We present an effective electrical circuit model that can be used for a quasianalytic analysis of electromagnetic oscillations in arrays of coupled elements, resonant in the microwave domain. The model accounts for electric and magnetic interactions between charges and currents excited in individual resonators. Respective coupling coefficients can be calculated from the field and current distributions in a subsystem of just one or two elements, provided by a finite-difference electromagnetic solver. The model was used to investigate current distributions and dispersion relations of wave propagation on chains of coupled split-ring resonators. The change of the dispersion characteristics from forward to backward propagating wave type observed experimentally is readily reproduced by the model.
Compensation of Nonlinear Phase Noise Using the Effective Negative
Nonlinearity of a Nonlinear Amplifying Loop Mirror
Klaus Sponsel,
Christian Stephan,
Georgy Onishchukov,
Bernhard Schmauss,
Gerd Leuchs
IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS
18
(2)
637-645
(2012)
| Journal
The nonlinear amplifying loop mirror (NALM) has been explored for use as a nonlinear phase-shift compensator (NPSC). Operation conditions for a tunable effective negative nonlinearity are considered and the NALM parameter optimization is discussed for direct bit-error-ratio (BER) improvement by post-compensation after a nonlinear transmission line. In this configuration, the fundamental limits for NPSC are estimated for differential quadrature phase-shift keying (DQPSK) using a simplified model. Numerical simulations of a 20 Gb/s RZ-DQPSK transmission system confirmed the applicability of this model and showed a significant BER improvement in a realistic transmission line. Alternatively, the fiber launch power per span could be increased by 2 dB for the same BER.
Entanglement of Gaussian states and the applicability to quantum key
distribution over fading channels
Vladyslav C. Usenko,
Bettina Heim,
Christian Peuntinger,
Christoffer Wittmann,
Christoph Marquardt,
Gerd Leuchs,
Radim Filip
Entanglement properties of Gaussian states of light as well as the security of continuous variable quantum key distribution with Gaussian states in free-space fading channels are studied. These qualities are shown to be sensitive to the statistical properties of the transmittance distribution in the cases when entanglement is strong or when channel excess noise is present. Fading, i.e. transmission fluctuations, caused by beam wandering due to atmospheric turbulence, is a frequent challenge in free-space communication. We introduce a method of fading discrimination and subsequent post-selection of the corresponding sub-states and show that it can improve the entanglement resource and restore the security of the key distribution over a realistic fading link. Furthermore, the optimal post-selection strategy in combination with an optimized entangled resource is shown to drastically increase the protocol's robustness to excess noise, which is confirmed for experimentally measured fading channel characteristics. The stability of the result against finite data ensemble size and imperfect channel estimation is also addressed.
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.
Optical mesh lattices with PT symmetry
Mohammad-Ali Miri,
Alois Regensburger,
Ulf Peschel,
Demetrios N. Christodoulides
We investigate a class of optical mesh periodic structures that are discretized in both the transverse and longitudinal directions. These networks are composed of waveguide arrays that are discretely coupled, while phase elements are also inserted to discretely control their effective potentials and can be realized both in the temporal and the spatial domain. Their band structure and impulse response are studied in both the passive and parity-time (PT)-symmetric regime. The possibility of band merging and the emergence of exceptional points, along with the associated optical dynamics, are considered in detail both above and below the PT-symmetry breaking point. Finally, unidirectional invisibility in PT-synthetic mesh lattices is also examined, along with possible superluminal light transport dynamics.
Probing guided modes in a monolayer colloidal crystal on a flat metal
film
Sergei G. Romanov,
Nicolas Vogel,
Karina Bley,
Katharina Landfester,
Clemens K. Weiss,
Sergej Orlov,
Alexander V. Korovin,
Gennady P. Chuiko,
Alois Regensburger, et al.
