We discuss the possibilities of studying in detail the dynamics of spontaneous emission of a single photon by a single atom and measuring the transient degree of squeezing by means of full solid angle fluorescence detection. (C) 2009 Elsevier B.V. All rights reserved.
The quantum vacuum at the foundations of classical electrodynamics
In the classical theory of electromagnetism, the permittivity epsilon (0) and the permeability mu (0) of free space are constants whose magnitudes do not seem to possess any deeper physical meaning. By replacing the free space of classical physics with the quantum notion of the vacuum, we speculate that the values of the aforementioned constants could arise from the polarization and magnetization of virtual pairs in vacuum. A classical dispersion model with parameters determined by quantum and particle physics is employed to estimate their values. We find the correct orders of magnitude. Additionally, our simple assumptions yield an independent estimate for the number of charged elementary particles based on the known values of epsilon (0) and mu (0) and for the volume of a virtual pair. Such an interpretation would provide an intriguing connection between the celebrated theory of classical electromagnetism and the quantum theory in the weak-field limit.
Coherent state quantum key distribution with multi letter phase-shift
keying
We present a protocol for quantum key distribution using discrete modulation of coherent states of light. Information is encoded in the variable phase of coherent states which can be chosen from a regular discrete set ranging from binary to continuous modulation, similar to phase-shift keying in classical communication. Information is decoded by simultaneous homodyne measurement of both quadratures and requires no active choice of basis. The protocol utilizes either direct or reverse reconciliation, both with and without postselection. We analyze the security of the protocol and show how to enhance it by the optimal choice of all variable parameters of the quantum signal.
Robustness of bipartite Gaussian entangled beams propagating in lossy
channels
F. A. S. Barbosa,
A. S. Coelho,
A. J. de Faria,
K. N. Cassemiro,
A. S. Villar,
P. Nussenzveig,
M. Martinelli
Subtle quantum properties offer exciting new prospects in optical communications. For example, quantum entanglement enables the secure exchange of cryptographic keys(1) and the distribution of quantum information by teleportation(2,3). Entangled bright beams of light are increasingly appealing for such tasks, because they enable the use of well-established classical communications techniques(4). However, quantum resources are fragile and are subject to decoherence by interaction with the environment. The unavoidable losses in the communication channel can lead to a complete destruction of entanglement(5-8), limiting the application of these states to quantum-communication protocols. We investigate the conditions under which this phenomenon takes place for the simplest case of two light beams, and analyse characteristics of states which are robust against losses. Our study sheds new light on the intriguing properties of quantum entanglement and how they may be harnessed for future applications.
Continuous-variable entanglement distillation of non-Gaussian mixed
states
Ruifang Dong,
Mikael Lassen,
Joel Heersink,
Christoph Marquardt,
Radim Filip,
Gerd Leuchs,
Ulrik L. Andersen
Many different quantum-information communication protocols such as teleportation, dense coding, and entanglement-based quantum key distribution are based on the faithful transmission of entanglement between distant location in an optical network. The distribution of entanglement in such a network is, however, hampered by loss and noise that is inherent in all practical quantum channels. Thus, to enable faithful transmission one must resort to the protocol of entanglement distillation. In this paper we present a detailed theoretical analysis and an experimental realization of continuous variable entanglement distillation in a channel that is inflicted by different kinds of non-Gaussian noise. The continuous variable entangled states are generated by exploiting the third order nonlinearity in optical fibers, and the states are sent through a free-space laboratory channel in which the losses are altered to simulate a free-space atmospheric channel with varying losses. We use linear optical components, homodyne measurements, and classical communication to distill the entanglement, and we find that by using this method the entanglement can be probabilistically increased for some specific non-Gaussian noise channels.
Accessing Higher Order Correlations in Quantum Optical States by Time
Multiplexing
M. Avenhaus,
K. Laiho,
M. V. Chekhova,
C. Silberhorn
We experimentally measured higher order normalized correlation functions (NCF) of pulsed light with a time-multiplexing detector. We demonstrate excellent performance of our device by verifying unity valued NCF up to the eighth order for coherent light and factorial dependence of the NCF for pseudothermal light. We applied our measurement technique to a type-II parametric down-conversion source to investigate mutual two-mode correlation properties and ascertain nonclassicality.
Naturally Phase-Matched Second-Harmonic Generation in a
Whispering-Gallery-Mode Resonator
J. U. Fuerst,
D. V. Strekalov,
D. Elser,
M. Lassen,
U. L. Andersen,
C. Marquardt,
G. Leuchs
We demonstrate for the first time natural phase matching for optical frequency doubling in a high-Q whispering-gallery-mode resonator made of lithium niobate. A conversion efficiency of 9% is achieved at 30 mu W in-coupled continuous wave pump power. The observed saturation pump power of 3.2 mW is almost 2 orders of magnitude lower than the state-of-the-art value. This suggests an application of our frequency doubler as a source of nonclassical light requiring only a low-power pump, which easily can be quantum noise limited. Our theoretical analysis of the three-wave mixing in a whispering-gallery-mode resonator provides the relative conversion efficiencies for frequency doubling in various modes.
