Quantum optics: Nonclassical states of light (singlephoton, twophoton, threephoton and squeezed), their generation through nonlinear optical processes and from singlephoton emitters; quantum nonlinear optics at the nanoscale.
Overcoming detection loss and noise in squeezingbased optical sensing
Gaetano Frascella, Sascha Agne, Farid Ya. Khalili, Maria V. Chekhova
npj Quantum Information
7
72
(2021)

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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 signaltonoise ratio in imaging and spectroscopy, and are already used in reallife gravitationalwave 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 losstolerant 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 shotnoise limit by 6 dB. Subshotnoise 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 SantiagoCruz, Anna Fedotova, Vitaliy Sultanov, Maximilian A. Weissflog, Dennis Arslan, Mohammadreza Younesi, Thomas Pertsch, Isabelle Staude, Frank Setzpfandt, et al.
Alldielectric optical metasurfaces are a workhorse in nanooptics, because of both their ability to manipulate light in different degrees of freedom and their excellent performance at light frequency conversion. Here, we demonstrate firsttime generation of photon pairs via spontaneous parametricdown conversion in lithium niobate quantum optical metasurfaces with electric and magnetic Mielike resonances at various wavelengths. By engineering the quantum optical metasurface, we tailor the photonpair 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 flatoptics sources of entangled photons—a new promising platform for quantum optics experiments.
Multimode optical parametric amplification in the phasesensitive regime
Gaetano Frascella, R. V. Zakharov, O. V. Tikhonova, Maria V. Chekhova
Phasesensitive optical parametric amplification of squeezed states helps to overcome detection loss and noise and thus increases the robustness of subshotnoise 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 phasesensitive amplification and verify them in an experiment where a pumped secondorder nonlinear crystal is seeded with a Gaussian coherent beam. Phasesensitive amplification is obtained by tightly focusing the seed into the crystal, rather than seeding with closetoplane waves. This suggests that phasesensitive amplification of subshotnoise 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 quantumenhanced spectroscopy.
Polarization of Light: In Classical, Quantum, and Nonlinear Optics
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 nonuniform 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
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 downconversion (SPDC) from subwavelength films. We achieve photon pair generation with a high coincidencetoaccidental 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 squeezingassisted interferometers by means of twochannel detection
Gaurav Shukla, Dariya Salykina, Gaetano Frascella, Devendra Kumar Mishra, Maria V. Chekhova, Farit Khalili
Optics Express
29(1)
413391
(2020)

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For a squeezingenhanced linear (socalled SU(2)) interferometer, we theoretically investigate the possibility to broaden the phase range of subshotnoise 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 phasesensitive amplifier, this sensitivity could be also tolerant to the detection loss.
Reconstructing twodimensional 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 twodimensional 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 highgain parametric downconversion. 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 highgain 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 highquality images. In this way, one can avoid using singlephoton 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 downconversion with low pump energies
We report the efficient generation of highgain parametric downconversion, 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 downconverted 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 downconverted beams in highly efficient parametric downconversion sources
Direct measurement of the coupled spatiotemporal coherence of parametric downconversion under negative groupvelocity dispersion
We present a direct measurement of the spatiotemporal coherence of parametric downconversion in the range of negative groupvelocity dispersion. In this case, the frequencyangular spectra are ringshaped, 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 nearfield space coherence simultaneously, with complete control over both variables. This technique is also suitable for the measurement of secondorder coher ence, where the main applications are related to twophoton 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 typeI broadband highgain parametric down conversion. The different contributions to the spectra of harmonics are analyzed. A new method for the measurement of secondorder correlation function g(2)(0) of parametric down conversion radiation is suggested.
Progress toward thirdorder parametric downconversion in optical fibers
A. Cavanna, J. Hammer, C. Okoth, E. OrtizRicardo, H. CruzRamirez, K. GarayPalmett, A. B. U’Ren, M. Frosz, X. Jiang, et al.
Optical fibers have been considered an optimal platform for thirdorder parametric downconversion since they can potentially overcome the weak thirdorder 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, G Frascella, A. M. Perez, O. V. Tikhonova, S. Lemieux, R. W. Boyd, G. Leuchs, M. V. Chekhova
Physical Review Research
2(1)
013371
(2020)

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A bright squeezed vacuum (BSV) is a nonclassical macroscopic state of light, which is generated through highgain parametric downconversion or fourwave 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 gainindependent 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 photonnumber 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 planewave 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 photonpair generation in a suspendedcore fiber
Jonas Hammer, Maria V. Chekhova, Daniel Häupl, Riccardo Pennetta, Nicolas Y. Joly
Physical Review Research
2(1)
012079(R)
(2020)

