Showing papers on "Coherent states published in 1989"
TL;DR: The quantum group SU(2)q is discussed in this paper by a method analogous to that used by Schwinger to develop the quantum theory of angular momentum such theory of the q-analogue of the quantum harmonic oscillator, as is required for this purpose.
Abstract: The quantum group SU(2)q is discussed by a method analogous to that used by Schwinger to develop the quantum theory of angular momentum Such theory of the q-analogue of the quantum harmonic oscillator, as is required for this purpose, is developed
1,555 citations
TL;DR: This paper is an expository survey of results on integral representations and discrete sum expansions of functions in $L^2 ({\bf R})$ in terms of coherent states, focusing on Weyl–Heisenberg coherent states and affine coherent states.
Abstract: This paper is an expository survey of results on integral representations and discrete sum expansions of functions in $L^2 ({\bf R})$ in terms of coherent states. Two types of coherent states are considered: Weyl–Heisenberg coherent states, which arise from translations and modulations of a single function, and affine coherent states, called ’wavelets,’ which arise as translations and dilations of a single function. In each case it is shown how to represent any function in $L^2 ({\bf R})$ as a sum or integral of these states. Most of the paper is a survey of literature, most notably the work of I. Daubechies, A. Grossmann, and J. Morlet. A few results of the authors are included.
1,121 citations
TL;DR: In an open quantum system, dissipation can cause decorrelation on a time scale significantly shorter than the relaxation time which characterizes the approach of the system to thermodynamic equilibrium, and it is demonstrated that the density matrix decays rapidly toward a mixture of ``approximate eigenstates'' of the ``pointer observable,'' which commutes with the system-environment interaction Hamiltonian.
Abstract: The effect of the environment on a quantum system is studied on an exactly solvable model: a harmonic oscillator interacting with a one-dimensional massless scalar field. We show that in an open quantum system, dissipation can cause decorrelation on a time scale significantly shorter than the relaxation time which characterizes the approach of the system to thermodynamic equilibrium. In particular, we demonstrate that the density matrix decays rapidly toward a mixture of ``approximate eigenstates'' of the ``pointer observable,'' which commutes with the system-environment interaction Hamiltonian. This observable can be regarded as continuously, if inaccurately, monitored by the scalar field environment. Both because in a harmonic oscillator the state of the system rotates in the phase space and because the effective environment ``measurement'' is weak, the system, on the short ``collision'' time scale (1/\ensuremath{\Gamma}), maintains a coherence in this pointer observable on time scales of order [\ensuremath{\gamma}/\ensuremath{\Omega}ln(\ensuremath{\Gamma}/\ensuremath{\Omega}${)]}^{1/2}$ and on longer time scales settles into a mixture of coherent states with a dispersion approximately consistent with the vacuum state. The master equation satisfied by the exact solution differs from the other master equations derived both for the high-temperature limit and for T=0. We discuss these differences and study the transition region between the high- and low-temperature regimes. We also consider the behavior of the system in the short-time ``transient'' regime. For T=0, we find that, in the long-time limit, the system behaves as if it were subject to ``1/f noise.'' The generality of our model is considered and its predictions are compared with previous treatments of related problems. Some of the possible applications of the results to experimentally realizable situations are outlined. The significance of the environment-induced reduction of the wave packet for cosmological models is also briefly considered.
460 citations
TL;DR: In this article, the effects of squeezing on number states and on thermal field states are discussed using the second-order correlation functions, and the quasiprobability of the Wigner, Q, and positive P representations are calculated and compared for the squeezed states.
Abstract: Much attention has been given in the past to two classes of squeezed states: the squeezed vacuum and coherent states. Here we study the effects of squeezing on number states and on thermal field states. The statistical properties of these various squeezed states are discussed using the second-order correlation functions. The quasiprobabilities of the Wigner, Q, and positive P representations are calculated and compared for the squeezed states. The Glauber P representation for the squeezed thermal state explicitly shows the limit of its applicability. The photon number distributions of the squeezed number and squeezed thermal states are extensively discussed and new interference effects in phase space are shown to lead to highly structured number distributions.
237 citations
TL;DR: In the Jaynes-Cummings model with the intensity-dependent coupling interacting with the Holstein-Primakoff SU(1,1) coherent state the revivals of the radiation squeezing are strictly periodical for any value of initial squeezing.
Abstract: We show that in the Jaynes-Cummings model with the intensity-dependent coupling interacting with the Holstein-Primakoff SU(1,1) coherent state the revivals of the radiation squeezing are strictly periodical for any value of initial squeezing. The expression for the atomic population inversion exhibiting the exact periodicity of the population revivals is obtained.