Noise-powered probabilistic concentration of phase information
Mario A. Usuga,
Christian R. Mueller,
Christoffer Wittmann,
Petr Marek,
Radim Filip,
Christoph Marquardt,
Gerd Leuchs,
Ulrik L. Andersen
Phase-insensitive optical amplification of an unknown quantum state is known to be a fundamentally noisy operation that inevitably adds noise to the amplified state(1-5). However, this fundamental noise penalty in amplification can be circumvented by resorting to a probabilistic scheme as recently proposed and demonstrated in refs 6-8. These amplifiers are based on highly non-classical resources in a complex interferometer. Here we demonstrate a probabilistic quantum amplifier beating the fundamental quantum limit using a thermal-noise source and a photon-number-subtraction scheme(9). The experiment shows, surprisingly, that the addition of incoherent noise leads to a noiselessly amplified output state with a phase uncertainty below the uncertainty of the state before amplification. This amplifier might become a valuable quantum tool in future quantum metrological schemes and quantum communication protocols.
Witnessing effective entanglement over a 2km fiber channel
Christoffer Wittmann,
Josef Fuerst,
Carlos Wiechers,
Dominique Elser,
Hauke Haeseler,
Norbert Luetkenhaus,
Gerd Leuchs
We present a fiber-based continuous-variable quantum key distribution system. In the scheme, a quantum signal of two non-orthogonal weak optical coherent states is sent through a fiber-based quantum channel. The receiver simultaneously measures conjugate quadratures of the light using two homodyne detectors. From the measured Q-function of the transmitted signal, we estimate the attenuation and the excess noise caused by the channel. The estimated excess noise originating from the channel and the channel attenuation including the quantum efficiency of the detection setup is investigated with respect to the detection of effective entanglement. The local oscillator is considered in the verification. We witness effective entanglement with a channel length of up to 2km. (C) 2010 Optical Society of America
Quantum optical coherence can survive photon losses using a
continuous-variable quantum erasure-correcting code
Mikael Lassen,
Metin Sabuncu,
Alexander Huck,
Julien Niset,
Gerd Leuchs,
Nicolas J. Cerf,
Ulrik L. Andersen
A fundamental requirement for enabling fault-tolerant quantum information processing is an efficient quantum error-correcting code that robustly protects the involved fragile quantum states from their environment(1-10). Just as classical error-correcting codes are indispensible in today's information technologies, it is believed that quantum error-correcting code will play a similarly crucial role in tomorrow's quantum information systems. Here, we report on the experimental demonstration of a quantum erasure-correcting code that overcomes the devastating effect of photon losses. Our quantum code is based on linear optics, and it protects a four-mode entangled mesoscopic state of light against erasures. We investigate two approaches for circumventing in-line losses, and demonstrate that both approaches exhibit transmission fidelities beyond what is possible by classical means. Because in-line attenuation is generally the strongest limitation to quantum communication, such an erasure-correcting code provides a new tool for establishing quantum optical coherence over longer distances.
Experimental demonstration of squeezed-state quantum averaging
Mikael Lassen,
Lars Skovgaard Madsen,
Metin Sabuncu,
Radim Filip,
Ulrik L. Andersen
We propose and experimentally demonstrate a universal quantum averaging process implementing the harmonic mean of quadrature variances. The averaged variances are prepared probabilistically by means of linear optical interference and measurement-induced conditioning. We verify that the implemented harmonic mean yields a lower value than the corresponding value obtained for the standard arithmetic-mean strategy. The effect of quantum averaging is experimentally tested for squeezed and thermal states as well as for uncorrelated and partially correlated noise sources. The harmonic-mean protocol can be used to efficiently stabilize a set of squeezed-light sources with statistically fluctuating noise levels.
