monochromatic pump. This configuration is important for measuring the squeezing produced by the first crystal and also for measuring a small phase shift introduced by a sample between the crystals. On the basis of the approximate quantum Rosenbluth formula for each crystal we develop an ana- lytic model for the field evolution in the interferometer. We report an experimental observation of the interference fringes, caused by the dispersion of the generated PDC waves in both crystals form- ing the interferometer. We observe a displacement of the interference pattern caused by a sample between the crystals and infer the phase shift within a band of 20 nm. The experimental data are in a good agreement with the predictions of the developed model, up to imperfections of the samples.

Indefinite-Mean Pareto Photon Distribution from Amplified Quantum Noise

Mathieu Manceau, Kirill Spasibko, Gerd Leuchs, Radim Filip, Maria Chekhova

Extreme events appear in many physics phenomena, whenever the probability distribution has a "heavy tail" differing very much from the equilibrium one. Most unusual are the cases of power-law (Pareto) probability distributions. Among their many manifestations in physics, from "rogue waves" in the ocean to Levy flights in random walks, Pareto dependences can follow very different power laws. For some outstanding cases, the power exponents are less than 2, leading to indefinite values not only for higher moments but also for the mean. Here we present the first evidence of indefinite-mean Pareto distribution of photon numbers at the output of nonlinear effects pumped by parametrically amplified vacuum noise, known as bright squeezed vacuum (BSV). We observe a Pareto distribution with power exponent 1.31 when BSV is used as a pump for supercontinuum generation, and other heavy-tailed distributions (however, with definite moments) when it pumps optical harmonics generation. Unlike in other fields, we can flexibly control the Pareto exponent by changing the experimental parameters. This extremely fluctuating light is interesting for ghost imaging and for quantum thermodynamics as a resource to produce more efficiently nonequilibrium states by single-photon subtraction, the latter of which we demonstrate experimentally.

Wide-field SU(1,1) interferometer

Gaetano Frascella, E. E. Mikhailov, N. Takanashi, R. V. Zakharov, O. V. Tikhonova, Maria Chekhova

An SU(1,1) interferometer uses a sequence of two optical parametric amplifiers for achieving sub-shot-noise sensitivity to a phase shift introduced in between. We present the first realization of a wide-field SU(1,1) interferometer, where the use of a focusing element enables spatially multimode operation within a broad angle. Over this angle, the interference phase is found to be flat. This property is important for the high sensitivity to the phase front disturbance. Further, -4.3 +/- 0.7 dB quadrature squeezing, an essential requirement to the high sensitivity, is experimentally demonstrated for plane-wave modes inside the interferometer. Such an interferometer is useful not only for quantum metrology, but also in remote sensing, enhanced sub-shot-noise imaging, and quantum information processing. (C) 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Separated Schmidt modes in the angular spectrum of biphotons

N. A. Borshchevskaia, F. Just, K. G. Katamadze, Andrea Cavanna, M. V. Chekhova

We prepared qudits based on angular multimode biphoton states by modulating the pump angular spectrum. The modes were prepared in the Schmidt basis and their intensity distributions did not overlap in space. This allows one to get rid of filtering losses while addressing single modes and to realize a single-shot qudit readout.

Seeded and unseeded high-order parametric down-conversion

Cameron Okoth, Andrea Cavanna, Nicolas Joly, Maria Chekhova

Spontaneous parametric down-conversion (SPDC) has been one of the foremost tools in quantum optics for over five decades. Over that time, it has been used to demonstrate some of the curious features that arise from quantum mechanics. Despite the success of SPDC, its higher-order analogs have never been observed, even though it has been suggested that they generate far more unique and exotic states than SPDC. An example of this is the emergence of non-Gaussian states without the need for postselection. Here we calculate the expected rate of emission for nth-order SPDC with and without external stimulation (seeding). Focusing primarily on third-order parametric down-conversion, we estimate the photon detection rates in a rutile crystal for both the unseeded and seeded regimes.

Study of broadband multimode light via non-phase-matched sum frequency generation

Denis Kopylov, Kirill Spasibko, Tatiana Murzina, Maria Chekhova

We propose non-phase-matched sum frequency generation (SFG) as a method for characterizing broadband multimode light. Both the central wavelength and the bandwidth are in this case not limited by the phase matching condition. As an example, we consider bright squeezed vacuum (BSV) generated through high-gain parametric down conversion (PDC). In the spectrum of SFG from BSV, we observe the coherent peak and the incoherent background. We show that the ratio of their widths is equal to the number of frequency modes in BSV, which in the case of low-gain PDC gives the degree of frequency entanglement for photon pairs. By generating the sum frequency in the near-surface region of a nonlinear crystal, we increase the SFG efficiency and get rid of the modulation caused by chromatic dispersion, known as Maker fringes. This allows one to use non-phasematched SFG as a wavelength-independent autocorrelator. Furthermore, we demonstrate efficient non-phase-matched three- and four-frequency summation of broadband multimode light, hardly possible under phase matching. We show that the latter contains the coherent peak while the former does not.

Overcoming inefficient detection in sub-shot-noise absorption measurement and imaging

Eugene Knyazev, Farid Khalili, Maria Chekhova

Photon-number squeezing and correlations enable measurement of absorption with an accuracy exceeding that of the shot-noise limit. However, sub-shot noise imaging and sensing based on these methods require high detection efficiency, which can be a serious obstacle if measurements are carried out in “difficult” spectral ranges. We show that this problem can be overcome through the phase-sensitive amplification before detection. Here we propose an experimental scheme of sub-shot-noise imaging with tolerance to detection losses.

A primary radiation standard based on quantum nonlinear optics

Samuel Lemieux, Enno Giese, Robert Fickler, Maria Chekhova, Robert Boyd

The black body remains the most prominent source of light for absolute radiometry. Its main alternative, synchrotron radiation, requires costly and large facilities. Quantum optics offers a new radiometric source: parametric down-conversion (PDC), a nonlinear optical process, in which pairwise photon correlations enable absolute calibration of photodetectors. Since the emission rate crucially depends on the brightness of the electromagnetic field, quantum-mechanical fluctuations of the vacuum can be seen as a seed of spontaneous PDC, and their amplitude is a natural radiometric standard. Thus, they allow for the calibration of the spectral radiance of light sources by measuring the ratio between seeded and unseeded PDC. Here, we directly use the frequency spectrum of the electromagnetic vacuum to trigger spontaneous PDC and employ the generated light to infer the spectral response of a spectrometer over a broad spectral range. Then, we deduce the absolute quantum efficiency from the spectral shape of PDC in the high-gain regime, without relying on a seed or reference detector. Our results compare well with the ones obtained with a reference lamp, demonstrating a promising primary radiation standard.

Multiphoton nonclassical light from clusters of single-photon emitters

Luo Qi, Mathieu Manceau, Andrea Cavanna, Fabian Gumpert, Luigi Carbone, Massimo de Vittorio, Alberto Bramati, Elisabeth Giacobino, Lukas Lachman, et al.

We study nonclassical features of multiphoton light emitted by clusters of single-photon emitters. As signatures of nonclassicality, we use violation of inequalities for normalized correlation functions of different orders or the probabilities of multiphoton detection. In particular, for clusters of 2–14 colloidal CdSe/CdS dot-in-rods we observe antibunching and nonclassicality of up to the fourth-order. Surprisingly, violation of certain classical inequalities gets even more pronounced for larger clusters.

Bright squeezed vacuum in a nonlinear interferometer: Frequency and temporal Schmidt-mode description

P.R. Sharapova, O.V. Tikhonova, S. Lemieux, R.W. Boyd, Maria Chekhova

Control over the spectral properties of the bright squeezed vacuum (BSV), a highly multimode nonclassical macroscopic state of light that can be generated through high-gain parametric down conversion, is crucial for many applications. In particular, in several recent experiments BSV is generated in a strongly pumped SU(1,1) interferometer to achieve phase supersensitivity, perform broadband homodyne detection, or tailor the frequency spectrum of squeezed light. In this work, we present an analytical approach to the theoretical description of BSV in the frequency domain based on the Bloch-Messiah reduction and the Schmidt-mode formalism. As a special case we consider a strongly pumped SU(1,1) interferometer. We show that different moments of the radiation at its output depend on the phase, dispersion, and the parametric gain in a nontrivial way, thereby providing additional insights on the capabilities of nonlinear interferometers. In particular, a dramatic change in the spectrum occurs as the parametric gain increases.

