A measure of non-classicality of quantum states based on the volume of the negative part of the Wigner function is proposed. We analyse this quantity for Fock states, squeezed displaced Fock states and cat-like states defined as coherent superposition of two Gaussian wavepackets.
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Anatole Kenfack and Karol Życzkowski 2004 J. Opt. B: Quantum Semiclass. Opt. 6 396
A I Lvovsky 2004 J. Opt. B: Quantum Semiclass. Opt. 6 S556
I propose an iterative expectation maximization algorithm for reconstructing the density matrix of an optical ensemble from a set of balanced homodyne measurements. The algorithm applies directly to the acquired data, bypassing the intermediate step of calculating marginal distributions. The advantages of the new method are made manifest by comparing it with the traditional inverse Radon transformation technique.
Joseph Emerson et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 S347
We describe a scalable stochastic method for the experimental measurement of generalized fidelities characterizing the accuracy of the implementation of a coherent quantum transformation. The method is based on the motion reversal of random unitary operators. In the simplest case our method enables direct estimation of the average gate fidelity. The more general fidelities are characterized by a universal exponential rate of fidelity loss. In all cases the measurable fidelity decrease is directly related to the strength of the noise affecting the implementation, quantified by the trace of the superoperator describing the non-unitary dynamics. While the scalability of our stochastic protocol makes it most relevant in large Hilbert spaces (when quantum process tomography is infeasible), our method should be immediately useful for evaluating the degree of control that is achievable in any prototype quantum processing device. By varying over different experimental arrangements and error-correction strategies, additional information about the noise can be determined.
Professor Wulf Lange and Dr Claire Bedrock 2005 J. Opt. B: Quantum Semiclass. Opt. 7 E02
The full text of this introduction is available in the PDF.
Young S Kim et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 S435
With this special issue, Journal of Optics B: Quantum and Semiclassical Optics contributes to the celebration of the World Year of Physics held in recognition of five brilliant papers written by Albert Einstein in 1905. There is no need to explain to the readers of this journal the content and importance of these papers, which are cornerstones of modern physics. The 51 contributions in this special issue represent current trends in quantum optics —100 years after the concept of light quanta was introduced. At first glance, in his famous papers of 1905, Einstein treated quite independent subjects—special relativity, the nature and statistical properties of light, electrodynamics of moving bodies and Brownian motion. We now know that all these phenomena are deeply related, and these relations are clearly shown in many papers in this issue.
Most of the papers are based on the talks and poster contributions from participants of the 9th International Conference on Squeezed States and Uncertainty Relations (ICSSUR'05), which took place in Besançon, France, 2–6 May, 2005. This was the continuation of a series of meetings, originating with the first workshops organized by Professor Y S Kim at the University of Maryland, College Park, USA, in 1991 and by Professor V I Man'ko at the Lebedev Physical Institute, Moscow in 1992.
One of the main topics of ICSSUR'05 and this special issue is the theory and applications of squeezed states and their generalizations. At first glance, one could think that this subject has no relation to Einstein's papers. However, this is not true: the theory of squeezed states is deeply related to special relativity, as far as it is based on the representations of the Lorentz group (see the paper by Kim Y S and Noz M E, S458–S467), which also links the current concepts of entanglement and decoherence with Lorentz-covariance. Besides, studies of the different quantum states of light imply, after all, the study of photon (or photo-electron) statistics and fluctuations of the electromagnetic field, whose importance was first emphasized by Einstein in 1905.
The squeezed states can also be considered as a generalization of the concept of coherent states, which turned out to be one of the most important theoretical tools for solving the numerous problems of quantum optics. It seems highly symbolical that the printed version of this special issue will appear in the same month when one of the prominent creators of the theory of coherent states and modern quantum optics—Professor Roy J Glauber—will receive his Nobel Prize in Stockholm. ICSSUR'05 was opened by the invited talk of R J Glauber, `What makes a quantum jump?', and we take great pleasure in congratulating him on this well deserved award. We are sure that all participants of ICSSUR'05 and all readers of this special issue share our feelings. Two other Nobel Prize winners of 2005—Professor J L Hall and Professor T W H\"ansch—also made great contributions to quantum optics. In particular, in 1986, J L Hall with collaborators, performed the first experiments on the generation of squeezed states by parametric down conversion, having obtained squeezing at the 50\% level (Wu L A, Kimble H J, Hall J L and Wu H 1986Phys. Rev. Lett. 57 2520).