Widely tunable optical delay generator
K. Jamshidi,
A. Wiatrek,
C. Bersch,
G. Onishchukov,
G. Leuchs,
T. Schneider
OPTICS LETTERS
35
(21)
3592-3594
(2010)
We propose and demonstrate a method for quasi storage of light based on periodic spectral filtering realized in the time domain by amplitude modulation using frequency-to-time conversion. The delay can be tuned in a wide range by changing the frequency of an electrical modulation signal. In our experiments, the delay of single 2.5 ps pulses varied by 66 pulse widths. The technique works equally well for more complex optical data packets. Contrary to known approaches, the method has a very large spectral bandwidth and can be implemented by either fiber or integrated solutions using existing technologies. Because of the large bandwidth, fractional delays up to several tens of thousands of pulse widths can be achieved potentially for subpicosecond pulses, which is a tremendous value regarding the implementation simplicity. (C) 2010 Optical Society of America
Thermal blinding of gated detectors in quantum cryptography
Lars Lydersen,
Carlos Wiechers,
Christoffer Wittmann,
Dominique Elser,
Johannes Skaar,
Vadim Makarov
It has previously been shown that the gated detectors of two commercially available quantum key distribution (QKD) systems are blindable and controllable by an eavesdropper using continuous-wave illumination and short bright trigger pulses, manipulating voltages in the circuit [Nat. Photonics 4, 686 (2010)]. This allows for an attack eavesdropping the full raw and secret key without increasing the quantum bit error rate (QBER). Here we show how thermal effects in detectors under bright illumination can lead to the same outcome. We demonstrate that the detectors in a commercial QKD system Clavis2 can be blinded by heating the avalanche photo diodes (APDs) using bright illumination, so-called thermal blinding. Further, the detectors can be triggered using short bright pulses once they are blind. For systems with pauses between packet transmission such as the plug-and-play systems, thermal inertia enables Eve to apply the bright blinding illumination before eavesdropping, making her more difficult to catch. (C) 2010 Optical Society of America
Free-Space Squeezing Assists Perfectly Matched Layers in Simulations on
a Tight Domain
Dzmitry M. Shyroki,
Aliaksandra M. Ivinskaya,
Andrei V. Lavrinenko
To minimize computer memory consumption in the finite-difference modeling, one tends to place computational domain boundaries as close to the simulated object as possible. Unfortunately, this leads to inaccurate solution in the case when evanescent electromagnetic field is expected to spread far outside the object, as in simulations of eigenmodes or scattering at a wavelength comparable to or larger than the object itself. Here, we show how, in addition to applying the perfectly matched layers (PMLs), outer free space can be squeezed to avoid cutting the evanescent field tails by the PMLs or computational domain borders. Adding the squeeze-transform layers to the standard PMLs requires no changes to the finite-difference algorithms.
On the Analogy between a Single Atom and an Optical Resonator
S. Heugel,
A. S. Villar,
M. Sondermann,
U. Peschel,
G. Leuchs
A single atom in free space can have a strong influence on a light beam and a single photon can have a strong effect on a single atom in free space. Regarding this interaction, two conceptually different questions can be asked: can a single atom fully absorb a single photon and can a single atom fully reflect a light beam. The conditions for achieving the full effect in either case are different. Here we discuss related questions in the context of an optical resonator. When shaping a laser pulse properly it will be fully absorbed by an optical resonator, i.e., no light will be reflected and all the pulse energy will accumulate inside the resonator before it starts leaking out. We show in detail that in this case the temporal pulse shape has to match the time-reversed pulse obtained by the cavity's free decay. On the other hand a resonator, made of highly reflecting mirrors which normally reflect a large portion of any incident light, may fully transmit the light, as long as the light is narrow band and resonant with the cavity. The analogy is the single atom-normally letting most of the light pass-which under special conditions may fully reflect the incident light beam. Using this analogy we are able to study the effects of practical experimental limitations in the atom-photon coupling, such as finite pulses, bandwidths, and solid angle coverage, and to use the optical resonator as a test bed for the implementation of the quantum experiment.
Interacting waves on chains of split-ring resonators in the presence of
retardation
V. Lomanets,
O. Zhuromskyy,
G. Onishchukov,
O. Sydoruk,
E. Tatartschuk,
E. Shamonina,
G. Leuchs,
U. Peschel
Wave propagation is studied experimentally in a one-dimensional periodic chain of magnetically coupled split-ring resonators with a spacing of about one tenth of the resonant wavelength. Retardation leads to a strong interaction between magnetoinductive and free-space waves. Two kinds of guided modes are observed: a slow backward wave which propagates far outside the light cone, and a fast forward wave close to the light cone. The two merge in a region of zero group velocity. The results are relevant for all one- and two-dimensional periodic systems interacting with waves of the surrounding space. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3462314]
Angular momenta and spin-orbit interaction of nonparaxial light in free
space
Konstantin Y. Bliokh,
Miguel A. Alonso,
Elena A. Ostrovskaya,
Andrea Aiello
We give an exact self-consistent operator description of the spin and orbital angular momenta, position, and spin-orbit interactions of nonparaxial light in free space. Both quantum-operator formalism and classical energy-flow approach are presented. We apply the general theory to symmetric and asymmetric Bessel beams exhibiting spin-and orbital-dependent intensity profiles. The exact wave solutions are clearly interpreted in terms of the Berry phases, quantization of caustics, and Hall effects of light, which can be readily observed experimentally.