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Nowadays fiber biphoton sources are nearly as popular as crystalbased 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 EinsteinPodolskyRosen states from non–phasematched parametric downconversion
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 downconversion (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 phasematching condition and reach record levels of transverse momentum entanglement. The degree of entanglement is estimated using both correlation measurements and stimulated emission tomography in wavevector space. The high entanglement of the state in wavevector 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 SantiagoCruz, Maria Chekhova
Physical Review Letters
123(26)
263602
(2019)

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We report, for the first time, the observation of spontaneous parametric downconversion (SPDC) free of phase matching (momentum conservation).We alleviate the need to conserve momentum by exploiting the
positionmomentum uncertainty relation and using a planar geometry source, a 6 μm thick layer of lithium niobate. Nonphasematched SPDC opens up a new platform on which to investigate fundamental quantum
effects but it also has practical applications. The ultrasmall thickness leads to a frequency spectrum an order of magnitude broader than that of phasematched SPDC. The strong twophoton correlations are still
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.
Detectiondeviceindependent verification of nonclassical light
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 onoff 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 singlephoton 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 continuousvariable 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 continuousvariable 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 fullscale implementation of quantum key distribution using bright light, thus bringing quantum communication closer to classical optics.
Experimental reconstruction of spatial Schmidt modes for a widefield 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 widefield SU(1, 1) interferometer, i.e. a nonlinear interferometer comprising two coherentlypumped spatiallymultimode optical parametric amplifiers placed in sequence with a focusing element in between. This device is expected to provide a phase sensitivity below the shotnoise limit for multiple modes over
a broad angular range. To reconstruct the spatial modes and their weights, we implement
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 spatiallyresolved 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 aperiodicallypoled crystals, where broadband squeezed light is generated by both crystals via parametric downconversion 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.
Widefield 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 subshotnoise sensitivity to a phase shift introduced in between. We present the first realization of a widefield 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 planewave modes inside the interferometer. Such an interferometer is useful not only for quantum metrology, but also in remote sensing, enhanced subshotnoise imaging, and quantum information processing. (C) 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
IndefiniteMean 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 powerlaw (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 indefinitemean 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 heavytailed 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 singlephoton subtraction, the latter of which we demonstrate experimentally.
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 singleshot qudit readout.
Properties of bright squeezed vacuum at increasing brightness
P. R. Sharapova, Gaetano Frascella, M. Riabinin, A. M. Perez, O. V. Tikhonova, S. Lemieux, R. W. Boyd, G Leuchs, Maria Chekhova
Bright squeezed vacuum (BSV) is a nonclassical macroscopic state of light, which can be gen erated through highgain parametric downconversion or fourwave mixing. Although 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 fails to explain the spectral broadening observed in experiment as the mean number of photons increases. On the other hand, the semiclassical description accounting for the broadening does not allow to decouple the intermodal photonnumber correlations. In this work, we present a new generalized theoretical approach to describe the spatial properties of BSV. This approach is based on exchanging the (k, t) and (ω, z) representations and solving a system of integrodifferential equations. Our approach pre dicts correctly the dynamics of the Schmidt modes and the broadening of the spectrum with the increase in the BSV mean photon number due to a stronger pumping. Moreover, the model succes fully 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 inter ference 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 frequency spectrum, frequency Schmidt modes and other experimental configurations.
Seeded and unseeded highorder parametric downconversion
Cameron Okoth, Andrea Cavanna, Nicolas Joly, Maria Chekhova
Spontaneous parametric downconversion (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 higherorder 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 nonGaussian states without the need for postselection. Here we calculate the expected rate of emission for nthorder SPDC with and without external stimulation (seeding). Focusing primarily on thirdorder parametric downconversion, we estimate the photon detection rates in a rutile crystal for both the unseeded and seeded regimes.
Study of broadband multimode light via nonphasematched sum frequency generation
Denis Kopylov, Kirill Spasibko, Tatiana Murzina, Maria Chekhova
New Journal of Physics
21
033024
(2019)

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We propose nonphasematched 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 highgain 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 lowgain PDC gives the degree of frequency entanglement for photon pairs. By generating the sum frequency in the nearsurface 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 nonphasematched SFG as a wavelengthindependent autocorrelator. Furthermore, we demonstrate efficient nonphasematched three and fourfrequency 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 subshotnoise absorption measurement and imaging
Eugene Knyazev, Farid Khalili, Maria Chekhova
Optics Express
27(6)
78687885
(2019)