Another area, which has attracted the attention of many researchers in the past decade and which is well represented in this special issue, is related to the problems of quantum correlations, entanglement and quantum nonlocality. It is also connected with the name of Einstein due to his famous `EPR' paper of 1935 written together with Podolsky and Rosen. For several decades this was an area of `thought experiments' only, but now this field is becoming a new part of physics, known as `quantum information'. The reader can find several papers which introduce new concepts in this area, such as applications of the Galois algebras and discrete Wigner functions. Solutions of different problems of the interaction between light and matter (which also take their origin in Einstein's paper of 1905), stationary and nonstationary Casimir effect, decoherence, new forms of uncertainty relations and their experimental verification, etc, can also be found in this issue. Many other contributions will be published in another special issue of the International Journal of Modern Physics B entitled `Quantum Information in Modern Optics'.
This special issue is also the last issue of Journal of Optics B: Quantum and Semiclassical Optics. For the past 15 years this journal and its predecessors—Quantum Optics and Quantum and Semiclassical Optics—gained great respect among the quantum optics community. Many breakthrough papers were published in its pages during this period (see, for example, Schrade G, Man'ko V I, Schleich W P and Glauber R J 1995 Wigner Functions in the Paul trap Quantum Semiclass. Opt. 7 307). Since 1999, Journal of Optics B: Quantum and Semiclassical Optics has published a special issue for each ICSSUR meeting. This is the fourth issue of this series. We would like to thank Institute of Physics Publishing and the staff of Journal of Optics B: Quantum and Semiclassical Optics for providing the opportunity to pursue this programme, hoping that such a cooperation will continue in the future. We would also like to thank the many colleagues, who served as referees and whose efforts helped immensely in the preparation of this issue at such a high standard. The 10th ICSSUR conference will be organized for 2007 in Bradford, UK, by Professor A Vourdas. We invite readers to join us in two years.
Boris A Malomed et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 R53
In the course of the past several years, a new level of understanding has been achieved about conditions for the existence, stability, and generation of spatiotemporal optical solitons, which are nondiffracting and nondispersing wavepackets propagating in nonlinear optical media. Experimentally, effectively two-dimensional (2D) spatiotemporal solitons that overcome diffraction in one transverse spatial dimension have been created in quadratic nonlinear media. With regard to the theory, fundamentally new features of light pulses that self-trap in one or two transverse spatial dimensions and do not spread out in time, when propagating in various optical media, were thoroughly investigated in models with various nonlinearities. Stable vorticity-carrying spatiotemporal solitons have been predicted too, in media with competing nonlinearities (quadratic–cubic or cubic–quintic). This article offers an up-to-date survey of experimental and theoretical results in this field. Both achievements and outstanding difficulties are reviewed, and open problems are highlighted. Also briefly described are recent predictions for stable 2D and 3D solitons in Bose–Einstein condensates supported by full or low-dimensional optical lattices.
P J Lee et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 S371
There are several known schemes for entangling trapped ion quantum bits for large-scale quantum computation. Most are based on an interaction between the ions and external optical fields, coupling internal qubit states of trapped ions to their Coulomb-coupled motion. In this paper, we examine the sensitivity of these motional gate schemes to phase fluctuations introduced through noisy external control fields, and suggest techniques for suppressing the resulting phase decoherence.
Kirk McKenzie et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 S421
Quantum optical states which have no coherent amplitude, such as squeezed vacuum states, cannot rely on standard readout techniques to generate error signals for control of the quadrature phase. Here we investigate the use of asymmetry in the quadrature variances to obtain a phase-sensitive readout and to lock the phase of a squeezed vacuum state, a technique which we call noise locking (NL). We carry out a theoretical derivation of the NL error signal and the associated stability of the squeezed and anti-squeezed lock points. Experimental data for the NL technique both in the presence and absence of coherent fields are shown, including a comparison with coherent locking techniques. Finally, we use NL to enable a stable readout of the squeezed vacuum state on a homodyne detector.