Two-dimensional slab hybrid metal-dielectric photonic crystals, which are prepared by assembling polymer colloidal spheres into closely packed monolayers of hexagonal symmetry on a gold-coated glass substrate, show an improved confinement of light compared with a colloidal monolayer on a glass substrate. We demonstrated that the optical response of such hybrid crystals consists of diffractively coupled waveguiding modes, Fabry-Perot resonances, and Mie resonances. Correspondingly, two major mechanisms, namely, band transport and hopping of localized excitations, participate in the in-plane light transport in such hybrid crystals.
Collecting more than half the fluorescence photons from a single ion
Robert Maiwald,
Andrea Golla,
Martin Fischer,
Marianne Bader,
Simon Heugel,
Benoit Chalopin,
Markus Sondermann,
Gerd Leuchs
We demonstrate the trapping of a single ion in the focus of a deep parabolic mirror that covers 81% of the solid angle surrounding the ion. Accounting for the reflectivity of the mirror we infer a photon collection efficiency of 54.8% for our setup. The underlying experimentally detected maximum fluorescence rate is 1.91 x 10(6) s(-1) from a single Yb-174(+) ion, mainly limited by the quantum efficiency of our photon detector. Besides the high collection efficiency, the integration of an ion trap into a parabolic mirror is a key ingredient for efficient coupling of light to a single ion in free space.
Plasmonic dimer antennas for surface enhanced Raman scattering
Katja Hoeflich,
Michael Becker,
Gerd Leuchs,
Silke Christiansen
Electron beam induced deposition (EBID) has recently been developed into a method to directly write optically active three-dimensional nanostructures. For this purpose a metal-organic precursor gas (here dimethyl-gold(III)-acetylacetonate) is introduced into the vacuum chamber of a scanning electron microscope where it is cracked by the focused electron beam. Upon cracking the aforementioned precursor gas, 3D deposits are realized, consisting of gold nanocrystals embedded in a carbonaceous matrix. The carbon content in the deposits hinders direct plasmonic applications. However, it is possible to activate the deposited nanostructures for plasmonics by coating the EBID structures with a continuous silver layer of a few nanometers thickness. Within this silver layer collective motions of the free electron gas can be excited. In this way, EBID structures with their intriguing precision at the nanoscale have been arranged in arrays of free-standing dimer antenna structures with nanometer sized gaps between the antennas that face each other with an angle of 90 degrees. These dimer antenna ensembles can constitute a reproducibly manufacturable substrate for exploiting the surface enhanced Raman effect (SERS). The achieved SERS enhancement factors are of the order of 10(4) for the incident laser light polarized along the dimer axes. To prove the signal enhancement in a Raman experiment we used the dye methyl violet as a robust test molecule. In future applications the thickness of such a silver layer on the dimer antennas can easily be varied for tuning the plasmonic resonances of the SERS substrate to match the resonance structure of the analytes to be detected.
Filtering of the absolute value of photon-number difference for two-mode
macroscopic quantum superpositions
M. Stobinska,
F. Toeppel,
P. Sekatski,
A. Buraczewski,
M. Zukowski,
M. V. Chekhova,
G. Leuchs,
N. Gisin
We discuss a device capable of filtering out two-mode states of light with mode populations differing by more than a certain threshold, while not revealing which mode is more populated. It would allow engineering of macroscopic quantum states of light in a way which is preserving specific superpositions. As a result, it would enhance optical phase estimation with these states as well as distinguishability of "macroscopic" qubits. We propose an optical scheme, which is a relatively simple, albeit nonideal, operational implementation of such a filter. It uses tapping of the original polarization two-mode field, with a polarization-neutral beam splitter of low reflectivity. Next, the reflected beams are suitably interfered on a polarizing beam splitter. It is oriented such that it selects unbiased polarization modes with respect to the original ones. The more an incoming two-mode Fock state is unequally populated, the more the polarizing beam-splitter output modes are equally populated. This effect is especially pronounced for highly populated states. Additionally, for such states we expect strong population correlations between the original fields and the tapped one. Thus, after a photon-number measurement of the polarizing beam-splitter outputs, a feed-forward loop can be used to let through a shutter the field, which was transmitted by the tapping beam splitter. This happens only if the counts at the outputs are roughly equal. In such a case, the transmitted field differs strongly in occupation number of the two modes, while information on which mode is more populated is nonexistent (a necessary condition for preserving superpositions).