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Photonnumber squeezing and correlations enable measurement of absorption with an accuracy exceeding that of the shotnoise limit. However, subshot 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 phasesensitive amplification before detection. Here we propose an experimental scheme of subshotnoise 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 downconversion (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, quantummechanical 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 highgain 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.
Indefinitemean Pareto photon distribution from amplified quantum noise
Mathieu Manceau, Kirill Spasibko, Gerd Leuchs, Radim Filip, Maria Chekhova
The existence of extreme events is a fascinating phenomenon in natural and social sciences. They appear whenever the probability distribution has a `heavy tail', differing very much from the equilibrium one. Examples are `rogue waves' in the ocean and their analogues in nonlinear optics, Levy flights, and other numerous examples in physics, biology, Earth science, etc. Most famous are the statistics of income and wealth with a powerlaw (Pareto) probability distribution describing social inequality and responsible for the renowned `80/20 rule'. The power laws can be however very different; for some outstanding cases the power exponents are less than 2 leading to indefinite mean values, to say nothing of higher moments. Here we present the first evidence of such probability distributions of photon numbers using nonlinear effects pumped by parametrically amplified vacuum noise, known as bright squeezed vacuum (BSV). We observe a Pareto distribution with power exponent 1.3 when BSV pumps supercontinuum generation, and other heavytailed distributions for the optical harmonics generated from BSV. Unlike in other fields, we can flexibly control the Pareto exponent by changing the experimental parameters. Besides photonic applications such as ghost imaging, this extremely fluctuating light is also interesting for quantum thermodynamics as a resource to produce more efficiently nonequlibrium states by singlephoton subtraction, which we demonstrate in experiment.
Multiphoton nonclassical light from clusters of singlephoton emitters
Luo Qi, Mathieu Manceau, Andrea Cavanna, Fabian Gumpert, Luigi Carbone, Massimo de Vittorio, Alberto Bramati, Elisabeth Giacobino, Lukas Lachman, et al.
New Journal of Physics
20
073013
(2018)

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We study nonclassical features of multiphoton light emitted by clusters of singlephoton 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 dotinrods we observe antibunching and nonclassicality of up to the fourthorder. Surprisingly, violation of certain classical inequalities gets even more pronounced for larger clusters.
Bright squeezed vacuum in a nonlinear interferometer: Frequency and temporal Schmidtmode 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 highgain 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 BlochMessiah reduction and the Schmidtmode 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 submicron tapers for thirdharmonic 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 threephoton states of light—the inverse of thirdharmonic generation (THG). Here we report gastuning of intermodal phasematched THG in submicrondiameter tapered optical fiber. By adjusting the pressure of the surrounding argon gas up to 50 bars, intermodally phasematched thirdharmonic 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 highgain 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 sumfrequency generation on the surface of a nonphasematched crystal, we measure a crosscorrelation peak with the temporal width of 90 fs.
Quantum tomography enhanced through parametric amplification
E. Knyazev, Kirill Spasibko, Maria V. Chekhova, F. Ya Khalili
NEW JOURNAL OF PHYSICS
20
013005
(2018)

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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 phasesensitive 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 proofofprinciple experiment with a travelingwave parametric amplifier. We show that with the stateoftheart optical elements, the protocol enables high fidelity tomographic reconstruction of bright nonclassical states of light. We consider two examples: bright squeezed vacuum and squeezed singlephoton state, with the latter being a nonGaussian state and both strongly affected by the losses.
Photonic crystal fibers for generating threephoton states
Maria V. Chekhova, Andrea Cavanna, M. Taheri, Cameron Okoth, Xin Jiang, Nicolas Joly, Philip St. J. Russell
Conference on Lasers and ElectroOptics
(2017)
Direct decay of pump photons into triplets is an interesting but notyetrealized nonlinear effect. We are exploring two approaches using photonic crystal fibers: a gasfilled hollowcore PCF and the recently designed hybrid solidcore PCF.
Improving the phase supersensitivity of squeezingassisted
interferometers by squeeze factor unbalancing
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 antisqueezer, 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 supersensitivity, 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 supersensitivity phase range and a better overall sensitivity can be achieved by gain unbalancing.
Characterization and shaping of the timefrequency Schmidt mode spectrum
of bright twin beams generated in gasfilled hollowcore photonic
crystal fibers
M. A. Finger, N. Y. Joly, P. St. J. Russell, M. V. Chekhova
We vary the timefrequency mode structure of ultrafast pulsepumped modulational instability (MI) twin beams in an argonfilled hollowcore kagomestyle photonic crystal fiber by adjusting the pressure, pump pulse chirp, fiber length, and parametric gain. Compared to solidcore systems, the pressuredependent 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 femtosecondpumped.(3) sources. We also characterize the resulting mode content, not only by measuring the multimode secondorder correlation function g((2)), but also by directly reconstructing the shapes and weights of timefrequency Schmidt (TFS) modes. We show that the number of modes directly influences the shottoshot pulseenergy and spectralshape 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.
Experimental demonstration of negativevalued polarization
quasiprobability distribution
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 onedimensional marginal probability distributions and therefore represent the natural choice for the probability distributions in classical hiddenvariable 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 photonnumber averaging detectors. Here we reconstruct the polarization quasiprobability distribution of a coherent state with photonnumber 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.
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 stateoftheart interferometry, enable subshotnoise phase sensitivity in spectral ranges with inefficient detection, and allow extension to quantum imaging.
Orbital angular momentum modes of highgain parametric downconversion
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 downconversion (PDC), signal and idler photons generated at low gain have perfectly anticorrelated OAM values. It is interesting to study the OAM properties of highgain PDC, where the same OAM modes can be populated with large, but correlated, numbers of photons. Here we investigate the OAM spectrum of highgain 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.
Multiphoton Effects Enhanced due to Ultrafast PhotonNumber Fluctuations
Kirill Yu. Spasibko, Denis A. Kopylov, Victor L. Krutyanskiy, Tatiana V. Murzina, Gerd Leuchs, Maria V. Chekhova
The rate of an nphoton effect generally scales as the nth order autocorrelation function of the incident light, which is high for light with strong photonnumber 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 24 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 photonnumber 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.
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
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 groupvelocity dispersion, its spectrum is restricted in both angle and wavelength. Detuning from exact collineardegenerate phasematching leads to a ring shape of the wavelengthangular 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
JOURNAL OF MODERN OPTICS
63(1 SI)
6470
(2016)

