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Showing papers on "Coherent states published in 1997"


Journal ArticleDOI
TL;DR: In this paper, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of oscillation depends on the energy.
Abstract: The notion of f-oscillators generalizing q-oscillators is introduced. For classical and quantum cases, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of oscillation depends on the energy. The f-coherent states (nonlinear coherent states) generalizing q-coherent states are constructed. Applied to quantum optics, photon distribution function, photon number means, and dispersions are calculated for the f-coherent states as well as the Wigner function and Q-function. As an example, it is shown how this nonlinearity may affect the Planck distribution formula.

571 citations


Journal ArticleDOI
TL;DR: In this paper, a quantum system composed of a cavity field interacting with a movable mirror can be used to generate a large variety of nonclassical states of both the cavity field and the mirror.
Abstract: We describe how a quantum system composed of a cavity field interacting with a movable mirror can be utilized to generate a large variety of nonclassical states of both the cavity field and the mirror. First we consider state preparation of the cavity field. The system dynamics will prepare a single mode of the cavity field in a multicomponent Schr\"odinger-cat state, in a similar manner to that in a Kerr medium. In addition, when two or more cavity modes interact with the mirror, they can be prepared in an entangled state, which may be regarded as a multimode generalization of the even and odd coherent states. We show also that near-number states of a single mode may be prepared by performing a measurement of the position of the mirror. Second we consider state preparation of the mirror and show that this macroscopic object may be placed in a Schr\"odinger-cat-like state by a quadrature measurement of the light field. In addition, we examine the effect of the damping of the motion of the mirror on the field states inside the cavity and compare this with the effect of cavity field damping.

434 citations


Journal ArticleDOI
M. Dakna1, T. Anhut1, Tomáš Opatrný1, Ludwig Knöll1, D.-G. Welsch1 
TL;DR: In this paper, a scheme for generating Schrodinger-cat-like states of a single-mode optical field by means of conditional measurement is proposed, where a squeezed vacuum is fed into a beam splitter and counting the photons in one of the output channels, the conditional states in the other output channel exhibit a number of properties similar to those of superpositions of two coherent states with opposite phases.
Abstract: A scheme for generating Schr\"odinger-cat-like states of a single-mode optical field by means of conditional measurement is proposed. Feeding a squeezed vacuum into a beam splitter and counting the photons in one of the output channels, the conditional states in the other output channel exhibit a number of properties that are very similar to those of superpositions of two coherent states with opposite phases. We present analytical and numerical results for the photon-number and quadrature-component distributions of the conditional states and their Wigner and Husimi functions. Further, we discuss the effect of realistic photocounting on the states.

344 citations


Journal ArticleDOI
TL;DR: In this paper, a non-Markovian generalisation of the stochastic Schrodinger equation is presented, which allows one to describe open quantum systems in terms of stochastically state vectors rather than density operators, without Markov approximation.

215 citations


Journal ArticleDOI
TL;DR: In this article, a supersymmetric generalization of the non-stationary Schrodinger equation is formulated, and the effect of supersymmetry on the generation of isospectral potentials is discussed.
Abstract: The recent developments in the theory of the generation of potentials for which the Schrodinger equation has an exact solution are discussed. The generalization of the Darboux transformation to the nonstationary Schrodinger equation is studied in detail. The supersymmetric generalization of the nonstationary Schrodinger equation is formulated. Versions corresponding to exact and spontaneously broken supersymmetry are discussed. New, exactly solvable nonstationary potentials are obtained as examples. The stationary Darboux transformation is viewed as a special case of the new transformation. Families of isospectral potentials with the spectra of the harmonic oscillator and the hydrogen-like atom are obtained. The effectiveness of these methods for describing the coherent states of the transformed Hamiltonians is demonstrated.

191 citations


Journal ArticleDOI
TL;DR: In this paper, the authors consider a physical process that leads to the generation of atomic Schr\"odinger cat states for a system of two level atoms, and study in detail the quasidistributions for these states and demonstrate how the Schr''odinger cats can lead to interesting interferences over the surface of a sphere.
Abstract: We consider a physical process that leads to the generation of atomic Schr\"odinger cat states for a system of two level atoms. The effective interaction between atoms in a dispersive cavity leads to the superposition of atomic coherent states. We study in detail the quasidistributions for these states and demonstrate how the Schr\"odinger cat states can lead to interesting interferences over the surface of a sphere.

190 citations


Journal ArticleDOI
TL;DR: In this paper, the exact Schr\"odinger wave functions for a harmonic oscillator with time-dependent mass and frequency were obtained using the Lewis and Riesenfeld invariant method.
Abstract: We use the Lewis and Riesenfeld invariant method [J. Math. Phys. 10, 1458 (1969)] to obtain the exact Schr\"odinger wave functions for a harmonic oscillator with time-dependent mass and frequency. Exact coherent states for such system are also constructed.