Tools for detecting entanglement between different degrees of freedom in
quadrature squeezed cylindrically polarized modes
C. Gabriel,
A. Aiello,
S. Berg-Johansen,
Ch Marquardt,
G. Leuchs
EUROPEAN PHYSICAL JOURNAL D
66
(7)
172
(2012)
| Journal
Quadrature squeezed cylindrically polarized modes contain entanglement not only in the polarization and spatial electric field variables but also between these two degrees of freedom [C. Gabriel et al., Phys. Rev. Lett. 106, 060502 (2011)]. In this paper we present tools to generate and detect this entanglement. Experimentally we demonstrate the generation of quadrature squeezing in cylindrically polarized modes by mode transforming a squeezed Gaussian mode. Specifically, -1.2dB +/- 0.1 dB of amplitude squeezing are achieved in the radially and azimuthally polarized mode. Furthermore, theoretically it is shown how the entanglement contained within these modes can be measured and how strong the quantum correlations are, depending on the measurement scheme.
The utilization of time-reversal symmetry in designing and implementing (quantum) optical experiments has become more and more frequent over the last few years. We review the basic idea underlying time-reversal methods, illustrate it with several examples and discuss a number of implications.
Radial mode dependence of optical beam shifts
N. Hermosa,
Andrea Aiello,
J. P. Woerdman
OPTICS LETTERS
37
(6)
1044-1046
(2012)
It is known that orbital angular momentum (OAM) couples the Goos-Hanchen and Imbert-Fedorov shifts. Here, we present the first study of these shifts when the OAM-endowed LG(l,p) beams have higher-order radial mode index (p > 0). We show theoretically and experimentally that the angular shifts are enhanced by p while the positional shifts are not. (C) 2012 Optical Society of America
Spectral properties of high-gain parametric down-conversion
High-gain parametric down-conversion (PDC) is a source of bright squeezed vacuum, which is a macroscopic nonclassical state of light and a promising candidate for quantum information applications. Here we study its properties, such as the intensity spectral width and the spectral width of pairwise correlations. In agreement with the theory, we observe an increase in the spectral width by 27% compared with the low-gain PDC. Frequency cross- and auto-correlations are registered by measuring the reduction of noise in the difference of PDC intensities at various pairs of wavelengths. The noise reduction plots also demonstrate super-bunching typical for collinear frequency-degenerate PDC. (C) 2012 Optical Society of America
Generation of a wave packet tailored to efficient free space excitation
of a single atom
A. Golla,
B. Chalopin,
M. Bader,
I. Harder,
K. Mantel,
R. Maiwald,
N. Lindlein,
M. Sondermann,
G. Leuchs
EUROPEAN PHYSICAL JOURNAL D
66
(7)
190
(2012)
| Journal
We demonstrate the generation of an optical dipole wave suitable for the process of efficiently coupling single quanta of light and matter in free space. We employ a parabolic mirror for the conversion of a transverse beam mode to a focused dipole wave and show the required spatial and temporal shaping of the mode incident onto the mirror. The results include a proof of principle correction of the parabolic mirror's aberrations. For the application of exciting an atom with a single photon pulse, we demonstrate the creation of a suitable temporal pulse envelope. We infer coupling strengths of 89% and success probabilities of up to 87% for the application of exciting a single atom for the current experimental parameters.
Quadrature phase shift keying coherent state discrimination via a hybrid
receiver
C. R. Mueller,
M. A. Usuga,
C. Wittmann,
M. Takeoka,
Ch Marquardt,
U. L. Andersen,
G. Leuchs
We propose and experimentally demonstrate a near-optimal discrimination scheme for the quadrature phase shift keying (QPSK) protocol. We show in theory that the performance of our hybrid scheme is superior to the standard scheme-heterodyne detection-for all signal amplitudes and underpin the predictions with our experimental results. Furthermore, our scheme provides hitherto the best performance in the domain of highly attenuated signals. The discrimination is composed of a quadrature measurement, a conditional displacement and a threshold detector.