Journal
We propose a method for tailoring the frequency spectrum of bright squeezed vacuum by generating it in a nonlinear interferometer, consisting of two downconverting 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.
Hybrid photonic crystal fiber for efficient singlemode thirdharmonic and triplet photon generation
Andrea Cavanna, Felix Just, Xin Jiang, Maria V. Chekhova, Gerd Leuchs, Philip St. J. Russell, Nicolas Y. Joly
Conference on Lasers and ElectroOptics
(2016)
Lownoise macroscopic twin beams
Timur Sh. Iskhakov, Vladyslav C. Usenko, Radim Filip, Maria V. Chekhova, Gerd Leuchs
Applying a multiphotonsubtraction technique to the twocolor macroscopic squeezed vacuum state of light generated via highgain parametric downconversion we conditionally prepare a different state of light: bright multimode lownoise 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 photonnumber correlations between the beams. The prepared lownoise 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 walkoff
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 walkoff 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
Nonlinear interferometers in quantum optics
M. V. Chekhova, Z. Y. Ou
ADVANCES IN OPTICS AND PHOTONICS
8(1)
104155
(2016)

Journal
Hybrid photoniccrystal fiber for singlemode 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
In a direct detection scheme, we observed 7.8 dB of twinbeam squeezing for multimode twocolor squeezed vacuum generated via parametric downconversion. Applying postselection, we conditionally prepared a subPoissonian 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 shotnoise level. Such pulses can be used in metrology (for instance, for radiometer calibration), as well as for probing multimode nonlinear optical effects. (C) 2016 Optical Society of America
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 highgain parametric down conversion or fourwave 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, photonnumber 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 singlemode fiber. Moreover, we show that the first Schmidt mode can be captured by simply maximizing the fibercoupled intensity. Importantly, the projection operation does not affect the targeted mode and leaves it usable for further applications.
Giant narrowband twinbeam generation along the pumpenergy propagation
direction
Angela M. Perez, Kirill Yu Spasibko, Polina R. Sharapova, Olga V. Tikhonova, Gerd Leuchs, Maria V. Chekhova
Walkoff effects, originating from the difference between the group and phase velocities, limit the efficiency of nonlinear optical interactions. While transverse walkoff can be eliminated by proper medium engineering, longitudinal walkoff is harder to avoid. In particular, ultrafast twinbeam generation via pulsed parametric downconversion and fourwave mixing is only possible in short crystals or fibres. Here we show that in highgain parametric downconversion, 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 whisperinggallery mode resonators.
Twophoton 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 keystone for stateoftheart 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 singlemode 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 twophoton spectral amplitude (TPSA) contains several nonoverlapping 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 downconversion 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 frequencytotime twodimensional 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.
RamanFree, NobleGasFilled PhotonicCrystal Fiber Source for
Ultrafast, Very Bright TwinBeam 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 highpressure argonfilled hollowcore kagomestyle photoniccrystal fiber. The source is Ramanfree and manifests strong photonnumber correlations for femtosecond pulses of squeezed vacuum with a record brightness of similar to 2500 photons per mode. The ultrabroadband (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 squeezedvacuum twinbeam sources in terms of brightness and low mode content.
Bright squeezed vacuum: Entanglement of macroscopic light beams
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 highgain parametric downconversion, manifests entanglement in both photon numbers and polarization. (C) 2014 Elsevier B.V. All rights reserved.
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 downconversion and fourwave 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 photonnumber spatial correlations that are found to be very well described by our theoretical approach.
Compensation of anisotropy effects in the generation of twophoton 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 downconversion (PDC) radiation in bulk crystals. In this method, a single nonlinear crystal is replaced by two consecutive crystals with opposite transverse walkoff 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
