Showing papers on "Coherent states published in 1994"

Quantum limits on bosonic communication rates

Abstract: The capacity C of a communication channel is the maximum rate at which information can be transmitted without error from the channel's input to its output. The authors review quantum limits on the capacity that can be achieved with linear bosonic communication channels that have input power P. The limits arise ultimately from the Einstein relation that a field quantum at frequency f has energy E=hf. A single linear bosonic channel corresponds to a single transverse mode of the bosonic field i.e., to a particular spatial dependence in the plane orthogonal to the propagation direction and to a particular spin state or polarization. For a single channel the maximum communication rate is CWB=( ln 2)2P3h bits/s. This maximum rate can be achieved by a "number-state channel," in which information is encoded in the number of quanta in the bosonic field and in which this information is recovered at the output by counting quanta. Derivations of the optimum capacity CWB are reviewed. Until quite recently all derivations assumed, explicitly or implicitly, a number-state channel. They thus left open the possibility that other techniques for encoding information on the bosonic field, together with other ways of detecting the field at the output, might lead to a greater communication rate. The authors present their own general derivation of the single-channel capacity upper bound, which applies to any physically realizable technique for encoding information on the bosonic field and to any physically realizable detection scheme at the output. They also review the capacities of coherent communication channels that encode information in coherent states and in quadrature-squeezed states. A three-dimensional bosonic channel can employ many transverse modes as parallel single channels. An upper bound on the information flux that can be transferred down parallel bosonic channels is derived.

Coherent states for isospectral oscillator Hamiltonians

Abstract: Coherent states for a family of isospectral oscillator Hamiltonians are derived from a suitable choice of annihilation and creation operators. The Fock-Bargmann representation is also considered.

Photon distribution for one-mode mixed light with a generic Gaussian Wigner function.

Abstract: For one-mode light described by the Wigner function of a generic Gaussian form with five real parameters, the photon distribution function is obtained explicitly in terms of the Hermite polynomial of two variables. The effective formulas reducing the two-dimensional Hermite polynomials to the classical (one-dimensional) orthogonal polynomials are given. The first and the second statistical moments of the photon distribution function are calculated. The generating function for the photon distribution is discussed. Various special cases, including the shifted thermal states, correlated and squeezed states, coherent states, etc., are considered.

Generation of nonclassical light by dissipative two-photon processes.

Abstract: Nonclassical states of light may be generated by processes involving the creation or annihilation of photons in pairs. A quadratic coupling, characteristic of a parametric amplifier, generates a squeezed vacuum from a normal vacuum, and a two-photon absorber can also generate a squeezed state (though not a minimum-uncertainty state) even though it is a purely dissipative process. We consider here the simultaneous action of a quadratic pump on a two-photon absorber and demonstrate how superpositions of distinct coherent states may be generated by their combined effects. We use standard master equations to describe the time development, employing split operators and direct numerical integrations to determine the field density-matrix elements and quasiprobabilities. The purities of the nonclassical states are determined by evaluating the field entropy. Provided one-photon dissipative processes may be ignored, a pure superposition state is formed in the steady state. This superposition is destroyed if one-photon loss processes are important.

Multidimensional Hermite polynomials and photon distribution for polymode mixed light

Abstract: The photon distribution function of an N-mode mixed state of light described by the Wigner function of generic Gaussian form is calculated explicitly in terms of the Hermite polynomials of 2N variables with equal pairs of indices. Simple formulas for the mean values and dispersions of photon numbers are found. The N-mode photon distribution functions for squeezed photon number states and for squeezed coherent states are expressed in terms of the Hermite polynomials of 2N and N variables, respectively.

Statistical and phase properties of the binomial states of the electromagnetic field.

Abstract: We investigate the nonclassical properties of the single-mode binomial states of the quantized electromagnetic field. We concentrate our analysis on the fact that the binomial states interpolate between the coherent states and the number states, depending on the values of the parameters involved. We discuss their statistical properties, such as squeezing (second and fourth order) and sub-Poissonian character. We show how the transition between those two fundamentally different states occurs, employing quasiprobability distributions in phase space, and we provide, at the same time, an interesting picture for the origin of second-order quadrature squeezing. We also discuss the phase properties of the binomial states using the Hermitian-phase-operator formalism.

Photon statistics of multimode even and odd coherent light

Abstract: The even and odd coherent states are generalized for the multimode case. The explicit forms for the photon distribution, Q function, and Wigner function are derived. In particular, it is shown that for the two-mode case there exist strong correlations between these modes, under certain conditions, which are responsible for two-mode squeezing in the case of even coherent states.

Comparison of quantum-state diffusion and quantum-jump simulations of two-photon processes in a dissipative environment.