On the use of a Continuous Wave Nd:YAG Laser in the Generation of Random
Numbers
M. Sabuncu
LASERS IN ENGINEERING
22
(3-4)
197-208
(2012)
The Nd:YAG laser is a solid state laser that has many applications in the industry, science and medicine. We in this paper use a continuous wave (CW) Nd:YAG laser emitting light at 1064 nm to generate random numbers. We first give a recipe of an experimental setup that is capable of measuring and recording the vacuum fluctuations with the help of our cw Nd:YAG laser. The basic scheme simply involves the Nd:YAG laser, detectors and some radio frequency electronic components. The laser source used in the demonstration provides us with a quantum noise limited CW at a radio frequency sideband of 14 MHz. The final data obtained after appropriate electronic signal processing are digitized voltage fluctuations that correspond to the vacuum fluctuations in the optical domain. The data randomly lies above or below zero due to its quantum mechanical probabilistic nature. We assign a '1' to the data that is positive and a '0' to the data that is negative, hence we are able to generate a random bit sequence by using a cw Nd:YAG laser. This result adds yet another interesting application to the many number of broad applications of the Nd:YAG laser system.
Informational completeness of continuous-variable measurements
D. Sych,
J. Rehacek,
Z. Hradil,
G. Leuchs,
L. L. Sanchez-Soto
We justify that homodyne tomography turns out to be informationally complete when the number of independent quadrature measurements is equal to the dimension of the density matrix in the Fock representation. Using this as our thread, we examine the completeness of other schemes when continuous-variable observations are truncated to discrete finite-dimensional subspaces.
Evaluation algorithms for multistep measurement of spatially varying
linear polarization and phase
Andreas Berger,
Vanusch Nercissian,
Klaus Mantel,
Irina Harder
OPTICS LETTERS
37
(19)
4140-4142
(2012)
Optical components manipulating both polarization and phase of wave fields find more and more applications in today's optical systems. In particular, the polarization orientation may vary across the aperture. New measurement techniques and evaluation algorithms are needed to simultaneously characterize the properties of such elements. In this Letter, a general measurement algorithm for locally linear polarization distributions is presented, extending the methods of phase shifting interferometry to the simultaneous determination of polarization and phase. A class of evaluation algorithms is derived, and some example algorithms are described and tested for their resilience against systematic and stochastic stepping errors. (C) 2012 Optical Society of America
Far field spectrum in surface plasmon-assisted Young's double-slit
interferometer
Bhaskar Kanseri,
Hem Chandra Kandpal,
Ramesh Chandra Budhani
We derive an expression for the resultant spectral density (spectrum) at a point in the far zone for the surface plasmons modulated Young's double-slit interference setup. The resultant spectral interference law has the same form as the standard spectral interference law for the scalar fields. This resemblance in turn provides a means for determination of the modified spectral degree of coherence at the two slits. The mathematical results also show that in an interesting situation when the field is incident at one slit only, the interference can still be observed at the observation plane. These findings are verified theoretically using a wide-band source, i.e. a black-body, having a spectrum following Planck's radiation law. (C) 2012 Elsevier B.V. All rights reserved.
Parity-time synthetic photonic lattices
Alois Regensburger,
Christoph Bersch,
Mohammad-Ali Miri,
Georgy Onishchukov,
Demetrios N. Christodoulides,
Ulf Peschel
The development of new artificial structures and materials is today one of the major research challenges in optics. In most studies so far, the design of such structures has been based on the judicious manipulation of their refractive index properties. Recently, the prospect of simultaneously using gain and loss was suggested as a new way of achieving optical behaviour that is at present unattainable with standard arrangements. What facilitated these quests is the recently developed notion of 'parity-time symmetry' in optical systems, which allows a controlled interplay between gain and loss. Here we report the experimental observation of light transport in large-scale temporal lattices that are parity-time symmetric. In addition, we demonstrate that periodic structures respecting this symmetry can act as unidirectional invisible media when operated near their exceptional points. Our experimental results represent a step in the application of concepts from parity-time symmetry to a new generation of multifunctional optical devices and networks.