Bright squeezedvacuum 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 travelingwave optical parametric amplifier (OPA). By constructing the OPA of two consecutive crystals separated by a large distance, we make the squeezed vacuum spatially singlemode without a significant decrease in the brightness or squeezing. (C) 2014 Optical Society of America
Possibility Investigation of Experimental Verification of General Bell
Inequality Violation for Polarization Scalar Light Based Realization
M. V. Chekhova, T. Sh. Iskhakov, G. O. Rytikov, K. Yu. Spasibko, O. A. Tscherbina
2014 INTERNATIONAL CONFERENCE ON COMPUTER TECHNOLOGIES IN PHYSICAL AND
ENGINEERING APPLICATIONS (ICCTPEA)
2728
(2014)
We discuss the fundamental problems of nonclassical correlations and microscopic entanglement experimental observation possibility for multiphoton quantum light beams. Optical beams of multiphoton nonclassical light are of practical interest due to possibility of applications in quantum metrology and quantum informatics. Quantum macroscopic states of light are the significant information carrier in practical realization of quantum computing algorithms, quantum dense coding, quantum key distribution, quantum teleportation and other cases of quantum communications. And quantum macroscopic light beam can be used as high sensitive probe field in special type spectroscopy and in light sources and detectors etalonless calibration.
Separable Schmidt modes of an entangled state
Alessio Avella, Marco Gramegna, Alexander Shurupov, Giorgio Brida, Maria Chekhova, Marco Genovese
Conference on Lasers and ElectroOptics
(2014)
TwoPhoton Spectral Amplitude of entangled states is engineered to produce a losslessly decomposition in nonoverlapping single Schmidt modes. The method relies on spontaneous parametric downconversion pumped by a comblike spectrum radiation.
Detection of nonclassical spacetime correlations with a novel type of
singlephoton 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, multipixel 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 nonclassical light from spontaneous parametric downconversion and use twophoton correlations for the absolute calibration of its quantum efficiency. (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 "dotinrods" and their small clusters are studied by measuring the secondorder 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 higherorder 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
Interference of macroscopic beams on a beam splitter: phase uncertainty
converted into photonnumber uncertainty
K. Yu Spasibko, F. Toeppel, T. Sh Iskhakov, M. Stobinska, M. V. Chekhova, G. Leuchs
Squeezedvacuum twin beams, commonly generated through parametric downconversion, are known to have perfect photonnumber 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 photonnumber fluctuations and observe this uncertainty as a typical 'Ushape' of the output photonnumber distribution. This effect, although reported for atomic ensembles and giving hope for phase superresolution, has never been observed for light beams. The shape of the normalized photonnumber difference distribution is similar to the one that would be observed for highorder Fock states. It can be also mimicked by classical beams with artificially mixed phase, but without any perspective for phase superresolution. 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
Twophoton states entangled in continuous variables such as wave vector or frequency represent a powerful resource for quantuminformation protocols in higherdimensional Hilbert spaces. At the same time, there is a problem of addressing separately the corresponding Schmidt modes. We propose a method of engineering twophoton 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 downconversion (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 FabryPerot interferometer. For the twophoton spectral amplitude (TPSA) to consist of nonoverlapping Schmidt modes, the crystal dispersion dependence, the length of the crystal, the FabryPerot 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 cavitybased SPDC.
Macroscopic HongOuMandel interference
T. Sh Iskhakov, K. Yu Spasibko, M. V. Chekhova, G. Leuchs
We report on a HongOuMandel interference experiment for twin beams with photon numbers per mode as large as 10(6) generated via highgain 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 photonnumber difference, we observe an extremely wellpronounced 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.
The Schmidt modes of biphoton qutrits: Poincaresphere representation
M. V. Chekhova, M. V. Fedorov
JOURNAL OF PHYSICS BATOMIC MOLECULAR AND OPTICAL PHYSICS
46(9)
095502
(2013)