A bridge between the single-photon and squeezed-vacuum states
Nitin Jain,
S. R. Huisman,
Erwan Bimbard,
A. I. Lvovsky
The two modes of the Einstein-Podolsky-Rosen quadrature entangled state generated by parametric down-conversion interfere on a beam splitter of variable splitting ratio. Detection of a photon in one of the beam splitter output channels heralds preparation of a signal state in the other, which is characterized using homodyne tomography. By controlling the beam splitting ratio, the signal state can be chosen anywhere between the single-photon and squeezed state. (C) 2010 Optical Society of America
Demonstration of a quasi-scalar angular Goos-Hanchen effect
M. Merano,
N. Hermosa,
A. Aiello,
J. P. Woerdman
OPTICS LETTERS
35
(21)
3562-3564
(2010)
We show experimentally that the angular Goos-Hanchen (GH) effect can be easily observed, also without employing its resonant enhancement at Brewster incidence. An s-polarized beam was used to decouple the polarization from the propagation dynamics of the beam. We found that, in this case, the angular GH effect can be strongly enhanced by increasing the angular aperture of the Gaussian beam. Our experiments suggest a route toward observing the angular GH effect for true scalar waves, such as acoustic waves and quantum matter waves. (C) 2010 Optical Society of America
Quantum key distribution with multi letter alphabets
D. Sych,
G. Leuchs
OPTICS AND SPECTROSCOPY
108
(3)
326-330
(2010)
| Journal
We present a new protocol for continuous variable quantum key distribution (CV QKD). The novelty of the protocol is a multi letter alphabet represented by coherent states of light with a fixed amplitude and variable phase. Information is encoded in the phase of a coherent state which can be chosen from a regular discrete set consisting, however, of an arbitrary number of letters. We evaluate the security of the protocol against the beam splitting attack. As a result we show the proposed protocol has advantages over the standard two letter coherent state QKD protocol, especially in the case when losses in the communication channel are low.
Demonstration of Coherent-State Discrimination Using a
Displacement-Controlled Photon-Number-Resolving Detector
We experimentally demonstrate a new measurement scheme for the discrimination of two coherent states. The measurement scheme is based on a displacement operation followed by a photon-number-resolving detector, and we show that it outperforms the standard homodyne detector which we, in addition, prove to be optimal within all Gaussian operations including conditional dynamics. We also show that the non-Gaussian detector is superior to the homodyne detector in a continuous variable quantum key distribution scheme.
Phase-shifting point-diffraction interferometry with common-path and
in-line configuration for microscopy
Peng Gao,
Irina Harder,
Vanusch Nercissian,
Klaus Mantel,
Baoli Yao
OPTICS LETTERS
35
(5)
712-714
(2010)
A new common-path and in-line point-diffraction interferometer for quantitative phase microscopy is proposed. The interferometer is constructed by introducing a grating pair into the point-diffraction interferometer, thus forming a common-path and in-line configuration for object and reference waves. Achromatic phase shifting is implemented by linearly moving one of the two gratings in its grating vector direction. The feasibility of the proposed configuration is demonstrated by theoretical analysis and experiments. (C) 2010 Optical Society of America
In a strongly pumped nondegenerate traveling-wave optical parametric amplifier, we produce a two-color squeezed vacuum with up to millions of photons per pulse. Our approach to registering this macroscopic quantum state is direct detection of a large number of transverse and longitudinal modes, which is achieved by making the detection time and area much larger than the coherence time and area, respectively. Using this approach, we obtain a record value of twin-beam squeezing for direct detection of bright squeezed vacuum. This makes direct detection of macroscopic squeezed vacuum a practical tool for quantum information applications.
Hacking commercial quantum cryptography systems by tailored bright
illumination
Lars Lydersen,
Carlos Wiechers,
Christoffer Wittmann,
Dominique Elser,
Johannes Skaar,
Vadim Makarov
The peculiar properties of quantum mechanics allow two remote parties to communicate a private, secret key, which is protected from eavesdropping by the laws of physics(1-4). So-called quantum key distribution (QKD) implementations always rely on detectors to measure the relevant quantum property of single photons(5). Here we demonstrate experimentally that the detectors in two commercially available QKD systems can be fully remote-controlled using specially tailored bright illumination. This makes it possible to tracelessly acquire the full secret key; we propose an eavesdropping apparatus built from off-the-shelf components. The loophole is likely to be present in most QKD systems using avalanche photodiodes to detect single photons. We believe that our findings are crucial for strengthening the security of practical QKD, by identifying and patching technological deficiencies.