Dispersion tuning in sub-micron tapers for third-harmonic and photon triplet generation

Jonas Hammer, Andrea Cavanna, Riccardo Pennetta, Maria Chekhova, Philip St. J. Russell, Nicolas Joly

Precise control of the dispersion landscape is of crucial importance if optical fibers are to be successfully used for the generation of three-photon states of light—the inverse of third-harmonic generation (THG). Here we report gas-tuning of intermodal phase-matched THG in sub-micron-diameter tapered optical fiber. By adjusting the pressure of the surrounding argon gas up to 50 bars, intermodally phase-matched third-harmonic light can be generated for pump wavelengths within a 15 nm range around 1.38 μm. We also measure the infrared fluorescence generated in the fiber when pumped in the visible and estimate that the accidental coincidence rate in this signal is lower than the predicted detection rate of photon triplets

Broadband bright twin beams and their upconversion

Maria Chekhova, Semen Germanskiy, Dmitri Horoshko, Galiya Kitaeva, Mikhail Kolobov, Gerd Leuchs, Chris Phillips, Pavel Prudkovskii

We report on the observation of broadband (40 THz) bright twin beams through high-gain parametric downconversion in an aperiodically poled lithium niobate crystal. The output photon number is shown to scale exponentially with the pump power and not with the pump amplitude, as in homogeneous crystals. Photon number correlations and the number of frequency/temporal modes are assessed by spectral covariance measurements. By using sum-frequency generation on the surface of a non-phase-matched crystal, we measure a cross-correlation peak with the temporal width of 90 fs.

Quantum tomography enhanced through parametric amplification

E. Knyazev, Kirill Spasibko, Maria V. Chekhova, F. Ya Khalili

Quantum tomography is the standard method of reconstructing the Wigner function of quantum states of light by means of balanced homodyne detection. The reconstruction quality strongly depends on the photodetectors quantum efficiency and other losses in the measurement setup. In this article we analyze in detail a protocol of enhanced quantum tomography, proposed by Leonhardt and Paul [1] which allows one to reduce the degrading effect of detection losses. It is based on phase-sensitive parametric amplification, with the phase of the amplified quadrature being scanned synchronously with the local oscillator phase. Although with sufficiently strong amplification the protocol enables overcoming any detection inefficiency, it was so far not implemented in the experiment, probably due to the losses in the amplifier. Here we discuss a possible proof-of-principle experiment with a traveling-wave parametric amplifier. We show that with the state-of-the-art optical elements, the protocol enables high fidelity tomographic reconstruction of bright non-classical states of light. We consider two examples: bright squeezed vacuum and squeezed single-photon state, with the latter being a non-Gaussian state and both strongly affected by the losses.

Orbital angular momentum modes of high-gain parametric down-conversion

Lina Beltran, Gaetano Frascella, Angela M. Perez, Robert Fickler, Polina R. Sharapova, Mathieu Manceau, Olga V. Tikhonova, Robert W. Boyd, Gerd Leuchs, et al.

Light beams with orbital angular momentum (OAM) are convenient carriers of quantum information. They can. also be. used for imparting rotational motion to particles and providing. high resolution in imaging. Due to the conservation of OAM in parametric down-conversion (PDC), signal and idler photons generated at low gain have perfectly anti-correlated OAM values. It is interesting to study the OAM properties of high-gain PDC, where the same OAM modes can be populated with large, but correlated, numbers of photons. Here we investigate the OAM spectrum of high-gain PDC and show that the OAM mode content can be controlled by varying the pump power and the configuration of the source. In our experiment, we use a source consisting of two nonlinear crystals separated by an air gap. We discuss the OAM properties of PDC radiation emitted by this source and suggest possible modifications.

Improving the phase super-sensitivity of squeezing-assisted interferometers by squeeze factor unbalancing

Mathieu Manceau, Farid Khalili, Maria Chekhova

The sensitivity properties of an SU(1,1) interferometer made of two cascaded parametric amplifiers, as well as of an ordinary SU(2) interferometer preceded by a squeezer and followed by an anti-squeezer, are theoretically investigated. Several possible experimental configurations are considered, such as the absence or presence of a seed beam, direct or homodyne detection scheme. In all cases we formulate the optimal conditions to achieve phase super-sensitivity, meaning a sensitivity overcoming the shotnoise limit. Weshow that for a given gain of the first parametric amplifier, unbalancing the interferometer by increasing the gain of the second amplifier improves the interferometer properties. In particular, a broader super-sensitivity phase range and a better overall sensitivity can be achieved by gain unbalancing.

Experimental demonstration of negative-valued polarization quasiprobability distribution

K. Yu. Spasibko, M. V. Chekhova, F. Ya. Khalili

Polarization quasiprobability distribution defined in the Stokes space shares many important properties with the Wigner function for position and momentum. Most notably, they both give correct one-dimensional marginal probability distributions and therefore represent the natural choice for the probability distributions in classical hidden-variable models. In this context, negativity of the Wigner function is considered as proof of nonclassicality for a quantum state. On the contrary, the polarization quasiprobability distribution demonstrates negativity for all quantum states. This feature comes from the discrete nature of Stokes variables; however, it was not observed in previous experiments, because they were performed with photon-number averaging detectors. Here we reconstruct the polarization quasiprobability distribution of a coherent state with photon-number resolving detectors, which allows us to directly observe for the first time its negativity. Furthermore we derive a theoretical polarization quasiprobability distribution for any linearly polarized quantum state.

Multiphoton Effects Enhanced due to Ultrafast Photon-Number Fluctuations

Kirill Yu. Spasibko, Denis A. Kopylov, Victor L. Krutyanskiy, Tatiana V. Murzina, Gerd Leuchs, Maria V. Chekhova

The rate of an n-photon effect generally scales as the nth order autocorrelation function of the incident light, which is high for light with strong photon-number fluctuations. Therefore, "noisy" light sources are much more efficient for multiphoton effects than coherent sources with the same mean power, pulse duration, and repetition rate. Here we generate optical harmonics of the order of 2-4 from a bright squeezed vacuum, a state of light consisting of only quantum noise with no coherent component. We observe up to 2 orders of magnitude enhancement in the generation of optical harmonics due to ultrafast photon-number fluctuations. This feature is especially important for the nonlinear optics of fragile structures, where the use of a noisy pump can considerably increase the effect without overcoming the damage threshold.

Detection Loss Tolerant Supersensitive Phase Measurement with an SU(1,1) Interferometer

Mathieu Manceau, Gerd Leuchs, Farid Khalili, Maria Chekhova

In an unseeded SU(1,1) interferometer composed of two cascaded degenerate parametric amplifiers, with direct detection at the output, we demonstrate a phase sensitivity overcoming the shot noise limit by 2.3 dB. The interferometer is strongly unbalanced, with the parametric gain of the second amplifier exceeding the gain of the first one by a factor of 2, which makes the scheme extremely tolerant to detection losses. We show that by increasing the gain of the second amplifier, the phase supersensitivity of the interferometer can be preserved even with detection losses as high as 80%. This finding can considerably improve the state-of-the-art interferometry, enable sub-shot-noise phase sensitivity in spectral ranges with inefficient detection, and allow extension to quantum imaging.

Characterization and shaping of the time-frequency Schmidt mode spectrum of bright twin beams generated in gas-filled hollow-core photonic crystal fibers

M. A. Finger, N. Y. Joly, P. St. J. Russell, M. V. Chekhova

We vary the time-frequency mode structure of ultrafast pulse-pumped modulational instability (MI) twin beams in an argon-filled hollow-core kagome-style photonic crystal fiber by adjusting the pressure, pump pulse chirp, fiber length, and parametric gain. Compared to solid-core systems, the pressure-dependent dispersion landscape brings increased flexibility to the tailoring of frequency correlations, and we demonstrate that the pump pulse chirp can be used to tune the joint spectrum of femtosecond-pumped.(3) sources. We also characterize the resulting mode content, not only by measuring the multimode second-order correlation function g((2)), but also by directly reconstructing the shapes and weights of time-frequency Schmidt (TFS) modes. We show that the number of modes directly influences the shot-to-shot pulse-energy and spectral-shape fluctuations in MI. Using this approach we control and monitor the number of TFS modes within the range from 1.3 to 4 using only a single fiber.