V V Dodonov 2002 J. Opt. B: Quantum Semiclass. Opt. 4 R1
Seventy five years ago, three remarkable papers by Schrödinger, Kennard and Darwin were published. They were devoted to the evolution of Gaussian wave packets for an oscillator, a free particle and a particle moving in uniform constant electric and magnetic fields. From the contemporary point of view, these packets can be considered as prototypes of the coherent and squeezed states, which are, in a sense, the cornerstones of modern quantum optics. Moreover, these states are frequently used in many other areas, from solid state physics to cosmology. This paper gives a review of studies performed in the field of so-called `nonclassical states' (squeezed states are their simplest representatives) over the past seventy five years, both in quantum optics and in other branches of quantum physics.
My starting point is to elucidate who introduced different concepts, notions and terms, when, and what were the initial motivations of the authors. Many new references have been found which enlarge the `standard citation package' used by some authors, recovering many undeservedly forgotten (or unnoticed) papers and names. Since it is practically impossible to cite several thousand publications, I have tried to include mainly references to papers introducing new types of quantum states and studying their properties, omitting many publications devoted to applications and to the methods of generation and experimental schemes, which can be found in other well known reviews. I also mainly concentrate on the initial period, which terminated approximately at the border between the end of the 1980s and the beginning of the 1990s, when several fundamental experiments on the generation of squeezed states were performed and the first conferences devoted to squeezed and `nonclassical' states commenced. The 1990s are described in a more `squeezed' manner: I have confined myself to references to papers where some new concepts have been introduced, and to the most recent reviews or papers with extensive bibliographical lists.
Tomasz M Brzozowski et al 2002 J. Opt. B: Quantum Semiclass. Opt. 4 62
We analyse the time-of-flight method of measuring the temperature of cold trapped atoms in the specific case of short distances of the probe beam from the trap centre and finite atomic cloud size. We theoretically examine the influence of the probe beam shape and its distance from the initial position of the cloud on the temperature evaluation. These results are then verified with a three-dimensional Monte Carlo simulation and applied to our experimental data to show that the proposed procedure allows accurate and reliable determination of the temperature.
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Young S Kim et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 S435
With this special issue, Journal of Optics B: Quantum and Semiclassical Optics contributes to the celebration of the World Year of Physics held in recognition of five brilliant papers written by Albert Einstein in 1905. There is no need to explain to the readers of this journal the content and importance of these papers, which are cornerstones of modern physics. The 51 contributions in this special issue represent current trends in quantum optics —100 years after the concept of light quanta was introduced. At first glance, in his famous papers of 1905, Einstein treated quite independent subjects—special relativity, the nature and statistical properties of light, electrodynamics of moving bodies and Brownian motion. We now know that all these phenomena are deeply related, and these relations are clearly shown in many papers in this issue.
Most of the papers are based on the talks and poster contributions from participants of the 9th International Conference on Squeezed States and Uncertainty Relations (ICSSUR'05), which took place in Besançon, France, 2–6 May, 2005. This was the continuation of a series of meetings, originating with the first workshops organized by Professor Y S Kim at the University of Maryland, College Park, USA, in 1991 and by Professor V I Man'ko at the Lebedev Physical Institute, Moscow in 1992.
One of the main topics of ICSSUR'05 and this special issue is the theory and applications of squeezed states and their generalizations. At first glance, one could think that this subject has no relation to Einstein's papers. However, this is not true: the theory of squeezed states is deeply related to special relativity, as far as it is based on the representations of the Lorentz group (see the paper by Kim Y S and Noz M E, S458–S467), which also links the current concepts of entanglement and decoherence with Lorentz-covariance. Besides, studies of the different quantum states of light imply, after all, the study of photon (or photo-electron) statistics and fluctuations of the electromagnetic field, whose importance was first emphasized by Einstein in 1905.