Role of spatial coherence in Goos-Hanchen and Imbert-Fedorov shifts:
reply to comment
Andrea Aiello,
J. P. Woerdman
OPTICS LETTERS
37
(6)
1057-1057
(2012)
Wang and Liu [Opt. Lett. 37, 1056 (2012)] comment on our previous Letter [Opt. Lett. 36, 3151 (2011)] regarding the validity of the theory we presented. We reply to their comment here. (C) 2012 Optical Society of America
Generation and Characterization of Multimode Quantum Frequency Combs
Olivier Pinel,
Pu Jian,
Renne Medeiros de Araujo,
Jinxia Feng,
Benoit Chalopin,
Claude Fabre,
Nicolas Treps
Multimode nonclassical states of light are an essential resource in quantum computation with continuous variables, for example, in cluster state computation. We report in this Letter the first experimental evidence of a multimode nonclassical frequency comb in a femtosecond synchronously pumped optical parametric oscillator. In addition to a global reduction of its quantum intensity fluctuations, the system features quantum correlations between different parts of its frequency spectrum. This allows us to show that the frequency comb is composed of several uncorrelated eigenmodes having specific spectral shapes, two of them at least being squeezed, and to characterize their spectral shapes.
Superbunched bright squeezed vacuum state
T. Sh. Iskhakov,
A. M. Perez,
K. Yu. Spasibko,
M. V. Chekhova,
G. Leuchs
OPTICS LETTERS
37
(11)
1919-1921
(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 high-gain parametric down conversion (PDC). The effects of bunching and superbunching of photons were observed for a single-mode PDC radiation by second-order intensity correlation function measurements with analog detectors. (C) 2012 Optical Society of America
Polarization-Entangled Light Pulses of 10(5) Photons
Timur Sh. Iskhakov,
Ivan N. Agafonov,
Maria V. Chekhova,
Gerd Leuchs
We experimentally demonstrate polarization entanglement for squeezed vacuum pulses containing more than 105 photons. We also study photon-number entanglement by calculating the Schmidt number and measuring its operational counterpart. Theoretically, our pulses are the more entangled the brighter they are. This promises important applications in quantum technologies, especially photonic quantum gates and quantum memories.
Optical Gap solitons and Truncated Nonlinear Bloch Waves in Temporal
Lattices
We experimentally demonstrate the formation and stable propagation of various types of discrete temporal solitons in an optical fiber system. Pulses interacting with a time-periodic potential and defocusing nonlinearity are shown to form gap solitons and nonlinear truncated Bloch waves. Multi-pulse solitons with defects, as well as novel structures composed of a strong soliton riding on a weaker truncated nonlinear Bloch wave are shown to propagate over up to eleven coupling lengths. The nonlinear dynamics of all pulse structures is monitored over the full propagation distance which provides detailed insight into the soliton dynamics.
Visualizing the quantum interaction picture in phase space
Bahar Mehmani,
Andrea Aiello
EUROPEAN JOURNAL OF PHYSICS
33
(5)
1367-1381
(2012)
| Journal
We present a graphical example of the interaction picture-time evolution. Our aim is to help students understand in a didactic manner the simplicity that this picture provides. Visualizing the interaction picture unveils its advantages, which are hidden behind the involved mathematics. Specifically, we show that the time evolution of a driven harmonic oscillator in the interaction picture corresponds to a local transformation of a phase space-reference frame into the one that is co-rotating with the Wigner function.