Autonomous absolute calibration of an ICCD camera in single-photon detection regime

Luo Qi, Felix Just, Gerd Leuchs, Maria V. Chekhova

Intensified charge coupled device (ICCD) cameras are widely used in vari-ous applications such as microscopy, astronomy, spectroscopy. Often they are used as single-photon detectors, with thresholding being an essential part of the readout. In this paper, we measure the quantum efficiency of an ICCD camera in the single-photon de-tection mode using the Klyshko absolute calibration technique. The quantum efficiency is obtained as a function of the threshold value and of the wavelength of the detected light. In addition, we study the homogeneity of the photon sensitivity over the camera chip area. The experiment is performed in the autonomous regime, without using any additional detectors. We therefore demonstrate the self-calibration of an ICCD camera.

Engineering the Frequency Spectrum of Bright Squeezed Vacuum via Group Velocity Dispersion in an SU(1,1) Interferometer

Samuel Lemieux, Mathieu Manceau, Polina R. Sharapova, Olga V. Tikhonova, Robert W. Boyd, Gerd Leuchs, Maria V. Chekhova

Bright squeezed vacuum, a promising tool for quantum information, can be generated by high-gain parametric down-conversion. However, its frequency and angular spectra are typically quite broad, which is undesirable for applications requiring single-mode radiation. We tailor the frequency spectrum of high-gain parametric down-conversion using an SU(1,1) interferometer consisting of two nonlinear crystals with a dispersive medium separating them. The dispersive medium allows us to select a narrow band of the frequency spectrum to be exponentially amplified by high-gain parametric amplification. The frequency spectrum is thereby narrowed from (56.5±0.1) to (1.22±0.02)  THz and, in doing so, the number of frequency modes is reduced from approximately 50 to 1.82±0.02. Moreover, this method provides control and flexibility over the spectrum of the generated light through the timing of the pump.

Hybrid photonic-crystal fiber for single-mode phase matched generation of third harmonic and photon triplets

Andrea Cavanna, Felix Just, Xin Jiang, Gerd Leuchs, Maria V. Chekhova, Philip St. J. Russell, Nicolas Y. Joly

All-fiber systems for third harmonic generation are of great interest because they can be used for the inverse process, namely, the generation of entangled photon triplets. Usually, chromatic dispersion prevents phase matching between the incident and generated radiation when they are both guided in an LP01-like mode. Here, we present a hybrid photonic crystal fiber that has been designed for phase matched third harmonic generation from 1596 to 532 nm in single-lobed modes. The third harmonic radiation is guided by an all-solid bandgap microstructure, while the pump frequency is confined by conventional total internal reflection. The fiber is also suitable for the generation of photon triplet states.

Nonlinear interferometers in quantum optics

M. V. Chekhova, Z. Y. Ou

We review the main works in the field of nonlinear interferometers, which has been developing ever since the start of nonlinear optics and has seen growing interest in recent years due to the applications in quantum information and quantum metrology. Because the class of schemes that are referred to as nonlinear interferometers is too broad, we restrict the consideration to the cases in which crystals, fibers, or atomic systems producing the nonlinear effect are placed inside the interferometer, and only linear phase shifts are imposed. As a nonlinear effect, we consider four-wave mixing and parametric down-conversion, at both low and high gain.

Ring-shaped spectra of parametric downconversion and entangled photons that never meet

Kirill Yu. Spasibko, Denis A. Kopylov, Tatiana V. Murzina, Gerd Leuchs, Maria V. Chekhova

We report on the observation of an unusual type of parametric downconversion. In the regime where collinear degenerate emission is in the anomalous range of group-velocity dispersion, its spectrum is restricted in both angle and wavelength. Detuning from exact collinear-degenerate phase-matching leads to a ring shape of the wavelength-angular spectrum, suggesting a new type of spatiotemporal coherence and entanglement of photon pairs. By imposing a phase varying in a specific way in both angle and wavelength, one can obtain an interesting state of an entangled photon pair, with the two photons being never at the same point at the same time. (C) 2016 Optical Society of America

Nonlinear interferometer for tailoring the frequency spectrum of bright squeezed vacuum

T. Sh. Iskhakov, S. Lemieux, A. Perez, R. W. Boyd, G. Leuchs, M. V. Chekhova

We propose a method for tailoring the frequency spectrum of bright squeezed vacuum by generating it in a nonlinear interferometer, consisting of two down-converting nonlinear crystals separated by a dispersive medium. Due to a faster dispersive spreading of higher order Schmidt modes, the spectral width of the radiation at the output is reduced as the length of the dispersive medium is increased. Preliminary results show 30% spectral narrowing.

Low-noise macroscopic twin beams

Timur Sh. Iskhakov, Vladyslav C. Usenko, Radim Filip, Maria V. Chekhova, Gerd Leuchs

Applying a multiphoton-subtraction technique to the two-color macroscopic squeezed vacuum state of light generated via high-gain parametric down-conversion we conditionally prepare a different state of light: bright multimode low-noise twin beams. A lower noise in the sum of the photon numbers opens a possibility to encode information into this variable while keeping the nonclassical character of the state. The obtained results demonstrate up to eightfold suppression of noise in each beam while preserving and even moderately improving the nonclassical photon-number correlations between the beams. The prepared low-noise macroscopic state, containing up to 2000 photons per mode, is not among the Gaussian states achievable through nonlinear optical processes. Apart from that, we suggest a method for measuring quantum efficiency, which is based on the Fano factor measurement. The proposed technique substantially improves the usefulness of twin beams for quantum communication and metrology.

Tunable optical parametric generator based on the pump spatial walk-off

Andrea Cavanna, Felix Just, Polina R. Sharapova, Michael Taheri, Gerd Leuchs, Maria V. Chekhova

We suggest a novel optical parametric generator (OPG) in which one of the downconverted beams is spontaneously generated along the Poynting vector of the pump beam. In this configuration, the generation takes advantage of the walk-off of the extraordinary pump, rather than being degraded by it. As a result, the generated signal and idler beams are bright due to a high conversion efficiency, spatially nearly single mode due to the preferred direction of the Poynting vector, tunable over a wide range of wavelengths and broadband. The two beams are also correlated in frequency and in the photon number per pulse. Furthermore, due to their thermal statistics, these beams can be used as a pump to efficiently generate other nonlinear processes. (C) 2016 Optical Society of America

Heralded source of bright multi-mode mesoscopic sub-Poissonian light

T. Sh. Iskhakov, V. C. Usenko, U. L. Andersen, R. Filip, M. V. Chekhova, G. Leuchs

In a direct detection scheme, we observed 7.8 dB of twin-beam squeezing for multi-mode two-color squeezed vacuum generated via parametric downconversion. Applying postselection, we conditionally prepared a sub-Poissonian state of light containing 6.3 . 10(5) photons per pulse on the average with the Fano factor 0.63 +/- 0.01. The scheme can be considered as the heralded preparation of pulses with the mean energy varying between tens and hundreds of fJ and the uncertainty considerably below the shot-noise level. Such pulses can be used in metrology (for instance, for radiometer calibration), as well as for probing multi-mode non-linear optical effects. (C) 2016 Optical Society of America

Giant narrowband twin-beam generation along the pump-energy propagation direction

Angela M. Perez, Kirill Yu Spasibko, Polina R. Sharapova, Olga V. Tikhonova, Gerd Leuchs, Maria V. Chekhova

Walk-off effects, originating from the difference between the group and phase velocities, limit the efficiency of nonlinear optical interactions. While transverse walk-off can be eliminated by proper medium engineering, longitudinal walk-off is harder to avoid. In particular, ultrafast twin-beam generation via pulsed parametric down-conversion and four-wave mixing is only possible in short crystals or fibres. Here we show that in high-gain parametric down-conversion, one can overcome the destructive role of both effects and even turn them into useful tools for shaping the emission. In our experiment, one of the twin beams is emitted along the pump Poynting vector or its group velocity matches that of the pump. The result is markedly enhanced generation of both twin beams, with the simultaneous narrowing of angular and frequency spectrum. The effect will enable efficient generation of ultrafast twin photons and beams in cavities, waveguides and whispering-gallery mode resonators.