Journal
For a generalform 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 singlephoton 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.
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 typeI OPA based on parametric downconversion (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 walkoff. 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 twophoton 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 highgain PDC.
Transverse Entanglement of Biphotons
Felix Just, Andrea Cavanna, Maria V. Chekhova, Gerd Leuchs
Conference on Lasers and ElectroOptics
(2013)
We study the transverse entanglement of biphotons generated via parametric downconversion as they propagate from the near to the far field. We obtain the Fedorov ratio and the Schmidt number and compare the results. (C) 2013 Optical Society of America
We measure the transverse entanglement of photon pairs on their propagation from the near to the far field of spontaneous parametric downconversion (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 firstorder 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
Photonnumber correlation measurements are performed on bright squeezed vacuum states using a standard Belltest setup, and quantum correlations are observed for conjugate polarizationfrequency 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
Entanglement of macroscopic Bell states
T. Iskhakov, B. Kanseri, G. Rytikov, M. Chekhova, G. Leuchs
2013 CONFERENCE ON AND INTERNATIONAL QUANTUM ELECTRONICS CONFERENCE
LASERS AND ELECTROOPTICS EUROPE (CLEO EUROPE/IQEC)
(2013)
Nonclassical features of the polarization quasiprobability distribution
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 socalled polarization sector of quantum states of light. We show here that due to its definition in terms of the discretevalued 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 photonnumber 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.
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 highquality singlephoton states with controllable narrow spectral bandwidths and central frequencies is key to facilitate efficient coupling of any atomic system to nonclassical 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, narrowband and efficient singlephoton source based on a whispering gallery mode resonator. Our diskshaped, monolithic and intrinsically stable resonator is made of lithium niobate and supports a cavityassisted spontaneous parametric downconversion 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 antibunching with g((2))(0) < 0.2.
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.
Threedimensional 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 threedimensional quantum polarization tomography. This method utilizes threedimensional (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.
PolarizationEntangled 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 photonnumber 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 twomode squeezing with photon number resolving
multipixel detectors
Dmitry A. Kalashnikov, SiHui Tan, Timur Sh. Iskhakov, Maria V. Chekhova, Leonid A. Krivitsky
OPTICS LETTERS
37(14)
28292831
(2012)
The measurement of the twomode 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
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 4mode squeezed vacuum states. Threedimensional 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.
Superbunched bright squeezed vacuum state
T. Sh. Iskhakov, A. M. Perez, K. Yu. Spasibko, M. V. Chekhova, G. Leuchs
OPTICS LETTERS
37(11)
19191921
(2012)
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 highgain parametric down conversion (PDC). The effects of bunching and superbunching of photons were observed for a singlemode PDC radiation by secondorder intensity correlation function measurements with analog detectors. (C) 2012 Optical Society of America
Filtering of the absolute value of photonnumber difference for twomode
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 twomode 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 twomode field, with a polarizationneutral 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 twomode Fock state is unequally populated, the more the polarizing beamsplitter 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 photonnumber measurement of the polarizing beamsplitter outputs, a feedforward 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 highgain parametric downconversion
Highgain parametric downconversion (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 lowgain PDC. Frequency cross and autocorrelations 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 superbunching typical for collinear frequencydegenerate PDC. (C) 2012 Optical Society of America
Macroscopic Bell States and their Quantum Polarization Tomography
Bhaskar Kanseri, Timur Iskhakov, Maria Chekhova, Gerd Leuchs
Conference on Lasers and ElectroOptics
(2012)
Using threedimensional quantum polarization tomography, the polarization properties of macroscopic Bell states are characterized. The reconstructed polarization quasiprobability distributions demonstrate squeezing in one or more Stokes parameters. (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
OPTICS AND SPECTROSCOPY
111(4)
565569
(2011)

Journal
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.
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
INTERNATIONAL JOURNAL OF QUANTUM INFORMATION
9
251262
(2011)

Journal
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 twomode squeezed vacuum at the output of a traveling wave OPA. However, in the new method, one measures the differencephotocurrent variance rather than the correlation function of photocurrents (number of coincidences), which makes the technique applicable for highgain OPA. In this work we test the new method versus the traditional one for the case of photoncounting detectors where both techniques are valid.
Systematic analysis of signaltonoise 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 signaltonoiseratio 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.
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 quantumtechnology 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, higherorder 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 shotnoise 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
EUROPEAN PHYSICAL JOURNALSPECIAL TOPICS
199(1)
127138
(2011)