Continuous-variable quantum information processing
Ulrik L. Andersen,
Gerd Leuchs,
Christine Silberhorn
Observables of quantum systems can possess either a discrete or a continuous spectrum. For example, upon measurements of the photon number of a light state, discrete outcomes will result whereas measurements of the light's quadrature amplitudes result in continuous outcomes. If one uses the continuous degree of freedom of a quantum system for encoding, processing or detecting information, one enters the field of continuous-variable (CV) quantum information processing. In this paper we review the basic principles of CV quantum information processing with main focus on recent developments in the field. We will be addressing the three main stages of a quantum information system; the preparation stage where quantum information is encoded into CVs of coherent states and single-photon states, the processing stage where CV information is manipulated to carry out a specified protocol and a detection stage where CV information is measured using homodyne detection or photon counting.
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(C) 2010 by WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim
Assessing the Polarization of a Quantum Field from Stokes Fluctuations
A. B. Klimov,
G. Bjoerk,
J. Soederholm,
L. S. Madsen,
M. Lassen,
U. L. Andersen,
J. Heersink,
R. Dong,
Ch. Marquardt, et al.
We propose an operational degree of polarization in terms of the variance of the Stokes vector minimized over all the directions of the Poincare sphere. We examine the properties of this second-order definition and carry out its experimental determination. Quantum states with the same standard (first-order) degree of polarization are correctly discriminated by this new measure. We argue that a comprehensive quantum characterization of polarization properties requires a whole hierarchy of higher-order degrees.
Extraordinary transmission through a single coaxial aperture in a thin
metal film
P. Banzer,
J. Kindler (nee Mueller),
S. Quabis,
U. Peschel,
G. Leuchs
We investigate experimentally the transmission properties of single sub-wavelength coaxial apertures in thin metal films (t = 110 nm). Enhanced transmission through a single sub-wavelength coaxial aperture illuminated with a strongly focused radially polarized light beam is reported. In our experiments we achieved up to four times enhanced transmission through a single coaxial aperture as compared to a (hollow) circular aperture with the same outer diameter. We attribute this enhancement of transmission to the excitation of a TEM-mode for illumination with radially polarized light inside the single coaxial aperture. A strong polarization contrast is observed between the transmission for radially and azimuthally polarized illumination. Furthermore, the observed transmission through a single coaxial aperture can be strongly reduced if surface plasmons are excited. The experimental results are in good agreement with finite difference time domain (FDTD) simulations. (C)2010 Optical Society of America
Avoiding the blinding attack in QKD reply
Lars Lydersen,
Carlos Wiechers,
Christoffer Wittmann,
Dominique Elser,
Johannes Skaar,
Vadim Makarov
We develop the quantum theory of transverse angular momentum of light beams. The theory applies to paraxial and quasiparaxial photon beams in vacuum and reproduces the known results for classical beams when applied to coherent states of the field. Both the Poynting vector, alias the linear momentum, and the angular-momentum quantum operators of a light beam are calculated including contributions from first-order transverse derivatives. This permits a correct description of the energy flow in the beam and the natural emergence of both the spin and the angular momentum of the photons. We show that for collimated beams of light, orbital angular-momentum operators do not satisfy the standard commutation rules. Finally, we discuss the application of our theory to some concrete cases.
Tuning the structural properties of femtosecond-laser-induced
nanogratings
Lourdes Patricia R. Ramirez,
Matthias Heinrich,
Soeren Richter,
Felix Dreisow,
Robert Keil,
Alexander V. Korovin,
Ulf Peschel,
Stefan Nolte,
Andreas Tuennermann
We present the results of our investigations on the formation process of nanogratings in fused silica and the influence of fabrication parameters, thereby identifying ways to systematically control the grating properties. Nanogratings, self-organized nanostructures with subwavelength periodicity, are formed in certain parameter ranges during femtosecond-laser processing of transparent materials, resulting in characteristic birefringent modifications. They provide the opportunity for the fabrication of arbitrary three-dimensional birefringent elements with position-dependent retardation. Based on our findings, we were able to fabricate birefringent elements with various precise retardations in otherwise isotropic fused silica.
A generator for unique quantum random numbers based on vacuum states
Christian Gabriel,
Christoffer Wittmann,
Denis Sych,
Ruifang Dong,
Wolfgang Mauerer,
Ulrik L. Andersen,
Christoph Marquardt,
Gerd Leuchs
Random numbers are a valuable component in diverse applications that range from simulations(1) over gambling to cryptography(2,3). The quest for true randomness in these applications has engendered a large variety of different proposals for producing random numbers based on the foundational unpredictability of quantum mechanics(4-11). However, most approaches do not consider that a potential adversary could have knowledge about the generated numbers, so the numbers are not verifiably random and unique(12-15). Here we present a simple experimental setup based on homodyne measurements that uses the purity of a continuous-variable quantum vacuum state to generate unique random numbers. We use the intrinsic randomness in measuring the quadratures of a mode in the lowest energy vacuum state, which cannot be correlated to any other state. The simplicity of our source, combined with its verifiably unique randomness, are important attributes for achieving high-reliability, high-speed and low-cost quantum random number generators.