Projective filtering of the fundamental eigenmode from spatially multimode radiation

A. M. Perez, P. R. Sharapova, S. S. Straupe, F. M. Miatto, O. V. Tikhonova, G. Leuchs, M. V. Chekhova

Lossless filtering of a single coherent (Schmidt) mode from spatially multimode radiation is a problem crucial for optics in general and for quantum optics in particular. It becomes especially important in the case of nonclassical light that is fragile to optical losses. An example is bright squeezed vacuum generated via high-gain parametric down conversion or four-wave mixing. Its highly multiphoton and multimode structure offers a huge increase in the information capacity provided that each mode can be addressed separately. However, the nonclassical signature of bright squeezed vacuum, photon-number correlations, are highly susceptible to losses. Here we demonstrate lossless filtering of a single spatial Schmidt mode by projecting the spatial spectrum of bright squeezed vacuum on the eigenmode of a single-mode fiber. Moreover, we show that the first Schmidt mode can be captured by simply maximizing the fiber-coupled intensity. Importantly, the projection operation does not affect the targeted mode and leaves it usable for further applications.

Two-photon spectral amplitude of entangled states resolved in separable Schmidt modes

A. Avella, G. Brida, M. Chekhova, M. Gramegna, A. Shurupov, M. Genovese

The ability to access high dimensionality in Hilbert spaces represents a demanding key-stone for state-of-the-art quantum information. The manipulation of entangled states in continuous variables, wavevector as well frequency, represents a powerful resource in this sense. The number of dimensions of the Hilbert space that can be used in practical information protocols can be determined by the number of Schmidt modes that it is possible to address one by one. In the case of wavevector variables, the Schmidt modes can be losslessly selected using single-mode fibre and a spatial light modulator, but no similar procedure exists for the frequency space. The aim of this work is to present a technique to engineer the spectral properties of biphoton light, emitted via ultrafast spontaneous parametric down conversion, in such a way that the two-photon spectral amplitude (TPSA) contains several non-overlapping Schmidt modes, each of which can be filtered losslessly in frequency variables. Such TPSA manipulation is operated by a fine balancing of parameters like the pump frequency, the shaping of pump pulse spectrum, the dispersion dependence of spontaneous parametric down-conversion crystals as well as their length. Measurements have been performed exploiting the group velocity dispersion induced by the passage of optical fields through dispersive media, operating a frequency-to-time two-dimensional Fourier transform of the TPSA. Exploiting this kind of measurement we experimentally demonstrate the ability to control the Schmidt modes structure in TPSA through the pump spectrum manipulation.

Schmidt modes in the angular spectrum of bright squeezed vacuum

P. Sharapova, A. M. Perez, O. V. Tikhonova, M. V. Chekhova

We investigate both theoretically and experimentally strong correlations in macroscopic (bright) quantum states of light generated via unseeded parametric down-conversion and four-wave mixing. The states generated this way contain only quantum noise, without a classical component, and are referred to as bright squeezed vacuum (BSV). Their important advantage is the multimode structure, which offers a larger capacity for the encoding of quantum information. For the theoretical description of these states and their correlation features we introduce a generalized fully analytical approach, based on the concept of independent collective (Schmidt) modes and valid for the cases of both weak and strong nonlinear interaction. In experiment, we generate states of macroscopic BSV with up to 1010 photons per mode and examine large photon-number spatial correlations that are found to be very well described by our theoretical approach.

Raman-Free, Noble-Gas-Filled Photonic-Crystal Fiber Source for Ultrafast, Very Bright Twin-Beam Squeezed Vacuum

Martin A. Finger, Timur Sh. Iskhakov, Nicolas Y. Joly, Maria V. Chekhova, Philip St. J. Russell

We report a novel source of twin beams based on modulational instability in high-pressure argon-filled hollow-core kagome-style photonic-crystal fiber. The source is Raman-free and manifests strong photonnumber correlations for femtosecond pulses of squeezed vacuum with a record brightness of similar to 2500 photons per mode. The ultra-broadband (similar to 50 THz) twin beams are frequency tunable and contain one spatial and less than 5 frequency modes. The presented source outperforms all previously reported squeezed-vacuum twin-beam sources in terms of brightness and low mode content.

Bright squeezed vacuum: Entanglement of macroscopic light beams

M. V. Chekhova, G. Leuchs, M. Zukowski

We discuss various methods to create macroscopic (bright) entangled light beams. As an example, bright squeezed vacuum is considered in detail. This state of light, obtained via high-gain parametric downconversion, manifests entanglement in both photon numbers and polarization. (C) 2014 Elsevier B.V. All rights reserved.

Detection of non-classical space-time correlations with a novel type of single-photon camera

Felix Just, Mykhaylo Filipenko, Andrea Cavanna, Thilo Michel, Thomas Gleixner, Michael Taheri, John Vallerga, Michael Campbell, Timo Tick, et al.

During the last decades, multi-pixel detectors have been developed capable of registering single photons. The newly developed hybrid photon detector camera has a remarkable property that it has not only spatial but also temporal resolution. In this work, we apply this device to the detection of non-classical light from spontaneous parametric down-conversion and use two-photon correlations for the absolute calibration of its quantum efficiency. (C) 2014 Optical Society of America

Bright squeezed-vacuum source with 1.1 spatial mode

A. M. Perez, T. Sh. Iskhakov, P. Sharapova, S. Lemieux, O. V. Tikhonova, M. V. Chekhova, G. Leuchs

Bright squeezed vacuum, a macroscopic nonclassical state of light, can be obtained at the output of a strongly pumped nonseeded traveling-wave optical parametric amplifier (OPA). By constructing the OPA of two consecutive crystals separated by a large distance, we make the squeezed vacuum spatially single-mode without a significant decrease in the brightness or squeezing. (C) 2014 Optical Society of America

Photon correlations for colloidal nanocrystals and their clusters

A. Shcherbina, G. A. Shcherbina, M. Manceau, S. Vezzoli, L. Carbone, M. De Vittorio, A. Bramati, E. Giacobino, M. V. Chekhova, et al.

of semiconductor "dot-in-rods" and their small clusters are studied by measuring the second-order correlation function with a spatially resolving intensified CCD camera. This measurement allows one to distinguish between a single dot and a cluster and, to a certain extent, to estimate the number of dots in a cluster. A more advanced measurement is proposed, based on higher-order correlations, enabling more accurate determination of the number of dots in a small cluster. Nonclassical features of the light emitted by such a cluster are analyzed. (C) 2014 Optical Society of America

Compensation of anisotropy effects in the generation of two-photon light

Andrea Cavanna, Angela M. Perez, Felix Just, Maria V. Chekhova, Gerd Leuchs

We analyse a method to compensate for anisotropy effects in the spatial distribution of parametric down-conversion (PDC) radiation in bulk crystals. In this method, a single nonlinear crystal is replaced by two consecutive crystals with opposite transverse walk-off directions. We implement a simple numerical model to calculate the spatial distribution of intensity and correlations, as well as the Schmidt mode structure, with an account for the anisotropy. Experimental results are presented which prove the validity of both the model and the method. (C) 2014 Optical Society of America

Interference of macroscopic beams on a beam splitter: phase uncertainty converted into photon-number uncertainty

K. Yu Spasibko, F. Toeppel, T. Sh Iskhakov, M. Stobinska, M. V. Chekhova, G. Leuchs

Squeezed-vacuum twin beams, commonly generated through parametric downconversion, are known to have perfect photon-number correlations. According to the Heisenberg principle, this is accompanied by a huge uncertainty in their relative phase. By overlapping bright twin beams on a beam splitter, we convert phase fluctuations into photon-number fluctuations and observe this uncertainty as a typical 'U-shape' of the output photon-number distribution. This effect, although reported for atomic ensembles and giving hope for phase super-resolution, has never been observed for light beams. The shape of the normalized photon-number difference distribution is similar to the one that would be observed for high-order Fock states. It can be also mimicked by classical beams with artificially mixed phase, but without any perspective for phase super-resolution. The probability distribution at the beam splitter output can be used for filtering macroscopic superpositions at the input.