177 citations


Journal ArticleDOI
TL;DR: In this paper, the authors show that the Wigner function is not everywhere positive for any finite rk, hence its interpretation as a classical distribution function in phase space is impossible without some coarse graining procedure.

147 citations


Journal ArticleDOI
TL;DR: In this article, the authors study counting statistics of electric current pumped by pulses of an external field, and develop an approach that allows them to calculate all counting statistics for various driving fields, optimal and non-optimal.
Abstract: We study counting statistics of electric current pumped by pulses of an external field. The fluctuations depend on the pulse shape, and can be minimized by choosing the pulse shape properly. For an optimal pulse shape, the fluctuations are reduced to the dc level, i.e., they do not depend on the duty cycle of the signal. We develop an approach that allows us to calculate all counting statistics for various driving fields, optimal and nonoptimal. The statistics depend in an interesting way on the analytic structure of the field time dependence, and display an analogy with coherent states and instantons.

144 citations


Journal ArticleDOI
TL;DR: In this article, an experimental configuration, within an ion trap, by which a quantum mechanical delta-kicked harmonic oscillator could be realized, and investigated, was proposed, and the sensitivity of the ion motion to small variations in the external parameters was measured.
Abstract: We propose an experimental configuration, within an ion trap, by which a quantum mechanical delta-kicked harmonic oscillator could be realized, and investigated. We show how to directly measure the sensitivity of the ion motion to small variations in the external parameters.

142 citations


Journal ArticleDOI
TL;DR: In this paper, the authors studied the quantization of systems with general first and second-class constraints from the point of view of coherent state phase-space path integration, and showed that all such cases may be treated, within the original classical phase space, by using suitable path-integral measures for the Lagrange multipliers which ensure that the quantum system satisfies the appropriate quantum constraint conditions.

Journal ArticleDOI
TL;DR: In this paper, the concept of even and odd nonlinear coherent states is introduced, and the statistical properties of such states are investigated with particular attention to their nonclassical effects.

Journal ArticleDOI
TL;DR: In this article, the authors derived asymptotics for the quantum evolution of coherent states, at any order in the Planck constant, with a control in large time of the remainder term depending explicitely on the stability matrix.
Abstract: Precise semiclassical estimates for the spreading of quantum wave packets are derived, when the initial wave packet is in a coherent state. We find asymptotics for the quantum evolution of coherent states, at any order in the Planck constant ~, with a control in large time of the remainder term depending explicitely on ~ and on the stability matrix. Our results extend Hagedorn's work on the propagation of Gaussian coherent states. We present here a proof simplifying Hagedorn's arguments, and extending it to general, possibly time-dependent Hamiltonians, not necessarily in the form of kinetic energy plus potential energy (p 2 +V (x)). Our proof also works for more general coherent states and extends recent results by Paul and Uribe. As a first application of our semiclassical estimates we show that, if the initial quantum state is a coherent state located around an unstable fixed point of the classical flow, the spreading of the quantum wave packet at time t grows like e 2t for times not larger than (=) log(1=~) ,w here is the classical instability exponent associated to the fixed point and is a numerical constant.

Journal ArticleDOI
TL;DR: In this paper, a degenerate Raman coupled model for the motion of a trapped two-level ion is presented, where an initial vibrational coherent state evolves into superpositions of coherent states correlated with the internal states of the ion.
Abstract: A proposal for realizing one- and two-mode degenerate Raman coupled models, of the type proposed by Knight [Phys. Scr. T 12, 51 (1986)] in the context of quantum optics, for the motion of a trapped two-level ion, is presented. The interaction has a dispersive effect on the vibrational motion of the ion. For the one-mode case, an initial vibrational coherent state evolves into superpositions of coherent states (Schr\"odinger-cat states) correlated with the internal states of the ion. In the two-mode case, with initial coherent states in each mode, entanglements of coherent states between the modes correlated with the internal ionic states are obtained. Detection of such states is briefly discussed.

Journal ArticleDOI
TL;DR: In this article, a robust semi-implicit central partial difference algorithm for the numerical solution of coupled stochastic parabolic partial differential equations (PDEs) is described, which can be used for calculating correlation functions of systems of interacting stochiastic fields.

Journal ArticleDOI
TL;DR: In this paper, the authors report the creation and full determination of several quantum states of motion of a 9Be+ ion bound in a RF (Paul) trap, which is coherently prepared from an ion which has been initially laser cooled to the zero-point of motion.
Abstract: We report the creation and full determination of several quantum states of motion of a 9Be+ ion bound in a RF (Paul) trap. The states are coherently prepared from an ion which has been initially laser cooled to the zero-point of motion. We create states having both classical and non-classical character including thermal, number, coherent, squeezed, and ‚Schrodinger cat‘ states. The motional quantum state is fully reconstructed using two novel schemes that determine the density matrix in the number state basis or the Wigner function. Our techniques allow well controlled experiments decoherence and related phenomena on the quantum-classical borderline.