A beam of light, reflected at a planar interface, does not follow perfectly the ray optics prediction. Diffractive corrections lead to beam shifts; the reflected beam is displaced (spatial Goos-Hanchen type shifts) and/or travels in a different direction (angular Imbert-Fedorov type shifts), as compared to geometric optics. How does the degree of spatial coherence of light influence these shifts? We investigate this issue first experimentally and find that the degree of spatial coherence influences the angular beam shifts, while the spatial beam shifts are unaffected.
Resonant metamaterials for contrast enhancement in optical lithography
Sabine Dobmann,
Dzmitry Shyroki,
Peter Banzer,
Andreas Erdmann,
Ulf Peschel
The transmission through ultra-thin metal films is noticeable and thus limits their potential for the formation of lithographic masks. By sub-wavelength patterning of a metal film with a post structure, a resonant metamaterial is formed, which can effectively suppress the transmission. Measurements as well as calculations identify the width of the metal islands as a critical geometrical feature. Hence, the extraordinarily low transmission effect can be explained by the resonant response of single scatterers known as Localized Surface Plasmon Resonances (LSPR). A potential application of this suppressed transmission effect to thin metal masks in optical lithography is experimentally investigated. (C) 2012 Optical Society of America
Probabilistic cloning of coherent states without a phase reference
Christian R. Mueller,
Christoffer Wittmann,
Petr Marek,
Radim Filip,
Christoph Marquardt,
Gerd Leuchs,
Ulrik L. Andersen
We present a probabilistic cloning scheme operating independently of any phase reference. The scheme is based solely on a phase-randomized displacement and photon counting, omitting the need for nonclassical resources and nonlinear materials. In an experimental implementation, we employ the scheme to clone coherent states from a phase covariant alphabet and demonstrate that the cloner is capable of outperforming the hitherto best-performing deterministic scheme. An analysis of the covariances between the output states shows that uncorrelated clones can be approached asymptotically. This simultaneously demonstrates how the effect of loss on coherent states can be compensated via noiseless preamplification.
Homodyne detection for atmosphere channels
A. A. Semenov,
F. Toeppel,
D. Yu Vasylyev,
H. V. Gomonay,
W. Vogel
We give a systematic theoretical description of homodyne detection in the case where both the signal and the local oscillator pass through the turbulent atmosphere. Imperfect knowledge of the local-oscillator amplitude is effectively included in a noisy density operator, leading to postprocessing noise. Alternatively, we propose a technique with monitored transmission coefficient of the atmosphere, which is free of postprocessing noise.
Measurement of two-mode squeezing with photon number resolving
multipixel detectors
Dmitry A. Kalashnikov,
Si-Hui Tan,
Timur Sh. Iskhakov,
Maria V. Chekhova,
Leonid A. Krivitsky
OPTICS LETTERS
37
(14)
2829-2831
(2012)
The measurement of the two-mode squeezed vacuum generated in an optical parametric amplifier (OPA) was performed with photon number resolving multipixel photon counters (MPPCs). Implementation of the MPPCs allows for the observation of noise reduction in a broad dynamic range of the OPA gain, which is inaccessible with standard single photon avalanche photodetectors. (c) 2012 Optical Society of America
Quantum polarization tomography of bright squeezed light
C. R. Mueller,
B. Stoklasa,
C. Peuntinger,
C. Gabriel,
J. Rehacek,
Z. Hradil,
A. B. Klimov,
G. Leuchs,
Ch Marquardt, et al.
We reconstruct the polarization sector of a bright polarization squeezed beam starting from a complete set of Stokes measurements. Given the symmetry that underlies the polarization structure of quantum fields, we use the unique SU(2) Wigner distribution to represent states. In the limit of localized bright states, the Wigner function can be approximated by an inverse three-dimensional Radon transform. We compare this direct reconstruction with the results of a maximum likelihood estimation, thus finding excellent agreement.