Separable Schmidt modes of a nonseparable state

A. Avella, M. Gramegna, A. Shurupov, G. Brida, M. Chekhova, M. Genovese

Two-photon states entangled in continuous variables such as wave vector or frequency represent a powerful resource for quantum-information protocols in higher-dimensional Hilbert spaces. At the same time, there is a problem of addressing separately the corresponding Schmidt modes. We propose a method of engineering two-photon spectral amplitude in such a way that it contains several nonoverlapping Schmidt modes, each of which can be filtered losslessly. The method is based on spontaneous parametric down-conversion (SPDC) pumped by radiation with a comblike spectrum. There are many ways of producing such a spectrum; here we consider the simplest one, namely, passing the pump beam through a Fabry-Perot interferometer. For the two-photon spectral amplitude (TPSA) to consist of nonoverlapping Schmidt modes, the crystal dispersion dependence, the length of the crystal, the Fabry-Perot free spectral range, and its finesse should satisfy certain conditions. We experimentally demonstrate the control of TPSA through these parameters. We also discuss a possibility to realize a similar situation using cavity-based SPDC.

Transverse entanglement of biphotons

F. Just, A. Cavanna, M. V. Chekhova, G. Leuchs

We measure the transverse entanglement of photon pairs on their propagation from the near to the far field of spontaneous parametric down-conversion (SPDC). The Fedorov ratio, depending on the widths of conditional and unconditional intensity measurements, is shown to be only able to characterize entanglement in the near and far field zones of the source. Therefore we also follow a different approach. By evaluating the first-order coherence of a subsystem of the state we can quantify its entanglement. Unlike previous measurements, which determine the Fedorov ratio via intensity correlations, our setup is sensitive to both phase and modulus of the biphoton state and thus always grants experimental access to the full transverse entanglement of the SPDC state. It is shown theoretically that this scheme represents a direct measurement of the Schmidt number.

Multiphoton nonclassical correlations in entangled squeezed vacuum states

Bhaskar Kanseri, Timur Iskhakov, Georgy Rytikov, Maria Chekhova, Gerd Leuchs

Photon-number correlation measurements are performed on bright squeezed vacuum states using a standard Bell-test setup, and quantum correlations are observed for conjugate polarization-frequency modes. We further test the entanglement witnesses for these states and demonstrate the violation of the separability criteria, which infers that all of the macroscopic Bell states, containing typically 10(6) photons per pulse, are polarization entangled. The study also reveals the symmetry of macroscopic Bell states with respect to local polarization transformations. DOI: 10.1103/PhysRevA.87.032110

The Schmidt modes of biphoton qutrits: Poincare-sphere representation

M. V. Chekhova, M. V. Fedorov

For a general-form polarization biphoton qutrit, physically corresponding to a pair of arbitrarily polarized photons in a single frequency and wavevector mode, we explicitly find polarization Schmidt modes. A simple method is suggested for factorizing the state vector and the explicit expressions for the factorizing photon creation operators are found. The degrees of entanglement and polarization of a qutrit are shown to depend directly on the commutation features of the factorizing operators. Clear graphic representations for the Stokes vectors of the qutrit state as a whole, its Schmidt modes and factorizing single-photon creation operators are given based on the Poincare sphere. An experimental scheme is proposed for measuring the parameters of the Schmidt decomposition as well as for demonstrating the operational meaning of qutrit entanglement.

A versatile source of single photons for quantum information processing

Michael Foertsch, Josef U. Fuerst, Christoffer Wittmann, Dmitry Strekalov, Andrea Aiello, Maria V. Chekhova, Christine Silberhorn, Gerd Leuchs, Christoph Marquardt

The generation of high-quality single-photon states with controllable narrow spectral bandwidths and central frequencies is key to facilitate efficient coupling of any atomic system to non-classical light fields. Such an interaction is essential in numerous experiments for fundamental science and applications in quantum communication and information processing, as well as in quantum metrology. Here we implement a fully tunable, narrow-band and efficient single-photon source based on a whispering gallery mode resonator. Our disk-shaped, monolithic and intrinsically stable resonator is made of lithium niobate and supports a cavity-assisted spontaneous parametric down-conversion process. The generated photon pairs are emitted into two highly tunable resonator modes. We verify wavelength tuning over 100 nm of both modes with controllable bandwidth between 7.2 and 13 MHz. Heralding of single photons yields anti-bunching with g((2))(0) < 0.2.

Compensation of anisotropy effects in a nonlinear crystal for squeezed vacuum generation

A. M. Perez, F. Just, A. Cavanna, M. V. Chekhova, G. Leuchs

Squeezed vacuum can be obtained by an optical parametric amplifier (OPA) with the quantum vacuum state at the input. We are interested in a degenerate type-I OPA based on parametric down-conversion (PDC) where, due to phase matching requirements, an extraordinary polarized pump must impinge onto a birefringent crystal with a large chi((2)) nonlinearity. As a consequence of the optical anisotropy of the medium, the spatial spectrum of the generated radiation is affected by the transverse walk-off. In this work we describe a method that reduces the spatial distortions, by using two consecutive crystals instead of one. We show that after anisotropy compensation the two-photon amplitude becomes symmetric, allowing for a simple Schmidt expansion, a procedure that in practice requires states that come from experimental systems free of anisotropy effects. Qualitative experimental observations are made for the case of high-gain PDC.

Macroscopic Hong-Ou-Mandel interference

T. Sh Iskhakov, K. Yu Spasibko, M. V. Chekhova, G. Leuchs

We report on a Hong-Ou-Mandel interference experiment for twin beams with photon numbers per mode as large as 10(6) generated via high-gain parametric down conversion (PDC). The standard technique of coincidence counting leads in this case to a dip with a very low visibility. By measuring, instead of coincidence counting rate, the variance of the photon-number difference, we observe an extremely well-pronounced peak. From the shape of the peak, one can infer information about the spectral properties of the PDC radiation, including the number of frequency/temporal modes.

Nonclassical features of the polarization quasiprobability distribution

M. V. Chekhova, F. Ya. Khalili

Polarization quasiprobability distribution is defined in the space of the Stokes observables. It can be reconstructed with the help of polarization quantum tomography and provides a full description of the so-called polarization sector of quantum states of light. We show here that due to its definition in terms of the discrete-valued Stokes operators, polarization quasiprobability distribution has singularities at integer values of the Stokes observables and takes negative values even for the quantum states typically considered as "classical" ones. In experiments with "bright" multiphoton states, the photon-number resolution is smeared due to the photodetectors' technical limitations. In this case, nonclassical features of the explored quantum states can be revealed by adding a strong coherent beam into the orthogonal polarization.

Entanglement witnesses and measures for bright squeezed vacuum

Magdalena Stobinska, Falk Toeppel, Pavel Sekatski, Maria V. Chekhova

Quantum entanglement is a fascinating phenomenon, especially if it is observed at the macroscopic scale. Importantly, macroscopic quantum correlations can be revealed only by accurate measurement outcomes and strategies. Here, we formulate feasible entanglement witnesses for bright squeezed vacuum in the form of the macroscopically populated polarization triplet Bell states. Their testing involves efficient photodetection and the measurement of the Stokes operators' variances. We also calculate the measures of entanglement for these states such as the Schmidt number and the logarithmic negativity. Our results show that the bright squeezed vacuum degree of polarization entanglement scales as the mean photon number squared. We analyze the applicability of an operational analog of the Schmidt number.

Filtering of the absolute value of photon-number difference for two-mode macroscopic quantum superpositions

M. Stobinska, F. Toeppel, P. Sekatski, A. Buraczewski, M. Zukowski, M. V. Chekhova, G. Leuchs, N. Gisin

We discuss a device capable of filtering out two-mode states of light with mode populations differing by more than a certain threshold, while not revealing which mode is more populated. It would allow engineering of macroscopic quantum states of light in a way which is preserving specific superpositions. As a result, it would enhance optical phase estimation with these states as well as distinguishability of "macroscopic" qubits. We propose an optical scheme, which is a relatively simple, albeit nonideal, operational implementation of such a filter. It uses tapping of the original polarization two-mode field, with a polarization-neutral beam splitter of low reflectivity. Next, the reflected beams are suitably interfered on a polarizing beam splitter. It is oriented such that it selects unbiased polarization modes with respect to the original ones. The more an incoming two-mode Fock state is unequally populated, the more the polarizing beam-splitter output modes are equally populated. This effect is especially pronounced for highly populated states. Additionally, for such states we expect strong population correlations between the original fields and the tapped one. Thus, after a photon-number measurement of the polarizing beam-splitter outputs, a feed-forward loop can be used to let through a shutter the field, which was transmitted by the tapping beam splitter. This happens only if the counts at the outputs are roughly equal. In such a case, the transmitted field differs strongly in occupation number of the two modes, while information on which mode is more populated is nonexistent (a necessary condition for preserving superpositions).