Journal ArticleDOI
TL;DR: In this article, a system comprising a cavity with a nonlinear medium of k-order and an external coherent field excitation is discussed. But the authors assume that the cavity field was initially in vacuum state.
Abstract: We discuss a system comprising a cavity with a nonlinear medium of k-order and an external coherent field excitation. We assume that the cavity field was initially in vacuum state. We show that for the case of weak external field our system behaves similarly to one described in finite-dimensional Hilbert space. Moreover, we perform numerical calculations simulating the dynamics of our system and compare the results with those of analytical attempts.

Journal ArticleDOI
TL;DR: In this article, the photon distribution function of a discrete series of excitations of squeezed coherent states is given explicitly in terms of Hermite polynomials of two variables, and the Wigner and the coherent-state quasiprobability are also presented in closed form through the Hermite priors and their limiting cases.
Abstract: The photon distribution function of a discrete series of excitations of squeezed coherent states is given explicitly in terms of Hermite polynomials of two variables. The Wigner and the coherent-state quasiprobabilities are also presented in closed form through the Hermite polynomials and their limiting cases. Expectation values of photon numbers and their dispersion are calculated. Some three-dimensional plots of photon distributions for different squeezing parameters demonstrating oscillatory behaviour are given.

Journal ArticleDOI
TL;DR: In this paper, optimal quantum control theory is applied to the quantum dissipative dynamics of systems linearly coupled to a Gaussian bath, which predicts the tailored light fields that best drive a system to a desired target.
Abstract: Optimal quantum control theory, which predicts the tailored light fields that best drive a system to a desired target, is applied to the quantum dissipative dynamics of systems linearly coupled to a Gaussian bath. To calculate the material response function required for optimizing the light field, the analytical solution is derived for the two-level Brownian harmonic oscillator model and the recently developed method for directly simulating the Gaussian force is implemented for anharmonic Brownian oscillators. This study confirms the feasibility of quantum control in favorable condensed phase environments and explores new quantum control features in the presence of dissipation, including memory effects and temperature dependence.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the destruction of quantum coherence by environmental influences, taking the damped harmonic oscillator and the dissipative two-state system as prototypical examples, and showed that the location of the coherent-incoherent transition depends to a large degree on the dynamical quantity under consideration.
Abstract: The destruction of quantum coherence by environmental influences is investigated taking the damped harmonic oscillator and the dissipative two-state system as prototypical examples. It is shown that the location of the coherent-incoherent transition depends to a large degree on the dynamical quantity under consideration.

Journal ArticleDOI
TL;DR: In this article, states with explicit quantum character, such as squeezed vacuum and bright squeezed light, as well as coherent states and incoherent superpositions of coherent states were generated and analyzed by tomographical methods.
Abstract: States with explicit quantum character, such as squeezed vacuum and bright squeezed light, as well as coherent states and incoherent superpositions of coherent states were generated and analysed by tomographical methods. Wigner functions, photon-number distributions, density matrices and phase distributions were reconstructed with high accuracy. Features such as photon number oscillations, sub-Poissonian and super-Poissonian photon statistics, bifurcations of the phase distribution, and loss of coherence were observed, demonstrating the usefulness of quantum state reconstruction as an analysing tool in quantum optics experiments.

Journal ArticleDOI
TL;DR: In this article, the authors introduce the negative binomial states with negative Binomial distribution as their photon number distribution, which are essentially the Perelomov's s u (1,1) coherent states via its Holstein-Primakoff realization.
Abstract: We introduce the negative binomial states with negative binomial distribution as their photon number distribution. They reduce to the ordinary coherent states and Susskind-Glogower phase states in different limits. The ladder and displacement operator formalisms are found and they are essentially the Perelomov's s u (1,1) coherent states via its Holstein-Primakoff realization. These states exhibit strong squeezing effect and they obey the super-Poissonian statistics. We discuss two methods to generate these states.