B. Sprenger,
H. G. L. Schwefel,
Z. H. Lu,
S. Svitlov,
L. J. Wang
OPTICS LETTERS
35
(17)
2870-2872
(2010)
A fiber laser is stabilized by introducing a calcium fluoride (CaF2) whispering-gallery-mode resonator as a filtering element in a ring cavity. It is set up using a semiconductor optical amplifier as a gain medium. The resonator is critically coupled through prisms, and used as a filtering element to suppress the laser linewidth. A three-cornered-hat method is used and shows a stability of 10(-11) after 10 mu s. Using the self-heterodyne beat technique, the linewidth is determined to be 13 kHz. This implies an enhancement factor of 10(3) with respect to the passive cavity linewidth. (C) 2010 Optical Society of America
Discrimination of binary coherent states using a homodyne detector and a
photon number resolving detector
We investigate quantum measurement strategies capable of discriminating two coherent states probabilistically with significantly smaller error probabilities than can be obtained using nonprobabilistic state discrimination. We apply a postselection strategy to the measurement data of a homodyne detector as well as a photon number resolving detector in order to lower the error probability. We compare the two different receivers with an optimal intermediate measurement scheme where the error rate is minimized for a fixed rate of inconclusive results. The photon number resolving (PNR) receiver is experimentally demonstrated and compared to an experimental realization of a homodyne receiver with postselection. In the comparison, it becomes clear that the performance of the PNR receiver surpasses the performance of the homodyne receiver, which we prove to be optimal within any Gaussian operations and conditional dynamics.
Broadband NIR photoluminescence from Bi-doped Ba2P2O7 crystals: Insights
into the nature of NIR-emitting Bismuth centers
Mingying Peng,
Benjamin Sprenger,
Markus A. Schmidt,
Harald G. L. Schwefel,
Lothar Wondraczek
We report on a novel type of Bi-doped crystal that exhibits ultrabroadband photoluminescence in the near infrared (NIR). Emission centers can be generated and degenerated reversibly by annealing the material in CO atmosphere and air, respectively, indicating that emission is related to the presence of Bi-species in low valence states. Correlating static and dynamic excitation and emission data with the size and charge of available lattice sites suggests that two types of Bi-0-species, each located on one of the two available Ba2+ lattice sites, are responsible for NIR photoemission. This is further confirmed by the absence of NIR emission in polycrystalline Ca2P2O7:Bi and Sr2P2O7:Bi. Excitation is assigned to transitions between the doubly degenerated ground state S-4(3/2) and the degenerated excited levels D-2(3/2), D-2(5/2) and P-2(1/2), respectively. NIR emission is attributed to D-2(3/2) -> S-4(3/2). The NIR emission center can coexist with Bi2+ species. Then, also Bi2+ is accommodated on one of the two Ba2+-sites. Energy transfer between Bi2+ ions occurs within a critical distance of 25.9 angstrom. (C) 2010 Optical Society of America
Environment-assisted quantum-information correction for continuous
variables
Metin Sabuncu,
Radim Filip,
Gerd Leuchs,
Ulrik L. Andersen
Quantum-information protocols are inevitably affected by decoherence which is associated with the leakage of quantum information into an environment. In this article we address the possibility of recovering the quantum information from an environmental measurement. We investigate continuous-variable quantum information, and we propose a simple environmental measurement that under certain circumstances fully restores the quantum information of the signal state although the state is not reconstructed with unit fidelity. We implement the protocol for which information is encoded into conjugate quadratures of coherent states of light and the noise added under the decoherence process is of Gaussian nature. The correction protocol is tested using both a deterministic as well as a probabilistic strategy. The potential use of the protocol in a continuous-variable quantum-key distribution scheme as a means to combat excess noise is also investigated.
Low-Threshold Optical Parametric Oscillations in a Whispering Gallery
Mode Resonator
J. U. Fuerst,
D. V. Strekalov,
D. Elser,
A. Aiello,
U. L. Andersen,
Ch. Marquardt,
G. Leuchs
In whispering gallery mode (WGM) resonator light is guided by continuous total internal reflection along a curved surface. Fabricating such resonators from an optically nonlinear material one takes advantage of their exceptionally high quality factors and small mode volumes to achieve extremely efficient optical frequency conversion. Our analysis of the phase-matching conditions for optical parametric down-conversion (PDC) in a spherical WGM resonator shows their direct relation to the sum rules for photons' angular momenta and predicts a very low parametric oscillation threshold. We realized such an optical parametric oscillator (OPO) based on naturally phase-matched PDC in lithium niobate. We demonstrated a single-mode, strongly nondegenerate OPO with a threshold of 6: 7 mu W and linewidth under 10 MHz. This work demonstrates the remarkable capabilities of WGM-based OPOs.