Spectral properties of high-gain parametric down-conversion

K. Yu Spasibko, T. Sh Iskhakov, M. V. Chekhova

High-gain parametric down-conversion (PDC) is a source of bright squeezed vacuum, which is a macroscopic nonclassical state of light and a promising candidate for quantum information applications. Here we study its properties, such as the intensity spectral width and the spectral width of pairwise correlations. In agreement with the theory, we observe an increase in the spectral width by 27% compared with the low-gain PDC. Frequency cross- and auto-correlations are registered by measuring the reduction of noise in the difference of PDC intensities at various pairs of wavelengths. The noise reduction plots also demonstrate super-bunching typical for collinear frequency-degenerate PDC. (C) 2012 Optical Society of America

Superbunched bright squeezed vacuum state

T. Sh. Iskhakov, A. M. Perez, K. Yu. Spasibko, M. V. Chekhova, G. Leuchs

In this Letter, we experimentally study the statistical properties of a bright squeezed vacuum state containing up to 10(13) photons per mode (10 mu J per pulse), produced via high-gain parametric down conversion (PDC). The effects of bunching and superbunching of photons were observed for a single-mode PDC radiation by second-order intensity correlation function measurements with analog detectors. (C) 2012 Optical Society of America

Polarization-Entangled Light Pulses of 10(5) Photons

Timur Sh. Iskhakov, Ivan N. Agafonov, Maria V. Chekhova, Gerd Leuchs

We experimentally demonstrate polarization entanglement for squeezed vacuum pulses containing more than 105 photons. We also study photon-number entanglement by calculating the Schmidt number and measuring its operational counterpart. Theoretically, our pulses are the more entangled the brighter they are. This promises important applications in quantum technologies, especially photonic quantum gates and quantum memories.

Measurement of two-mode squeezing with photon number resolving multipixel detectors

Dmitry A. Kalashnikov, Si-Hui Tan, Timur Sh. Iskhakov, Maria V. Chekhova, Leonid A. Krivitsky

The measurement of the two-mode squeezed vacuum generated in an optical parametric amplifier (OPA) was performed with photon number resolving multipixel photon counters (MPPCs). Implementation of the MPPCs allows for the observation of noise reduction in a broad dynamic range of the OPA gain, which is inaccessible with standard single photon avalanche photodetectors. (c) 2012 Optical Society of America

Three-dimensional quantum polarization tomography of macroscopic Bell states

Bhaskar Kanseri, Timur Iskhakov, Ivan Agafonov, Maria Chekhova, Gerd Leuchs

The polarization properties of macroscopic Bell states are characterized using three-dimensional quantum polarization tomography. This method utilizes three-dimensional (3D) inverse Radon transform to reconstruct the polarization quasiprobability distribution function of a state from the probability distributions measured for various Stokes observables. The reconstructed 3D distributions obtained for the macroscopic Bell states are compared with those obtained for a coherent state with the same mean photon number. The results demonstrate squeezing in one or more Stokes observables.

Polarization tomography of bright states of light

I. N. Agafonov, M. V. Chekhova, T. Sh. Iskhakov, B. Kanseri, G. Leuchs

Polarization quantum tomography is performed on 4-mode squeezed vacuum states. Three-dimensional polarization quasiprobability functions are obtained and compared to that of an equal intensity coherent state. These distributions clearly demonstrate the difference in the polarization properties of the considered states. The reconstruction quality of the coherent state distribution is also analyzed by comparing the theoretically and experimentally obtained shapes for this state.

Accessing photon bunching with a photon number resolving multi-pixel detector

Dmitry A. Kalashnikov, Si Hui Tan, Maria V. Chekhova, Leonid A. Krivitsky

In quantum optics and its applications, there is an urgent demand for photon-number resolving detectors. Recently, there appeared multi-pixel counters (MPPC) that are able to distinguish between 1,2,..10 photons. At the same time, strong coupling between different pixels (crosstalk) hinders their photon-number resolution. In this work, we suggest a method for 'filtering out' the crosstalk effect in the measurement of intensity correlation functions. The developed approach can be expanded to the analysis of higher-order intensity correlations by using just a single MPPC. (C) 2011 Optical Society of America

Macroscopic Pure State of Light Free of Polarization Noise

Timur Sh. Iskhakov, Maria V. Chekhova, Georgy O. Rytikov, Gerd Leuchs

The preparation of completely nonpolarized light is seemingly easy; an everyday example is sunlight. The task is much more difficult if light has to be in a pure quantum state, as required by most quantum-technology applications. The pure quantum states of light obtained so far are either polarized or, in rare cases, manifest hidden polarization; even if their intensities are invariant to polarization transformations, higher-order moments are not. We experimentally demonstrate the preparation of the macroscopic singlet Bell state, which is pure, is completely nonpolarized, and has no polarization noise. Simultaneous fluctuation suppression in three Stokes observables below the shot-noise limit is demonstrated, opening perspectives for noiseless polarization measurements. The state is shown to be invariant to polarization transformations. This robust highly entangled isotropic state promises to fuel important applications in photonic quantum technologies.

Intensity correlations of thermal light

T. Iskhakov, A. Allevi, D. A. Kalashnikov, V. G. Sala, M. Takeuchi, M. Bondani, M. Chekhova

We demonstrate measurement of normalized Glauber's intensity correlation functions of different orders using an array photodetector. As the light source, we use a laser beam scattered by a rotating ground-glass disc, which has statistics close to that of thermal light. We compare the measurements of the normalized correlation functions to that of the difference-intensity variance and show that they are in a certain sense complementary. The independence of the variance measurement on the number of temporal modes has been demonstrated for the first time. Different versions of high-order ghost imaging are also realized and characterized quantitatively.

Absolute calibration of photodetectors: photocurrent multiplication versus photocurrent subtraction

I. N. Agafonov, M. V. Chekhova, T. S. Iskhakov, A. N. Penin, G. O. Rytikov, O. A. Shcherbina

We report testing of the new absolute method of photodetector calibration based on the difference-signal measurement for two-mode squeezed vacuum by comparison with the traditional absolute method based on coincidence counting. Using low-gain parametric downconversion, we have measured the quantum efficiency of a counting detector by both methods. The difference-signal method was adapted for the counting detectors by taking into account the dead-time effect. (c) 2011 Optical Society of America

Generation of bright squeezed vacuum in the Karassiov states

M. V. Chekhova, T. Sh. Iskhakov, G. Leuchs, G. O. Rytikov

We suggest an experimental procedure allowing one to prepare squeezed vacuum in a special type of generalized Bell states, first introduced by V.P. Karassiov. We present the first results on the experimental generation of such states and observation of their polarization properties.

Polarization properties of macroscopic Bell states

Timur Sh. Iskhakov, Ivan N. Agafonov, Maria V. Chekhova, Georgy O. Rytikov, Gerd Leuchs

The four two-photon polarization Bell states are one of the main instruments in the toolbox of quantum optics and quantum information. In our experiment we produce their multiphoton counterparts, macroscopic Bell states. These are relevant to applications in quantum technologies because they provide efficient interactions with material quantum objects and with each other via nonlinear interactions. Furthermore, we study the polarization properties of these states using the concept of second-order degree of polarization and its higher-order generalization.

Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light

G. Brida, M. V. Chekhova, G. A. Fornaro, M. Genovese, E. D. Lopaeva, I. Ruo Berchera

We present a complete and exhaustive theory of signal-to-noiseratio in bipartite ghost imaging with classical (thermal) and quantum (twin beams) light. The theory is compared with experiment for both twin beams and thermal light in a certain regime of interest.

COMPARATIVE TEST OF TWO METHODS OF QUANTUM EFFICIENCY ABSOLUTE MEASUREMENT BASED ON SQUEEZED VACUUM DIRECT DETECTION

I. N. Agafonov, M. V. Chekhova, A. N. Penin, G. O. Rytikov, O. A. Shumilkina, T. Sh Iskhakov

We realize and test in experiment a method recently proposed for measuring absolute quantum efficiency of analog photodetectors. Similar to the traditional (Klyshko) method of absolute calibration, the new one is based on the direct detection of two-mode squeezed vacuum at the output of a traveling wave OPA. However, in the new method, one measures the difference-photocurrent variance rather than the correlation function of photocurrents (number of coincidences), which makes the technique applicable for high-gain OPA. In this work we test the new method versus the traditional one for the case of photon-counting detectors where both techniques are valid.