Abstract: Recent work on the dynamics of open systems has shown how the density operator may be unraveled into component state-vector trajectories using quantum-state diffusion or the quantum-jump model. In traditional dissipative environments the coherent evolution is stochastically perturbed by the action of the reservoir or environment, so that superposition states are dephased. We examine a system in which both coherent driving and dissipative damping involve the simultaneous creation and annihilation of pairs of photons. This has unusual consequences for the creation and decay of coherences. We analyze this problem using the two recently proposed simulation methods and compare the results of the simulation methods with each other and with density-matrix calculations. We also demonstrate the formation of Schr\"odinger ``cat'' states of the field through the action of dissipation and depict them using the Wigner and Husimi quasiprobability functions.

Nonideal lasers, nonclassical light, and deformed photon states.

Abstract: We show that both super-Poissonian and sub-Poissonian photo statistics may be modeled by the use of the recently introduced [ital M]-type [ital q]-deformed coherent states, while [ital P]-type [ital q]-deformed coherent states exhibit nonclassical sub-Poissonian photon statistics. Applications to the characterization of the photon statistics of laser outputs reasonably close to threshold, single-atom resonance fluorescence, the micromaser field, and absorption by two-level atoms are considered.

Squeezed Vacua and the Quantum Statistics of Cosmological Particle Creation

Abstract: We use the language of squeezed states to give a systematic description of two issues in cosmological particle creation: (a) Dependence of particle creation on the initial state specified; we consider in particular the number state, the coherent state and the squeezed state; (b) the relation of spontaneous and stimulated particle creation and their dependence on the initial state. We also present results for the fluctuations in particle number in anticipation of its relevance to defining noise in quantum fields and the vacuum susceptibility of space–time.

Evolution of quantum superpositions in open environments - quantum trajectories, jumps, and localization in phase-space

Abstract: The decay of coherence when a quantum system interacts with a much larger environment is usually described by a master equation for the system reduced density matrix and emphasizes the evolution of an entire ensemble. We consider two methods that have been developed recently to simulate the evolution of single realizations. Quantum-state diffusion involves both diffusion, where the individual quantum trajectory fluctuates through a Wiener process deriving from the environment, and localization to a coherent state, an eigenstate of the relevant Lindblad operator describing the coupling of the system to the environment. We demonstrate the localization process for different initial states and utilize the Wigner function to depict this localization in phase space. We concentrate on quantum states that can be expressed as a superposition of appropriate coherent states. For an initial superposition of two coherent states (a Schr\"odinger ``cat''), one of the two components will dominate the evolution. For initial Fock states, which can be described as a continuous superposition of coherent states on a ring, localization takes place when one coherent state is selected from that ring where each component has nearly the same energy as the original Fock state. We also consider the localization from a nonclassical squeezed ground state, which can be expressed as a superposition of coherent states along a line in phase space. The second simulation method considered is the state vector Monte Carlo, or ``quantum jump,'' approach, which relates to the direct counting of decay quanta. In the case of an initial Schr\"odinger ``cat,'' we find that when no quantum is detected the ``cat'' shrinks, but when a quantum is detected, the Schr\"odinger ``cat'' ``jumps'' from one type of ``cat'' to another with different internal phase. For an initial squeezed state we show how quantum jumps lead to individual realizations which are superpositions of two squeezed states.

Displaced and squeezed parity operator: Its role in classical mappings of quantum theories

Abstract: The displaced parity operators are shown to have properties that bear a deep relationship with those of the Wigner functions. By exploiting these properties we show that these operators play an important role in linking together many of the aspects of the various exact phase-space mappings of quantum mechanics. These include the Wigner and Weyl representations, coherent states and the Bargmann representation, the P and Q representations, the Weyl correspondence, and the Moyal star product formalism. We also introduce corresponding displaced Fourier operators and show that their squares are just the displaced parity operators. The formalism is extended to squeezed and displaced parity operators, and their corresponding central role in the theory of squeezed coherent states and general squeezing is explained. We also elucidate the part played by the displaced parity operators in the Moyal star product and its extensions, as a first step towards a potential application of these operators in such modern developments as deformation theory and quantum groups. Finally, we indicate how the apparatus developed might also find applications in other recent exact classical mappings of many-particle quantum mechanics or quantum field theory, which are not special cases of deformation theory. Prime examples here include the powerful so-called independent-cluster method techniques, which incorporate the coupled-cluster method formalism with its inbuilt supercoherent states. Throughout the work we stress the central and unifying role played by the displaced parity operator and its generalizations.

Hypersensitivity to perturbation in the quantum kicked top.