Journal ArticleDOI
TL;DR: In this paper, the path integral representation of the density matrix propagator of quantum Brownian motion is derived for times greater than the so-called localization time, where δ is the dissipation and T the temperature of the thermal environment.
Abstract: Using the path integral representation of the density matrix propagator of quantum Brownian motion, we derive its asymptotic form for times greater than the so-called localization time ({h_bar}/{gamma}kT){sup 1/2}, where {gamma} is the dissipation and T the temperature of the thermal environment. The localization time is typically greater than the decoherence time, but much shorter than the relaxation time {gamma}{sup {minus}1}. We use this result to show that the reduced density operator rapidly evolves into a state which is approximately diagonal in a set of generalized coherent states. We thus reproduce, using a completely different method, a result we previously obtained using the quantum state diffusion picture [Phys. Rev. D {bold 52}, 7294 (1995)]. We also go beyond this earlier result, in that we derive an explicit expression for the weighting of each phase space localized state in the approximately diagonal density matrix, as a function of the initial state. For sufficiently long times it is equal to the Wigner function, and we confirm that the Wigner function is positive for times greater than the localization time (multiplied by a number of order 1). {copyright} {ital 1997} {ital The American Physical Society}

Journal ArticleDOI
TL;DR: In this paper, it was shown that it is possible to produce superpositions of distinct coherent states in a cavity where the field is pumped by two-photon parametric amplification and simultaneously undergoes absorption by a beam of three-level atoms that travel through the cavity interacting with the cavity field.
Abstract: We show that it is possible to produce superpositions of distinct coherent states ~even or odd coherent states! in a cavity where the field is pumped by two-photon parametric amplification and simultaneously undergoes two-photon absorption by a beam of three-level atoms that travel through the cavity interacting with the cavity field. Previous studies modeled the absorber with an effective Hamiltonian without involving real atomic excitation or entanglement, a procedure justified only for weak coupling of the two-photon absorbing atoms. We examine the validity of this assumption by modeling the atomic absorber dynamics from the onset. In order to study the system numerically we make use of a Monte Carlo wave-function method in which the two-photon absorbing atoms can interact with the cavity and evolve with large Rabi angles. @S1050-2947~97!01405-4#

Journal ArticleDOI
TL;DR: In this article, the non-classical properties of Schrodinger cat states given as superpositions of two-mode SU(1, 1) and SU(2) coherent states were studied.
Abstract: We study the non-classical properties of Schrodinger cat states given as superpositions of two-mode SU(1, 1) and SU(2) coherent states. The SU(1, 1) and SU(2) coherent states themselves have strong non-classical properties and we find that these properties are enhanced at least for some superpositions. We propose a method of generating such states in the context of cavity quantum electrodynamics.

Journal ArticleDOI
TL;DR: In this article, a coherent state formulation of determinantal wavefunctions is proposed to describe the electronic degrees of freedom of the electron nuclear dynamics theory with a coherent phase space.

Journal ArticleDOI
TL;DR: The photon-number-bandwidth correlation of the emerging soliton produces squeezing in the photon number of the filtered soliton, and bandwidth oscillations caused by the interference of the soliton with the quantum-noise continuum give oscillations of the photon- number squeezing and prevent achievement of arbitrarily high values of squeezing through spectral filtering.
Abstract: We study the quantum fluctuations of an optical nonlinear Schrodinger soliton after spectral filtering. The photon-number–bandwidth correlation of the emerging soliton produces squeezing in the photon number of the filtered soliton. Bandwidth oscillations caused by the interference of the soliton with the quantum-noise continuum, however, give oscillations of the photon-number squeezing and, in addition, prevent achievement of arbitrarily high values of squeezing through spectral filtering.

Journal ArticleDOI
TL;DR: In this paper, the authors define a metric in the space of quantum states taking the Monge distance between corresponding Husimi distributions (Q--functions), which fulfills the axioms of a metric and satisfies the following semiclassical property: the distance between two coherent states is equal to the Euclidean distance between correspondences in the classical phase space.
Abstract: We define a metric in the space of quantum states taking the Monge distance between corresponding Husimi distributions (Q--functions). This quantity fulfills the axioms of a metric and satisfies the following semiclassical property: the distance between two coherent states is equal to the Euclidean distance between corresponding points in the classical phase space. We compute analytically distances between certain states (coherent, squeezed, Fock and thermal) and discuss a scheme for numerical computation of Monge distance for two arbitrary quantum states.

Journal ArticleDOI
TL;DR: In this paper, a model for quantum dots is proposed, in which the motion of a few electrons in a three-dimensional harmonic oscillator potential under the influence of a homogeneous magnetic field of arbitrary direction is studied.
Abstract: A model for quantum dots is proposed, in which the motion of a few electrons in a three-dimensional harmonic oscillator potential under the influence of a homogeneous magnetic field of arbitrary direction is studied. The spectrum and the wave functions are obtained by solving the classical problem. The ground state of the Fermi-system is obtained by minimizing the total energy with regard to the confining frequencies. From this a dependence of the equilibrium shape of the quantum dot on the electron number, the magnetic field parameters and the slab thickness is found.

Journal ArticleDOI
TL;DR: In this paper, the squeezed and rotated quadrature of an ion in a Paul trap is discussed in connection with reconstructing its quantum state using the symplectic tomography method, and the density matrices in the Fock basis are expressed explicitly in terms of these marginal distributions.