The squeezed states can also be considered as a generalization of the concept of coherent states, which turned out to be one of the most important theoretical tools for solving the numerous problems of quantum optics. It seems highly symbolical that the printed version of this special issue will appear in the same month when one of the prominent creators of the theory of coherent states and modern quantum optics—Professor Roy J Glauber—will receive his Nobel Prize in Stockholm. ICSSUR'05 was opened by the invited talk of R J Glauber, `What makes a quantum jump?', and we take great pleasure in congratulating him on this well deserved award. We are sure that all participants of ICSSUR'05 and all readers of this special issue share our feelings. Two other Nobel Prize winners of 2005—Professor J L Hall and Professor T W H\"ansch—also made great contributions to quantum optics. In particular, in 1986, J L Hall with collaborators, performed the first experiments on the generation of squeezed states by parametric down conversion, having obtained squeezing at the 50\% level (Wu L A, Kimble H J, Hall J L and Wu H 1986Phys. Rev. Lett. 57 2520).
Another area, which has attracted the attention of many researchers in the past decade and which is well represented in this special issue, is related to the problems of quantum correlations, entanglement and quantum nonlocality. It is also connected with the name of Einstein due to his famous `EPR' paper of 1935 written together with Podolsky and Rosen. For several decades this was an area of `thought experiments' only, but now this field is becoming a new part of physics, known as `quantum information'. The reader can find several papers which introduce new concepts in this area, such as applications of the Galois algebras and discrete Wigner functions. Solutions of different problems of the interaction between light and matter (which also take their origin in Einstein's paper of 1905), stationary and nonstationary Casimir effect, decoherence, new forms of uncertainty relations and their experimental verification, etc, can also be found in this issue. Many other contributions will be published in another special issue of the International Journal of Modern Physics B entitled `Quantum Information in Modern Optics'.
This special issue is also the last issue of Journal of Optics B: Quantum and Semiclassical Optics. For the past 15 years this journal and its predecessors—Quantum Optics and Quantum and Semiclassical Optics—gained great respect among the quantum optics community. Many breakthrough papers were published in its pages during this period (see, for example, Schrade G, Man'ko V I, Schleich W P and Glauber R J 1995 Wigner Functions in the Paul trap Quantum Semiclass. Opt. 7 307). Since 1999, Journal of Optics B: Quantum and Semiclassical Optics has published a special issue for each ICSSUR meeting. This is the fourth issue of this series. We would like to thank Institute of Physics Publishing and the staff of Journal of Optics B: Quantum and Semiclassical Optics for providing the opportunity to pursue this programme, hoping that such a cooperation will continue in the future. We would also like to thank the many colleagues, who served as referees and whose efforts helped immensely in the preparation of this issue at such a high standard. The 10th ICSSUR conference will be organized for 2007 in Bradford, UK, by Professor A Vourdas. We invite readers to join us in two years.
Professor Wulf Lange and Dr Claire Bedrock 2005 J. Opt. B: Quantum Semiclass. Opt. 7 E02
The full text of this introduction is available in the PDF.
2005 J. Opt. B: Quantum Semiclass. Opt. 7 381
The PDF file provided contains web links to all articles in this volume.
L S Aguiar et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 S769
We investigate the entanglement properties of a system of two dipole–dipole coupled two-level atoms resonantly interacting with a thermal field in a high-Q cavity. We obtain the evolution operator for this system in an analytical form, and use it to evaluate the atom–atom entanglement through the calculation of the negativity. We find that, despite the destructive effect of thermal noise, the dipole interaction yields a considerable amount of entanglement between the two atoms.
C Sudheesh et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 S728
We investigate the squeezing and higher-order squeezing properties of photon-added coherent states propagating through a Kerr-like medium, particularly close to instants of revivals and fractional revivals of the state. The Wigner functions at these instants are obtained, and the extent of non-classicality quantified.
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Ramon van Handel et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 S179
The goal of this article is to provide a largely self-contained introduction to the modelling of controlled quantum systems under continuous observation, and to the design of feedback controls that prepare particular quantum states. We describe a bottom-up approach, where a field-theoretic model is subjected to statistical inference and is ultimately controlled. As an example, the formalism is applied to a highly idealized interaction of an atomic ensemble with an optical field. Our aim is to provide a unified outline for the modelling, from first principles, of realistic experiments in quantum control.
A Kaplan et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 R103
We perform spectroscopy on the ground-state hyperfine splitting of 85Rb atoms trapped in far-off-resonance optical traps. The existence of a spatially dependent shift in the energy levels is shown to induce an inherent dephasing effect, which causes a broadening of the spectroscopic line and hence an inhomogeneous loss of atomic coherence at a much faster rate than the homogeneous one caused by spontaneous photon scattering. We present here a number of approaches for reducing this inhomogeneous broadening, based on trap geometry, additional laser fields, and novel microwave pulse sequences. We then show how hyperfine spectroscopy can be used to study the quantum dynamics of optically trapped atoms.