Goos-Hanchen and Imbert-Fedorov shifts: a novel perspective
When a beam of light is reflected by a smooth surface its behavior deviates from geometrical optics predictions. Such deviations are quantified by the so-called spatial and angular Goos-Hanchen (GH) and Imbert-Fedorov (IF) shifts of the reflected beam. These shifts depend upon the shape of the incident beam, its polarization and on the material composition of the reflecting surface. In this paper we suggest a novel approach that allows one to unambiguously isolate the beam-shape dependent aspects of GH and IF shifts. We show that this separation is possible as a result of some universal features of shifted distribution functions which are presented and discussed.
Three-dimensional quantum polarization tomography of macroscopic Bell
states
Bhaskar Kanseri,
Timur Iskhakov,
Ivan Agafonov,
Maria Chekhova,
Gerd Leuchs
The polarization properties of macroscopic Bell states are characterized using three-dimensional quantum polarization tomography. This method utilizes three-dimensional (3D) inverse Radon transform to reconstruct the polarization quasiprobability distribution function of a state from the probability distributions measured for various Stokes observables. The reconstructed 3D distributions obtained for the macroscopic Bell states are compared with those obtained for a coherent state with the same mean photon number. The results demonstrate squeezing in one or more Stokes observables.
Polarization tomography of bright states of light
I. N. Agafonov,
M. V. Chekhova,
T. Sh. Iskhakov,
B. Kanseri,
G. Leuchs
Polarization quantum tomography is performed on 4-mode squeezed vacuum states. Three-dimensional polarization quasiprobability functions are obtained and compared to that of an equal intensity coherent state. These distributions clearly demonstrate the difference in the polarization properties of the considered states. The reconstruction quality of the coherent state distribution is also analyzed by comparing the theoretically and experimentally obtained shapes for this state.
Studying free-space transmission statistics and improving free-space
quantum key distribution in the turbulent atmosphere
C. Erven,
B. Heim,
E. Meyer-Scott,
J. P. Bourgoin,
R. Laflamme,
G. Weihs,
T. Jennewein
The statistical fluctuations in free-space links in the turbulent atmosphere are important for the distribution of quantum signals. To that end, we first study statistics generated by the turbulent atmosphere in an entanglement-based free-space quantum key distribution (QKD) system. Using the insights gained from this analysis, we study the effect of link fluctuations on the security and key generation rate of decoy state QKD concluding that it has minimal effect in the typical operating regimes. We then investigate the novel idea of using these turbulent fluctuations to our advantage in QKD experiments. We implement a signal-to-noise ratio filter (SNRF) in our QKD system which rejects measurements during periods of low transmission efficiency, where the measured quantum bit error rate is temporarily elevated. Using this, we increase the total secret key generated by the system from 78 009 bits to 97 678 bits, representing an increase of 25.2% in the final secure key rate, generated from the same raw signals. Lastly, we present simulations of a QKD exchange with an orbiting low earth orbit satellite and show that an SNRF will be extremely useful in such a situation, allowing many more passes to extract a secret key than would otherwise be possible.
Narrow-bandwidth high-order harmonics driven by long-duration hot spots
Maxim Kozlov,
Ofer Kfir,
Avner Fleischer,
Alex Kaplan,
Tal Carmon,
Harald G. L. Schwefel,
Guy Bartal,
Oren Cohen
We predict and investigate the emission of high-order harmonics by atoms that cross intense laser hot spots that last for a nanosecond or longer. An atom that moves through a nanometer-scale hot spot at characteristic thermal velocity can emit high-order harmonics in a similar fashion to an atom that is irradiated by a short-duration (picosecond-scale) laser pulse. We analyze the collective emission from a thermal gas and from a jet of atoms. In both cases, the line shape of a high-order harmonic exhibits a narrow spike with spectral width that is determined by the bandwidth of the driving laser. Finally, we discuss a scheme for producing long-duration laser hot spots with intensity in the range of the intensity threshold for high-harmonic generation. In the proposed scheme, the hot spot is produced by a long laser pulse that is consecutively coupled to a high-quality micro-resonator and a metallic nano-antenna. This system may be used for generating ultra-narrow bandwidth extreme-ultraviolet radiation through frequency up-conversion of a low-cost compact pump laser.