Testing Ultrafast Two-Photon Spectral Amplitudes via Optical Fibres

G. Brida, V. Caricato, M. V. Chekhova, M. Genovese, M. Gramegna, T. Sh. Iskhakov

We test two-dimensional TPSA of biphoton light emitted via ultrafast spontaneous parametric down-conversion (SPDC) using the effect of group-velocity dispersion in optical fibres. Further, we apply this technique to demonstrate the engineering of biphoton spectral properties by acting on the pump pulse shape. (C) 2010 Optical Society of America

Accessing Higher Order Correlations in Quantum Optical States by Time Multiplexing

M. Avenhaus, K. Laiho, M. V. Chekhova, C. Silberhorn

We experimentally measured higher order normalized correlation functions (NCF) of pulsed light with a time-multiplexing detector. We demonstrate excellent performance of our device by verifying unity valued NCF up to the eighth order for coherent light and factorial dependence of the NCF for pseudothermal light. We applied our measurement technique to a type-II parametric down-conversion source to investigate mutual two-mode correlation properties and ascertain nonclassicality.

Two-color bright squeezed vacuum

Ivan N. Agafonov, Maria V. Chekhova, Gerd Leuchs

In a strongly pumped nondegenerate traveling-wave optical parametric amplifier, we produce a two-color squeezed vacuum with up to millions of photons per pulse. Our approach to registering this macroscopic quantum state is direct detection of a large number of transverse and longitudinal modes, which is achieved by making the detection time and area much larger than the coherence time and area, respectively. Using this approach, we obtain a record value of twin-beam squeezing for direct detection of bright squeezed vacuum. This makes direct detection of macroscopic squeezed vacuum a practical tool for quantum information applications.

Generation and Direct Detection of Broadband Mesoscopic Polarization-Squeezed Vacuum

Timur Iskhakov, Maria V. Chekhova, Gerd Leuchs

Using a traveling-wave optical parametric amplifier with two orthogonally oriented type-I BBO crystals pumped by picosecond pulses, we generate vertically and horizontally polarized squeezed vacuum states within a broad frequency-angular range. Depending on the phase between these states, fluctuations in one or another Stokes parameter are suppressed below the shot-noise limit. Because of the large number of photon pairs produced, no local oscillator is required, and 3 dB squeezing is observed by means of direct detection.

Experimental verification of high spectral entanglement for pulsed waveguided spontaneous parametric down-conversion

Malte Avenhaus, Maria V. Chekhova, Leonid A. Krivitsky, Gerd Leuchs, Christine Silberhorn

We study the spectral properties of spontaneous parametric down-conversion (SPDC) in a periodically poled waveguided structure of potassium-titanyl-phosphate (KTP) crystal pumped by ultrashort pulses. Our theoretical analysis reveals a strongly entangled and asymmetric structure of the two-photon spectral amplitude for type-II SPDC. We confirm these predictions experimentally by measuring single-photon spectra, on one hand, and the dependence of Hong-Ou-Mandel interference visibility on the width of spectral filtering, on the other hand.

High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light

I. N. Agafonov, M. V. Chekhova, T. Sh. Iskhakov, A. N. Penin

Difference-phase (or Hanbury Brown-Twiss type) intensity interference of classical light is considered in higher orders in the intensity. It is shown that, while the visibility of sum-phase (NOON-type) interference for classical sources drops with the order of interference,. the visibility of difference-phase interference has opposite behavior. For three-photon and four-photon interference of two coherent sources, the visibility can be as high as 81.8% and 94.4%, respectively. High-visibility three-photon and four-photon interference of space-time and polarization types has been observed in experiment, for both coherent and pseudothermal light.

Generation of different Bell states within the spontaneous parametric down-conversion phase-matching bandwidth

Giorgio Brida, Maria Chekhova, Marco Genovese, Leonid Krivitsky

We study the frequency-angular line shape for a phase-matched nonlinear process producing entangled states and show that there is a continuous variety of maximally entangled states generated for different mismatch values within the natural bandwidth. Detailed considerations are made for two specific methods of polarization entanglement preparation, based on type-II spontaneous parametric down-conversion (SPDC) and on SPDC in two subsequent type-I crystals producing orthogonally polarized photon pairs. It turns out that different Bell states are produced at the center of the SPDC line and on its slopes, corresponding to about half-maximum intensity level. These Bell states can be filtered out by either frequency selection or angular selection, or both. Our theoretical calculations are confirmed by a series of experiments, performed for the two above-mentioned schemes of producing polarization-entangled photon pairs and with two kinds of measurements: frequency selective and angular selective.

Interference structure of two-photon amplitude revealed by dispersion spreading

G. Brida, M. Genovese, L. A. Krivitsky, M. V. Chekhova

We study the interference structure of the second-order intensity correlation function for polarization-entangled two-photon light obtained from type-II collinear frequency-degenerate spontaneous parametric down conversion. The structure is visualized due to the spreading of the two-photon amplitude in an optical fiber with group-velocity dispersion. A birefringent material inserted at the output of the nonlinear crystal leads to a more complicated interference structure of the correlation function.

Quantum reconstruction of an intense polarization squeezed optical state

Ch. Marquardt, J. Heersink, R. Dong, M. V. Chekhova, A. B. Klimov, L. L. Sanchez-Soto, U. L. Andersen, G. Leuchs

We perform a reconstruction of the polarization sector of the density matrix of an intense polarization squeezed beam starting from a complete set of Stokes measurements. By using an appropriate quasidistribution, we map this onto the Poincare space, providing a full quantum mechanical characterization of the measured polarization state.

Multiphoton correlations in parametric down-conversion and their measurement in the pulsed regime

O. A. Ivanova, T. Sh. Iskhakov, A. N. Penin, M. V. Chekhova

We consider normalised intensity correlation functions (CFs) of different orders for light emitted via parametric down-conversion (PDC) and their dependence on the number of photons per mode. The main problem in measuring such correlation functions is their extremely small width, which considerably reduces their contrast. It is shown that if the radiation under study is modulated by a periodic sequence of pulses that are short compared to the CF width, no decrease in the contrast occurs. A procedure is proposed for measuring normalised CFs of various orders in the pulsed regime. For nanosecond-pulsed PDC radiation, normalised second-order CF is measured experimentally as a function of the mean photon number.

Possibility of absolute calibration of analog detectors by using parametric downconversion: a systematic study

Giorgio Brida, Marco Genovese, Ivano Ruo-Berchera, Maria Chekhova, Alexander Penin

Prompted by the need for various studies ranging from quantum information to foundations of quantum mechanics, we systematically study the possibility of the absolute calibration of analog photodetectors based on the properties of parametric amplifiers. Our results show that such a method can be effectively developed with interesting possible applications in metrology. (c) 2006 Optical Society of America.

Dispersion spreading of biphotons in optical fibers and two-photon interference

G Brida, MV Chekhova, M Genovese, M Gramegna, LA Krivitsky

We present the first observation of two-photon polarization interference structure in the second-order Glauber correlation function of two-photon light generated via type-II spontaneous parametric down-conversion. In order to obtain this result, two-photon light is transmitted through an optical fiber and the coincidence distribution is analyzed by means of the start-stop method. Beyond the experimental demonstration of an interesting effect in quantum optics, these results also have considerable relevance for quantum communications.

Spectral properties of three-photon entangled states generated via three-photon parametric down-conversion in a chi((3)) medium

MV Chekhova, OA Ivanova, V Berardi, A Garuccio

We consider the quantum state of light produced via direct parametric decay of pump photons into photon triples in a medium with cubic nonlinearity. For this state generated in the near-collinear frequency-degenerate regime, the third- and second-order Glauber's correlation functions are calculated and the intensity distribution over frequency and wave vector is found. It is shown that the number of photons generated into a single mode via the three-photon down-conversion is proportional to the width of the frequency-angular intensity distribution for the corresponding two-photon phase matching (spontaneous parametric down-conversion). The intensity of three-photon parametric down-conversion is shown to have an extremely broad frequency spectrum, even for a fixed angle of scattering.