Flexible beam shaping system using fly's eye condenser
Norbert Lindlein,
Andreas Bich,
Martin Eisner,
Irina Harder,
Maik Lano,
Reinhard Voelkel,
Ken Weible,
Maik Zimmermann
Normally, fly's eye condensers are used to homogenize light. However, in the case of fully coherent light, a fly's eye condenser, in connection with some simple optical elements, such as a diffractive axicon, a grating, and a telescope, can be used as a quite flexible beam shaping system, forming arrays of rings, parts of rings, or other structures with varying diameters. We present the principle, some simulation results, and some first experimental results. (C) 2010 Optical Society of America
Near-unit-fidelity entanglement distribution scheme using Gaussian
communication
We show how to distribute with percentage success probabilities almost perfectly entangled qubit memory pairs over repeater channel segments of the order of the optical attenuation distance. In addition to some weak, dispersive light-matter interactions, only Gaussian state transmissions and measurements are needed for this scheme. Our protocol outperforms the existing coherent-state-based schemes for entanglement distribution, even those using error-free non-Gaussian measurements. This is achieved through two innovations: First, optical squeezed states are utilized instead of coherent states. Second, the amplitudes of the bright signal pulses are reamplified at each repeater station. This latter variation is a strategy reminiscent of classical repeaters and would be impossible in single-photon-based schemes.
Atmospheric channel characteristics for quantum communication with
continuous polarization variables
B. Heim,
D. Elser,
T. Bartley,
M. Sabuncu,
C. Wittmann,
D. Sych,
C. Marquardt,
G. Leuchs
We investigate the properties of an atmospheric channel for free space quantum communication with continuous polarization variables. In our prepare-and-measure setup, coherent polarization states are transmitted through an atmospheric quantum channel of 100 m length on the flat roof of our institute's building. The signal states are measured by homodyne detection with the help of a local oscillator (LO) which propagates in the same spatial mode as the signal, orthogonally polarized to it. Thus the interference of signal and LO is excellent and atmospheric fluctuations are auto-compensated. The LO also acts as a spatial and spectral filter, which allows for unrestrained daylight operation. Important characteristics for our system are atmospheric channel influences that could cause polarization, intensity and position excess noise. Therefore we study these influences in detail. Our results indicate that the channel is suitable for our quantum communication system in most weather conditions.
The multi-pass solution for surface measurements with the help of a Shack-Hartmann sensor (SHS) on the basis of a Fizeau cavity enables fast access to surface deviation data due to the high speed of the SHS and easy referencing of the measured data through difference measurements. The multi-pass solution described in a previous publication [J. Schwider, Opt. Express 16, 362 (2008)], provides highly sensitive measurements of small displacements caused by thermal non-equilibrium states of the test set up. Here, we want to demonstrate how a pulsed thermal load changes the surface geometry. In addition the temporal response for different plate materials is monitored through a fast wave front measurement with very high sensitivity. The thermal load close to a delta-function in time will be applied from the back-side of a plane plate by heating a small Peltier element with a heat impulse of known order of magnitude. The development of the surface deviation on the time axis can be monitored by storing a set of successive deviation pictures. (c) 2010 Optical Society of America
A novel method for polarization squeezing with Photonic Crystal Fibers
Josip Milanovic,
Mikael Lassen,
Ulrik L. Andersen,
Gerd Leuchs
Photonic Crystal Fibers can be tailored to increase the effective Kerr nonlinearity, while producing smaller amounts of excess noise compared to standard silicon fibers. Using these features of Photonic Crystal Fibers we create polarization squeezed states with increased purity compared to standard fiber squeezing experiments. Explicit we produce squeezed states in counter propagating pulses along the same fiber axis to achieve near identical dispersion properties. This enables the production of polarization squeezing through interference in a polarization type Sagnac interferometer. We observe Stokes parameter squeezing of -3.9 +/- 0.3dB and anti-squeezing of 16.2 +/- 0.3dB. (C) 2010 Optical Society of America
Quantum-optical state engineering up to the two-photon level
Erwan Bimbard,
Nitin Jain,
Andrew MacRae,
A. I. Lvovsky
The ability to prepare arbitrary quantum states within a certain Hilbert space is the holy grail of quantum information technology. It is particularly important for light, as this is the only physical system that can communicate quantum information over long distances. We propose and experimentally verify a scheme to produce arbitrary single-mode states of a travelling light field up to the two-photon level. The desired state is remotely prepared in the signal channel of spontaneous parametric down-conversion by means of conditional measurements on the idler channel. The measurement consists of bringing the idler field into interference with two ancilla coherent states, followed by two single-photon detectors, which, in coincidence, herald the preparation event. By varying the amplitudes and phases of the ancillae, we can prepare any arbitrary superposition of zero-, one- and two-photon states.