Analytical expansion of highly focused vector beams into vector
spherical harmonics and its application to Mie scattering
The analytical expansion of linearly, azimuthally, and radially polarized rigorous beam-type solutions of Maxwell's equations into vector spherical harmonics (VSHs) is presented. We report on the dominance of higher order multipoles in highly focused radially and azimuthally polarized beams compared to linearly polarized beams under similar conditions. Furthermore, we theoretically investigate a scenario in which highly focused azimuthally and radially polarized beams interact with a linear polarizer placed in the focal plane and expand the resulting fields into VSHs. The generalized Mie theory is used afterwards to investigate the scattering of the studied beams off a spherical gold nanoparticle.
Observation of Orbital Angular Momentum Sidebands due to Optical
Reflection
We investigate how the orbital angular momentum of a paraxial light beam is affected upon reflection at a planar interface. Theoretically, the unavoidable angular spread of the beam leads to orbital angular momentum sidebands, which are found to be already significant for a modest beam spread (0.05). In analogy to the polarization Fresnel coefficients, we develop an analytical theory based upon spatial Fresnel coefficients; this allows a straightforward prediction of the strength of the sidebands. We confirm this by experiment and numerical simulation.
The role of self-trapped excitons and defects in the formation of
nanogratings in fused silica
Soeren Richter,
Fei Jia,
Matthias Heinrich,
Sven Doering,
Ulf Peschel,
Andreas Tuennermann,
Stefan Nolte
OPTICS LETTERS
37
(4)
482-484
(2012)
We investigate the role of self-trapped excitons (STEs) and defects in the formation of femtosecond laser pulse induced nanogratings (NGs) in fused silica. Our experiments reveal strongly enhanced NG formation for pulse separations up to the STE lifetime. In addition, the absorption spectra show that the weaker cumulative action of laser pulses for longer temporal separations is predominantly mediated by dangling-bond-type lattice defects that emerge from decaying STEs. (C) 2012 Optical Society of America
Dipole pulse theory: Maximizing the field amplitude from 4 pi focused
laser pulses
Ivan Gonoskov,
Andrea Aiello,
Simon Heugel,
Gerd Leuchs
We present a class of exact nonstationary solutions of Maxwell equations in vacuum from dipole pulse theory: electric and magnetic dipole pulses. These solutions can provide for a very efficient focusing of electromagnetic field and can be generated by 4 pi focusing systems, such as parabolic mirrors, by using radially polarized laser pulses with a suitable amplitude profile. The particular cases of a monochromatic dipole wave and a short dipole pulse with either quasi-Gaussian or Gaussian envelopes in the far-field region are analyzed and compared in detail. As a result, we propose how to increase the maximum field amplitude in the focus by properly shaping the temporal profile of the input laser pulses with given main wavelength and peak power.
Quantum polarization characterization and tomography
J. Soederholm,
G. Bjoerk,
A. B. Klimov,
L. L. Sanchez-Soto,
G. Leuchs
We present a complete polarization characterization of any quantum state of two orthogonal polarization modes and give a systematic measurement procedure to collect the necessary data. Full characterization requires measurements of the photon number in both modes and linear optics. In the case where only the photon-number difference can be determined, a limited but useful characterization is obtained. The characteristic Stokes moment profiles are given for several common quantum states.
All photons are equal but some photons are more equal than others
Two photons are said to be identical if they are prepared in the same quantum state. Given the latter, there is a unique way to achieve this. Conversely, there are many different ways of preparing two non-identical photons: they may differ in frequency, polarization, amplitude, etc. Therefore, photon distinguishability depends upon the specific degree of freedom being varied. By means of a careful analysis of the coincidence probability distribution in a Hong-Ou-Mandel experiment, we can show that photon distinguishability can be actually quantified by the rate of distinguishability of photons, an experimentally measurable parameter that crucially depends on both the photon quantum state and the degree of freedom under control.
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