Abstract: For the quantum kicked top we study numerically the distribution of Hilbert-space vectors evolving in the presence of a small random perturbation. For an initial coherent state centered in a chaotic region of the classical dynamics, the evolved perturbed vectors are distributed essentially like random vectors in Hilbert space. In contrast, for an initial coherent state centered near an elliptic (regular) fixed point of the classical dynamics, the evolved perturbed vectors remain close together, explore only a few dimensions of Hilbert space, and do not explore them randomly. These results support and extend the results of earlier studies, thereby providing additional support for a characterization of quantum chaos that uses concepts from information theory.

Unified approach to the analogues of single-photon and multiphoton coherent states for generalized bosonic oscillators

Abstract: A large class of bosonic coherent states known in the literature have been constructed in a unified way by Shanta et. al. (1994). It is shown that this method can be easily extended to generalized bosonic-oscillator systems.

Coherent state representation of quantum fluctuations in the early Universe.

Abstract: Using the squeezed state formalism the coherent state representation of quantum fluctuations in an expanding universe is derived. It is shown that this provides a useful alternative to the Wigner function as a phase space representation of quantum fluctuations. The quantum to classical transition of fluctuations is naturally implemented by decohering the density matrix in this representation. The entropy of the decohered vacua is derived. It is shown that the decoherence process breaks the physical equivalence between vacua that differ by a coordinate dependent phase generated by a surface term in the Lagrangian. In particular, scale invariant power spectra are only obtained for a special choice of surface term.

Wave function in the invariant representation and squeezed-state function of the time-dependent harmonic oscillator

Abstract: The two quantum invariant operators are found from the time-dependent Hamiltonian of the harmonic oscillator with an auxiliary condition. The solution of the Schr\"odinger equation for the system, such as the eigenfunctions, eigenvalues, and minimum uncertainty, is derived by utilizing these invariant operators. The coherent states of this system are not the squeezed states, and the eigenfunction of the invariant operator is not the eigenfunction of the Hamiltonian of the system unless it is in the invariant representation. The squeezing function, which is an eigenfunction of the Hamiltonian of the system in the invariant representation and which also gives the minimum uncertainty, is obtained by a set of unitary transformed operators, i.e., squeezing operators.

Semiclassical versus quantum behavior in fourth-order interference

Abstract: A theoretical construct is presented for fourth-order interference between the signal and the idler beams of a parametric downconverter. Previous quantum treatments of fourth-order interference have employed correlated single-photon wave packets. The introduced approach, however, relies on Gaussian-state field correlations, which were previously used to characterize quadrature-noise squeezing produced by an optical parametric amplifier and nonclassical twin-beam generation in an optical parametric oscillator. Three principal benefits accrue from the correlation-function formalism. First, the quantum theory of fourth-order interference is unified with that for the other nonclassical effects of χ(2) interactions, i.e., squeezing and twin-beam production. Second, the semiclassical photodetection limit on Gaussian-state fourth-order interference is established; a purely quantum effect can be claimed at fringe visibilities substantially below the 50% level. Finally, both photon-coincidence counting (within the low-photon-flux regime) and intensity interferometry (in the high-photon-flux limit) are easily analyzed within a common framework.

Large-scale fluctuations in the driven Jaynes-Cummings model.

Abstract: We study the dynamics of the driven Jaynes-Cummings model where an atom interacts with a single-mode cavity field but is also directly driven by an external radiation field. We show that the dynamic variables can be described in terms of ordinary Jaynes-Cummings dynamic variables with a different initial condition. We investigate the special case of an initial coherent state. We find collapses and revivals in the average number of photons at a much larger time scale than their Jaynes-Cummings model counterparts. We show that these ``super-revivals'' are related to the large-time-scale revivals that occur in the average electric field in the ordinary Jaynes-Cummings model. We also examine the photon statistics in the driven Jaynes-Cummings model and show that the cavity field is sub-Poissonian for certain interaction times.

Towards a theory of the integer quantum Hall transition: From the nonlinear sigma model to superspin chains

Abstract: A careful study of the supersymmetric version of Pruisken's nonlinear σ model for the integer quantum Hall effect is presented. The lattice regularized model is cast in Hamiltonian form by taking the anisotropic limit and interpreting the topological density as an alternating sum of Wess Zumino terms. It is argued that the relevant large-scale physics of the model is preserved by projection of the quantum Hamiltonian on its sector of degenerate strong-coupling ground states. For values of the Hall conductivity close to e2/2h (mod e2/h), where a delocalization transition occurs, this yields the Hamiltonian of a quantum superspin chain which is closely related to an anisotropic version of the Chalker-Coddington model. The relation implies that the ratio of magnetic length over potential correlation length is an irrelevant parameter at the transition. The superspin chain resembles a 1 d isotropic antiferromagnet with spin 1/2. It has an alternating structure which however permits an invariance under translation by one site. The conductance coefficients of a quantum Hall system with N small contacts translate into N-superspin correlation functions which are governed by conformal invariance. The superspin formalism provides a framework for studying the crossover from classical to quantum percolation. It does not however encompass the frequency-dependent correlations of wave amplitudes at criticality.