How orbital angular momentum affects beam shifts in optical reflection
It is well known that reflection of a Gaussian light beam (TEM(00)) by a planar dielectric interface leads to four beam shifts when compared to the geometrical-optics prediction. These are the spatial Goos-Hanchen (GH) shift, the angular GH shift, the spatial Imbert-Fedorov (IF) shift, and the angular IF shift. We report here, theoretically and experimentally, that endowing the beam with orbital angular momentum leads to coupling of these four shifts; this is described by a 4 x 4 mixing
Effect of fabrication errors on the diffraction pattern produced by
sawtooth gratings
Francisco Jose Torcal-Milla,
Irina Harder,
Norbert Lindlein
In this work we investigate, analytically and numerically, the effect on the diffracted field produced by typical fabrication errors in sawtooth gratings. The analysis is carried out for the near and far field, showing the effects on the intensity and on the diffraction orders efficiency. When the grating profile is not perfect but presents a curved profile or overdevelopment error, some different diffraction orders appear, changing the intensity and the efficiency of each order. In addition, when roughness is present, a decreasing of efficiency is produced, but without generating different diffraction orders than the first one. We show the analytical dependence of these modifications in terms of the profile of the grating, corroborating the results with numerical methods. (C) 2010 Optical Society of America
Discrimination of optical coherent states using a photon number
resolving detector
Christoffer Wittmann,
Ulrik L. Andersen,
Gerd Leuchs
The discrimination of non-orthogonal quantum states with reduced or without errors is a fundamental task in quantum measurement theory. In this work, we investigate a quantum measurement strategy capable of discriminating two coherent states probabilistically with significantly smaller error probabilities than can be obtained using non-probabilistic state discrimination. We find that appropriate postselection of the measurement data of a photon number resolving detector can be used to discriminate two coherent states with small error probability. We compare our new receiver to an optimal intermediate measurement between minimum error discrimination and unambiguous state discrimination.
Optics in Curved Space
Vincent H. Schultheiss,
Sascha Batz,
Alexander Szameit,
Felix Dreisow,
Stefan Nolte,
Andreas Tuennermann,
Stefano Longhi,
Ulf Peschel
We experimentally study the impact of intrinsic and extrinsic curvature of space on the evolution of light. We show that the topology of a surface matters for radii of curvature comparable with the wavelength, whereas for macroscopically curved surfaces only intrinsic curvature is relevant. On a surface with constant positive Gaussian curvature we observe periodic refocusing, self-imaging, and diffractionless propagation. In contrast, light spreads exponentially on surfaces with constant negative Gaussian curvature. For the first time we realized two beam interference in negatively curved space.
We consider spatial solitons as, for example, self-confined optical beams in spaces of constant curvature, which are a natural generalization of flat space. Due to the symmetries of these spaces we are able to define respective dynamical parameters, for example, velocity and position. For positively curved space we find stable multiple-hump solitons as a continuation from the linear modes. In the case of negatively curved space we show that no localized solution exists and a bright soliton will always decay through a nonlinear tunneling process.
Complex source beam: A tool to describe highly focused vector beams
analytically
The scalar-complex-source model is used to develop an accurate description of highly focused radially, azimuthally, linearly, and circularly polarized monochromatic vector beams. We investigate the power and full beam widths at half maximum of vigorous Maxwell equation solutions. The analytical expressions are employed to compare the vector complex source beams with the real beams produced by various high-numerical-aperture (NA) focusing systems. We find a parameter set for which the spatial extents of the analytical beams are the same as those of experimentally realized ones. We ensure the same shape of the considered beams by investigating an overlap of the complex source beams with high-NA beams. We demonstrate that the analytical expressions are good approximations for realistic highly focused beams.
On the experimental investigation of the electric and magnetic response
of a single nano-structure
We demonstrate an experimental method to separately test the optical response of a single sub-wavelength nano-structure to tailored electric and magnetic field distributions in the optical domain. For this purpose a highly focused y-polarized TEM10-mode is used which exhibits spatially separated longitudinal magnetic and transverse electric field patterns. By displacing a single sub-wavelength nano-structure, namely a single split-ring resonator (SRR), in the focal plane, different coupling scenarios can be achieved. It is shown experimentally that the single split-ring resonator tested here responds dominantly as an electric dipole. A much smaller but yet statistically significant magnetic dipole contribution is also measured by investigating the interaction of a single SRR with a magnetic field component perpendicular to the SRR plane (which is equivalent to the curl of the electric field) as well as by analyzing the intensity and polarization distribution of the scattered light with high spatial resolution. The developed experimental setup as well as the measurement techniques presented in this paper are a versatile tool to investigate the optical properties of single sub-wavelength nano-structures. (C) 2010 Optical Society of America
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