Journal
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 groundglass disc, which has statistics close to that of thermal light. We compare the measurements of the normalized correlation functions to that of the differenceintensity 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 highorder ghost imaging are also realized and characterized quantitatively.
Polarization properties of macroscopic Bell states
Timur Sh. Iskhakov, Ivan N. Agafonov, Maria V. Chekhova, Georgy O. Rytikov, Gerd Leuchs
The four twophoton 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 secondorder degree of polarization and its higherorder generalization.
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
OPTICS LETTERS
36(8)
13291331
(2011)
We report testing of the new absolute method of photodetector calibration based on the differencesignal measurement for twomode squeezed vacuum by comparison with the traditional absolute method based on coincidence counting. Using lowgain parametric downconversion, we have measured the quantum efficiency of a counting detector by both methods. The differencesignal method was adapted for the counting detectors by taking into account the deadtime effect. (c) 2011 Optical Society of America
Accessing photon bunching with a photon number resolving multipixel
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 photonnumber resolving detectors. Recently, there appeared multipixel counters (MPPC) that are able to distinguish between 1,2,..10 photons. At the same time, strong coupling between different pixels (crosstalk) hinders their photonnumber 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 higherorder intensity correlations by using just a single MPPC. (C) 2011 Optical Society of America
We test twodimensional TPSA of biphoton light emitted via ultrafast spontaneous parametric downconversion (SPDC) using the effect of groupvelocity 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 timemultiplexing 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 typeII parametric downconversion source to investigate mutual twomode correlation properties and ascertain nonclassicality.
In a strongly pumped nondegenerate travelingwave optical parametric amplifier, we produce a twocolor 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 twinbeam 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
PolarizationSqueezed Vacuum
Using a travelingwave optical parametric amplifier with two orthogonally oriented typeI BBO crystals pumped by picosecond pulses, we generate vertically and horizontally polarized squeezed vacuum states within a broad frequencyangular range. Depending on the phase between these states, fluctuations in one or another Stokes parameter are suppressed below the shotnoise 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.
Highvisibility intensity interference and ghost imaging with pseudothermal light
Ivan N. Agafonov, Maria V. Chekhova, Timur Sh. Iskhakov, LingAn Wu
JOURNAL OF MODERN OPTICS
56(23)
PII 905301666
422431
(2009)

Journal
We consider higherorder intensity correlations in thermal light and show that they can be used for observing highvisibility interference of the Hanbury BrownTwisstype as well as highvisibility ghost imaging. Experimental results are obtained for third and fourthorder intensity interference, by processing images made with a digital photographic camera.
Experimental verification of high spectral entanglement for pulsed
waveguided spontaneous parametric downconversion
Malte Avenhaus, Maria V. Chekhova, Leonid A. Krivitsky, Gerd Leuchs, Christine Silberhorn
We study the spectral properties of spontaneous parametric downconversion (SPDC) in a periodically poled waveguided structure of potassiumtitanylphosphate (KTP) crystal pumped by ultrashort pulses. Our theoretical analysis reveals a strongly entangled and asymmetric structure of the twophoton spectral amplitude for typeII SPDC. We confirm these predictions experimentally by measuring singlephoton spectra, on one hand, and the dependence of HongOuMandel interference visibility on the width of spectral filtering, on the other hand.
Highvisibility multiphoton interference of Hanbury BrownTwiss type for classical light
I. N. Agafonov, M. V. Chekhova, T. Sh. Iskhakov, A. N. Penin
Differencephase (or Hanbury BrownTwiss type) intensity interference of classical light is considered in higher orders in the intensity. It is shown that, while the visibility of sumphase (NOONtype) interference for classical sources drops with the order of interference,. the visibility of differencephase interference has opposite behavior. For threephoton and fourphoton interference of two coherent sources, the visibility can be as high as 81.8% and 94.4%, respectively. Highvisibility threephoton and fourphoton interference of spacetime and polarization types has been observed in experiment, for both coherent and pseudothermal light.
Generation of different Bell states within the spontaneous parametric downconversion phasematching bandwidth
Giorgio Brida, Maria Chekhova, Marco Genovese, Leonid Krivitsky
We study the frequencyangular line shape for a phasematched 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 typeII spontaneous parametric downconversion (SPDC) and on SPDC in two subsequent typeI 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 halfmaximum 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 abovementioned schemes of producing polarizationentangled photon pairs and with two kinds of measurements: frequency selective and angular selective.
Quantum reconstruction of an intense polarization squeezed optical state
Ch. Marquardt, J. Heersink, R. Dong, M. V. Chekhova, A. B. Klimov, L. L. SanchezSoto, 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.
Interference structure of twophoton amplitude revealed by dispersion spreading
G. Brida, M. Genovese, L. A. Krivitsky, M. V. Chekhova
We study the interference structure of the secondorder intensity correlation function for polarizationentangled twophoton light obtained from typeII collinear frequencydegenerate spontaneous parametric down conversion. The structure is visualized due to the spreading of the twophoton amplitude in an optical fiber with groupvelocity dispersion. A birefringent material inserted at the output of the nonlinear crystal leads to a more complicated interference structure of the correlation function.
Possibility of absolute calibration of analog detectors by using parametric downconversion: a systematic study
Giorgio Brida, Marco Genovese, Ivano RuoBerchera, Maria Chekhova, Alexander Penin
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA BOPTICAL PHYSICS
23(10)
21852193
(2006)