D I Tsomokos et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 R73
The interaction of mesoscopic interference devices with nonclassical electromagnetic fields is studied. The external quantum fields induce a phase factor in the electric charges. This phase factor, which is a generalization of the standard Aharonov–Bohm phase factor, is in the case of nonclassical electromagnetic fields a quantum mechanical operator. Its expectation value depends on the density matrix describing the nonclassical photons and determines the interference. Several examples are discussed, which show that the quantum noise of the nonclassical photons partly destroys the electron interference fringes. An interesting application arises in the context of distant electron interference devices, irradiated with entangled photons. In this case the interfering electrons in the two devices become entangled. The same ideas are applied in the context of SQUID rings irradiated with nonclassical electromagnetic fields. It is shown that the statistics of the Cooper pairs tunnelling through the Josephson junction depends on the statistics of the photons.
Hong-yi Fan and Alfred Wünsche 2005 J. Opt. B: Quantum Semiclass. Opt. 7 R88
Two-mode entangled-state wavefunctions and with complex variables z and y are introduced and investigated. They are direct analogues of the wavefunctions and in the single-mode case or are linearly related to each other by two-dimensional Fourier transformation. The states and are eigenstates of two pairs of commuting operators (Z,Z†) (or (Q+,P−)) and (Y,Y†) (or (P+,Q−)) to eigenvalues (z,z*) and (y,y*), respectively, and are normalized by means of the two-dimensional delta function. The entangled states and are represented as two limiting cases of two-mode squeezed coherent states. Different representations of these states, in particular, the analogue of the Agarwal–Simon representation of squeezed vacuum states, are derived and the properties of these states are discussed. The transition from the single-mode to the two-mode case is made using the common property of the squeezing operators to belong to different realizations of the abstract SU(1,1) group. The Wigner quasiprobability in representation of the states and is discussed and is explicitly calculated for two-mode squeezed vacuum (and squeezed coherent) states.
J Piilo and K-A Suominen 2005 J. Opt. B: Quantum Semiclass. Opt. 7 R37
The invention of laser cooling methods for neutral atoms allows optical and magnetic trapping of cold atomic clouds in the temperature regime below 1 mK. In the past, light-assisted cold collisions between laser cooled atoms have been widely studied in magneto-optical atom traps (MOTs). We describe here theoretical studies of dynamical interactions, specifically cold collisions, between atoms trapped in near-resonant, dissipative optical lattices. The extension of collision studies to the regime of optical lattices introduces several complicating factors. For the lattice studies, one has to account for the internal substates of atoms, position-dependent matter–light coupling, and position-dependent couplings between the atoms, in addition to the spontaneous decay of electronically excited atomic states. The developed one-dimensional quantum-mechanical model combines atomic cooling and collision dynamics in a single framework. The model is based on Monte Carlo wavefunction simulations and is applied when the lattice-creating lasers have frequencies both below (red-detuned lattice) and above (blue-detuned lattice) the atomic resonance frequency. It turns out that the radiative heating mechanism affects the dynamics of atomic cloud in a red-detuned lattice in a way that is not directly expected from the MOT studies. The optical lattice and position-dependent light–matter coupling introduces selectivity of collision partners. The atoms which are most mobile and energetic are strongly favoured to participate in collisions, and are more often ejected from the lattice, than the slow ones in the laser parameter region selected for study. Consequently, the atoms remaining in the lattice have a smaller average kinetic energy per atom than in the case of non-interacting atoms. For blue-detuned lattices, we study how optical shielding emerges as a natural part of the lattice and look for ways to optimize the effect. We find that the cooling and shielding dynamics do not mix and it is possible to achieve efficient shielding with a very simple arrangement. The simulations are computationally very demanding and would obviously benefit from the simplification schemes. We present some steps in this direction by showing how it is possible to calculate collision rates in near-resonant lattices in a fairly simple way. The method can then be used to combine quantum-mechanical and semiclassical models for cold collision studies in optical lattices.