Generation of mixtures of Schrödinger-cat states from a competitive two-photon process.

Abstract: We study the formation of mixtures of superposition states of the coherent states \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}\ensuremath{\alpha}〉, also known as Schr\"odinger-cat states, from a competitive process involving a two-photon parametric process and two-photon absorption. Using the fact that photons are created or destroyed in pairs, we deduce the long-time steady-state form of the density operator. We numerically study the evolution at all times and show that generally the field is in a mixed state. We also examine nonclassical properties of the field such as squeezing and sub-Poissonian statistics, and also the evolution of the Q function.

Single-atom interference method for generating Fock states

Abstract: An atomic interference method is presented that can be used to construct arbitrary superpositions of coherent states with equal mean photon number in a single-mode cavity by sending only one atom through the apparatus. The method is suitable to generate any quantum state that has a one-dimensional coherent state representation on a circle in phase space. This method is demonstrated in the case of generating Fock states.

Preparation of stationary Fock states in a one-atom Raman laser.

Abstract: We demonstrate the possibility of preparing low-photon-number eigenstates of a single damped cavity mode coupled to a single three-level atom in a Raman lambda configuration. As an example we discuss cesium and show that both the atom-field coupling strength and the cavity loss rate needed for an experimental realization of the proposed scheme lie within 1 order of magnitude of what is achievable in current experimental setups.

Adelic model of harmonic oscillator

Abstract: Adelic quantum mechanics is formulated. The corresponding model of the harmonic oscillator is considered. The adelic harmonic oscillator exhibits many interesting features. One of them is a softening of the uncertainty relation.

Coherent States of a Harmonic Oscillator in a Finite-dimensional Hilbert Space and Their Squeezing Properties

Abstract: New coherent states of a harmonic oscillator in a finite-dimensional Fock space are introduced. Some properties of these coherent states are discussed. The second-order squeezing of these coherent states with respect to the quadrature operators is studied in detail. In particular, for a two-state system the arbitrary higher-order squeezing of these states is investigated. It is shown that these coherent states exhibit much richer squeezing properties than the coherent states of a usual harmonic oscillator in an infinite-dimensional Fock space. It is found that these coherent states have not only second-order squeezing but also higher-order squeezing with respect to the quadrature operators of the field under consideration.

Decoherence produces coherent states: An explicit proof for harmonic chains

Abstract: We study the behavior of infinite systems of coupled harmonic oscillators as the time t\ensuremath{\rightarrow}\ensuremath{\infty}, and generalize the central limit theorem (CLT) to show that their reduced Wigner distributions become Gaussian under quite general conditions. This shows that generalized coherent states tend to be produced naturally. A sufficient condition for this to happen is shown to be that the spectral function is analytic and nonlinear. For a chain of coupled oscillators, the nonlinearity requirement means that waves must be dispersive, so that localized wave packets become suppressed. Virtually all harmonic heat-bath models in the literature satisfy this constraint, and we have good reason to believe that coherent states and their generalizations are not merely a useful analytical tool, but that nature is indeed full of them. Standard proofs of the CLT rely heavily on the fact that probability densities are non-negative. Although the CLT is generally not applicable if the densities are allowed to take negative values, we show that a CLT does indeed hold for a special class of such functions. We find that, intriguingly, nature has arranged things so that all Wigner functions belong to this class.

Thermal coherent states in the Bargmann representation.

Abstract: The thermal coherent states considered previously by the present authors represent an alternative mixed-state generalization of the usual pure-state coherent states. They describe displaced harmonic oscillators in thermodynamic equilibrium with a heat bath at nonzero temperature. We show how they provide a "random" (or "thermal" or "noisy") basis on a quantum-mechanical Hilbert space scrH. Their usefulness rests on the fact that the corresponding statistical density operator provides a probability operator measure on scrH. We thereby show how the thermal coherent states permit a generalization to nonzero temperatures of the well-known P and Q representations of operators in scrH. Particular emphasis here is placed on imbedding the formulation in the Bargmann or holomorphic representation of scrH. We examine the corresponding Bargmann representations of both state vectors and operators, and show how the former relate to the usual position and momentum representations and the latter to the usual P, Q, and W (or Weyl) representations. A particularly important and unexpected result is that the present temperature-dependent generalized P and Q representations are the analytic continuations to negative temperatures of each other. The usual Q and P representations thus represent the limits as the temperature approaches zero along the positive and negative real axes, respectively, of the enlarged generalized Q representation, suitably analytically continued to negative temperatures. We discuss the possible physical applications of the present thermal coherent states to both quantum optics situations involving coherent signals in the presence of thermal noise and to signal and image processing.