Qutrit state engineering with biphotons

Y. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh, M. K. Tey

The novel experimental realization of three-level optical quantum systems is presented. We use the polarization state of biphotons to generate a specific sequence of states that are used in the extended version of four-state QKD protocol quantum key distribution protocol. We experimentally verify the orthogonality of the basic states and demonstrate the ability to easily switch between them. The tomography procedure is employed to reconstruct the density matrices of generated states.

Orthogonality of biphoton polarization states

MV Chekhova, LA Krivitsky, SP Kulik, GA Maslennikov

Orthogonality of two-photon polarization states belonging to a single frequency and spatial mode is demonstrated experimentally, in a generalization of the well-known anticorrelation "dip" experiment.

Conditional unitary transformation on biphotons

G Brida, MV Chekhova, M Genovese, M Gramegna, LA Krivitsky, SP Kulik

A conditional unitary transformation (90degrees polarization rotation) is performed at single-photon level. The transformation is realized by rotating polarization for one of the photons of a polarization-entangled biphoton state (signal photon) by means of a Pockel cell triggered by the detection of the other (idler) photon after polarization selection. As a result, the state of the signal photon is losslessly changed from being completely unpolarized to being partially polarized, so that the final polarization degree is given by the idler detector quantum efficiency. This experiment can be used for developing a different method of absolute quantum efficiency calibration.

Experimental entanglement concentration and universal Bell-state synthesizer

YH Kim, SP Kulik, MV Chekhova, WP Grice, Y Shih

We report a Bell-state synthesizer in which an interferometric entanglement concentration scheme is used. An initially mixed polarization state from type-II spontaneous parametric down-conversion becomes entangled after the interferometric entanglement concentration. This Bell-state synthesizer is universal in the sense that the output polarization state is not affected by spectral filtering, crystal thickness, and, most importantly, the choice of pump source. It is also robust against environmental disturbance and a more general state, partially mixed-partially entangled state, can be readily generated as well.

Entangled two-photon wave packet in a dispersive medium

A Valencia, MV Chekhova, A Trifonov, Y Shih

We report an experimental study of group-velocity dispersion effect on an entangled two-photon wave packet, generated via spontaneous parametric down-conversion and propagating through a dispersive medium. Even in the case of using cw laser beam for pump, the biphoton wave packet and the second-order correlation function spread significantly. The study and understanding of this phenomenon is of great importance for quantum information applications, such as quantum communication and distant clock synchronization.

Collinear two-photon state with spectral properties of type-I and polarization properties of type-II spontaneous parametric down-conversion: Preparation and testing

AV Burlakov, MV Chekhova, OA Karabutova, SP Kulik

Two beams of collinear type-I biphotons generated via spontaneous parametric down-conversion (SPDC) from coherent pump beams are transformed without a loss into a state of correlated photons with orthogonal (in the general case, elliptical) polarizations. This alternative state manifests remarkable properties: while having the spectrum of type-I SPDC, it has polarization properties similar to type-II SPDC. To test the state, we use the anticorrelation effect ("anticorrelation dip").

Two-photon diffraction and quantum lithography

M D'Angelo, MV Chekhova, Y Shih

We report a proof-of-principle experimental demonstration of quantum lithography. Utilizing the entangled nature of a two-photon state, the experimental results have beaten the classical diffraction limit by a factor of 2. This is a quantum mechanical two-photon phenomenon but not a violation of the uncertainty principle.

Anticorrelation effect in femtosecond-pulse pumped type-II spontaneous parametric down-conversion

YH Kim, V Berardi, MV Chekhova, YH Shih

We report an experimental demonstration of an anticorrelation effect in femtosecond-pulse pumped type-II spontaneous parametric down-conversion. Our experimental data, which is different from that of Atature et al. [Phys. Rev. Lett. 83, 1323 (2000)], confirmed the shallow symmetric "dip" that is predicted theoretically by Keller and Rubin [Phys. Rev. A 56, 1534 (1997)] and Grice and Walmsley [Phys. Rev. A 56, 1627 (1997)]. We show in this paper that the asymmetric dip observed in the literature is an artifact, which is caused by the asymmetric optical elements introduced into the beam path after the down-conversion process. The "partial distinguishability" theory suggested by Atature et al. is therefore incorrect.

Interferometric Bell-state preparation using femtosecond-pulse-pumped spontaneous parametric down-conversion

YH Kim, MV Chekhova, SP Kulik, MH Rubin, YH Shih

We present a theoretical and experimental study of preparing maximally entangled two-photon polarization states, or Bell states, using femtosecond-pulse-pumped spontaneous parametric down-conversion (SPDC). First, we show how the inherent distinguishability in femtosecond-pulse-pumped type-II SPDC can be removed by using an interferometric technique without spectral and amplitude postselection. We then analyze the recently introduced Bell-state preparation scheme using type-I SPDC. Theoretically, both methods offer the same results, however, type-I SPDC provides experimentally superior methods of preparing Bell states in femtosecond-pulse-pumped SPDC. Such a pulsed source of highly entangled photon pairs is useful in quantum communications, quantum cryptography, quantum teleportation, etc.

Biphoton interference with a multimode pump

AV Burlakov, MV Chekhova, OA Karabutova, SP Kulik

We study the interference of biphotons generated via spontaneous parametric down-conversion from a pump with several longitudinal modes. It is shown that biphotons can interfere if the time difference between their birth moments is a multiple, to an accuracy of the pump coherence time, of T=2L/c, where L is the pump cavity length. This effect, although observed with a cw pump, is similar to a recently reported interference of biphotons generated from time-separated pump pulses.

Temporal indistinguishability and quantum interference

YH Kim, V Berardi, MV Chekhova, A Garuccio, Y Shih

A chi((2)) nonlinear optical crystal is pumped by two temporally well-distinguishable femtosecond laser pulses to generate entangled photon pairs in the process of spontaneous parametric down-conversion. We have observed first- and second-order interference between amplitudes generated from the first and the second pump pulse as a function of the time delay between the two pump pulses. The criteria for first- and second-order interference are found to be very different, which reflect the quantum entanglement nature of the state of spontaneous parametric down-conversion.

First-order interference of nonclassical light emitted spontaneously at different times

YH Kim, MV Chekhova, SP Kulik, Y Shih, MH Rubin

We study the first-order interference in spontaneous parametric down-conversion generated by two pump pulses that are well distinguishable in time. The observed modulation in the angular distribution of the signal photon can only be explained in terms of a quantum-mechanical description based on biphoton states. The condition for observing interference in the signal channel is shown to depend on the parameters of the idler photon.

Polarization state of a biphoton: Quantum ternary logic

AV Burlakov, MV Chekhova, OA Karabutova, DN Klyshko, SP Kulik

The polarization state of biphoton light generated via colinear frequency-degenerate spontaneous parametric down-conversion is considered. A biphoton is described by a three-component polarization vector, its arbitrary transformations relating to the SU(3) group. A subset of such transformations, available with retardation plates, is realized experimentally. In particular, two biphoton beams, formed by colinearly polarized photons (type I) are transformed into a single biphoton beam formed by orthogonally polarized photons (type II). Polarized biphotons are suggested as ternary analogs of two-state quantum systems (qubits). [S1050-2947(99)51312-7].

Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions

AV Burlakov, MV Chekhova, DN Klyshko, SP Kulik, AN Penin, YH Shih, DV Strekalov

Two types of interference were observed using two-photon spontaneous parametric radiation from two nonlinear interaction regions. Two experimental setups analogous to the Young and Mach-Zehnder interferometers were used. An interesting feature of the two-photon Young interference is the opposite conditions for its observation by two different methods: by measuring intensity of light at a single frequency and by measuring correlation of intensities at two conjugated frequencies (method of coincidences). Two-photon Mach-Zehnder interference resembles the Ramsey method of separated fields, which is used in beam spectroscopy. A simple macroscopic quantum model agrees well with the experimental results and enables their interpretation in terms of ''biphotons'' carrying information about the pump phase.

Intensity interference in Bragg scattering by acoustic waves with thermal statistics

MV Chekhova, SP Kulik, AN Penin, PA Prudkovskii

Angular distributions of the intensity and the fourth-order correlation function are studied for light scattered by acoustic waves with thermal statistics. In the case when the beam diameter exceeds the coherence length of the acoustic wave, the fourth-order correlation function is found to contain an interference structure, whereas the intensity angular distribution has a one-peak shape.