Journal
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.
Multiphoton correlations in parametric downconversion 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 downconversion (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 nanosecondpulsed PDC radiation, normalised secondorder CF is measured experimentally as a function of the mean photon number.
Dispersion spreading of biphotons in optical fibers and twophoton interference
G Brida, MV Chekhova, M Genovese, M Gramegna, LA Krivitsky
We present the first observation of twophoton polarization interference structure in the secondorder Glauber correlation function of twophoton light generated via typeII spontaneous parametric downconversion. In order to obtain this result, twophoton light is transmitted through an optical fiber and the coincidence distribution is analyzed by means of the startstop method. Beyond the experimental demonstration of an interesting effect in quantum optics, these results also have considerable relevance for quantum communications.
Spectral properties of threephoton entangled states generated via threephoton parametric downconversion in a chi((3)) medium
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 nearcollinear frequencydegenerate regime, the third and secondorder 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 threephoton downconversion is proportional to the width of the frequencyangular intensity distribution for the corresponding twophoton phase matching (spontaneous parametric downconversion). The intensity of threephoton parametric downconversion 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 threelevel 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 fourstate 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 twophoton polarization states belonging to a single frequency and spatial mode is demonstrated experimentally, in a generalization of the wellknown 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 singlephoton level. The transformation is realized by rotating polarization for one of the photons of a polarizationentangled 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 Bellstate synthesizer
We report a Bellstate synthesizer in which an interferometric entanglement concentration scheme is used. An initially mixed polarization state from typeII spontaneous parametric downconversion becomes entangled after the interferometric entanglement concentration. This Bellstate 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 mixedpartially entangled state, can be readily generated as well.
Entangled twophoton wave packet in a dispersive medium
We report an experimental study of groupvelocity dispersion effect on an entangled twophoton wave packet, generated via spontaneous parametric downconversion and propagating through a dispersive medium. Even in the case of using cw laser beam for pump, the biphoton wave packet and the secondorder 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 twophoton state with spectral properties of typeI and polarization properties of typeII spontaneous parametric downconversion: Preparation and testing
Two beams of collinear typeI biphotons generated via spontaneous parametric downconversion (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 typeI SPDC, it has polarization properties similar to typeII SPDC. To test the state, we use the anticorrelation effect ("anticorrelation dip").
We report a proofofprinciple experimental demonstration of quantum lithography. Utilizing the entangled nature of a twophoton state, the experimental results have beaten the classical diffraction limit by a factor of 2. This is a quantum mechanical twophoton phenomenon but not a violation of the uncertainty principle.
Anticorrelation effect in femtosecondpulse pumped typeII spontaneous parametric downconversion
We report an experimental demonstration of an anticorrelation effect in femtosecondpulse pumped typeII spontaneous parametric downconversion. 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 downconversion process. The "partial distinguishability" theory suggested by Atature et al. is therefore incorrect.
Interferometric Bellstate preparation using femtosecondpulsepumped spontaneous parametric downconversion
We present a theoretical and experimental study of preparing maximally entangled twophoton polarization states, or Bell states, using femtosecondpulsepumped spontaneous parametric downconversion (SPDC). First, we show how the inherent distinguishability in femtosecondpulsepumped typeII SPDC can be removed by using an interferometric technique without spectral and amplitude postselection. We then analyze the recently introduced Bellstate preparation scheme using typeI SPDC. Theoretically, both methods offer the same results, however, typeI SPDC provides experimentally superior methods of preparing Bell states in femtosecondpulsepumped SPDC. Such a pulsed source of highly entangled photon pairs is useful in quantum communications, quantum cryptography, quantum teleportation, etc.
We study the interference of biphotons generated via spontaneous parametric downconversion 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 timeseparated 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 welldistinguishable femtosecond laser pulses to generate entangled photon pairs in the process of spontaneous parametric downconversion. We have observed first and secondorder 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 secondorder interference are found to be very different, which reflect the quantum entanglement nature of the state of spontaneous parametric downconversion.
Firstorder interference of nonclassical light emitted spontaneously at different times
We study the firstorder interference in spontaneous parametric downconversion 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 quantummechanical 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
PHYSICAL REVIEW A
60(6)
R4209R4212
(1999)

Journal
The polarization state of biphoton light generated via colinear frequencydegenerate spontaneous parametric downconversion is considered. A biphoton is described by a threecomponent 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 twostate quantum systems (qubits). [S10502947(99)513127].
Interference effects in spontaneous twophoton parametric scattering from two macroscopic regions
AV Burlakov, MV Chekhova, DN Klyshko, SP Kulik, AN Penin, YH Shih, DV Strekalov
PHYSICAL REVIEW A
56(4)
32143225
(1997)

Journal
Two types of interference were observed using twophoton spontaneous parametric radiation from two nonlinear interaction regions. Two experimental setups analogous to the Young and MachZehnder interferometers were used. An interesting feature of the twophoton 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). Twophoton MachZehnder 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
PHYSICAL REVIEW A
54(6)
R4645R4648
(1996)

Journal
Angular distributions of the intensity and the fourthorder 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 fourthorder correlation function is found to contain an interference structure, whereas the intensity angular distribution has a onepeak shape.