144 citations
TL;DR: In this paper, even and odd coherent states are discussed and the change of these two effects and the amplitude-squared squeezing when the two states are displaced are studied. And the authors showed that the displaced even coherent state can exhibit amplitude-quare squeezing.
122 citations
TL;DR: It is shown that under certain circumstances a simple quantum harmonic oscillator driven by a quantum current evolves to unique pure states even if started as a mixed state, or more interestingly resemble macroscopic superpositions.
Abstract: We show that under certain circumstances a simple quantum harmonic oscillator driven by a quantum current evolves to unique pure states even if started as a mixed state. In various limits, these states exhibit nonclassical properties such as sub-Poissonian statistics, or more interestingly resemble macroscopic superpositions.
99 citations
TL;DR: In this article, a two-level atom with the radiation field is studied when the radiation is initially in a strongly squeezed coherent state and the mean, variance, and entropy for the photon-number distribution are calculated and found to show behavior similar to that of the atomic inversion.
Abstract: The Jaynes–Cummings interaction of a two-level atom with the radiation field is studied when the radiation is initially in a strongly squeezed coherent state. The dynamic response of the atomic inversion shows echoes after each revival when the squeezed coherent state exhibits an oscillatory photon-counting distribution due to the phase-space interference effect. The sensitivity of the dynamic behavior to approximations used in computing the atomic inversion is discussed. Comparison is made with the intensity-dependent interaction model of Buck and Sukumar [ Phys. Lett.81A, 132 ( 1981)]; this model does not exhibit echoes. The mean, variance, and entropy for the photon-number distribution are calculated and found to show behavior similar to that of the atomic inversion.
83 citations
01 Jan 1989
TL;DR: In this article, the effect of measurement on interference in Phase-Space was investigated and the effects of interference in phase space on the number of number-phase squeezed states were investigated.
Abstract: Quantum Noise Reduction in Optical Systems.- Laser Stabilization Using Squeezed Light.- Pulsed Squeezed Light.- Quantum Fluctuations in Optical Measurements.- Squeezing Thermal Microwave Radiation.- Classical and Quantum Statistics in Partition of Highly Degenerate Light.- Giant Quantum Oscillators from Rydberg Atoms: Atomic Coherent States and their Squeezing from Rydberg Atoms.- Quantum Statistical Properties of Strongly Driven Atoms Coupled to Frequency-Dependent Reservoirs.- Generation and Detection of Subpoissonian Fields in Micromasers.- Phase Space, Correspondence Principle and Dynamical Phases: Photon Count Probabilities of Coherent and Squeezed States via Interfering Areas in Phase Space.- The Effect of Measurement on Interference in Phase-Space.- Squeezing in Optical Bistability.- Squeezed-Light Generation in Optical Waveguides.- Generation of Number-Phase Squeezed States.- Quantum Optics of Dielectric Media.- Gravitational Wave Detection and Quantum Optics.- Subharmonic Generation and Squeezing in a Damped Oscillator.- Mechanisms for the Generation of Nonclassical Light.- Interferometric Measurements Beyond the Shot-Noise Limit.- Realization of Measurement and the Standard Quantum Limit.- The Correlated Spontaneous Emission Laser: Theory and Recent Developments.- Multiphoton and Fractional-photon Squeezed States.- Squeezing in Fourth-Order Parametric Downconversion.- Group photo.
83 citations
TL;DR: The semiclassical limit of the stationary Schr\"odinger equation in the coherent-state representation simultaneously for the groups ${W}_{1}$, SU(2), and SU(1,1) is analyzed.
Abstract: We analyze the semiclassical limit of the stationary Schr\"odinger equation in the coherent-state representation simultaneously for the groups ${W}_{1}$, SU(2), and SU(1,1). A simple expression for the first two orders for the wave function and the associated semiclassical quantization rule is obtained if a definite choice for the classical Hamiltonian and expansion parameter is made. The behavior of the modulus of the wave function, which is a distribution function in a curved phase space, is studied for the three groups. The results are applied to the quantum triaxial rotor.
80 citations
TL;DR: In this paper, the statistical properties of fields in SU(2) generalized coherent states built on the bosonic representation of the generators of SU (2) Lie algebra were investigated.
Abstract: We have investigated the statistical properties of fields in the SU(2) generalized coherent state built on the bosonic (Schwinger) representation of the generators of SU(2) Lie algebra. We have shown that there are sub-Poissonian photon statistics as well as anticorrelations. Schemes for the generation of the states under consideration are discussed. We show that in the relevant processes either fields that are highly sub-Poissonian can be generated or a field in one mode with sub-Poissonian statistics can be transformed into another field that also has sub-Poissonian statistics.
TL;DR: It is shown that, for a certain choice of this phase, ``coherent trapping'' occurs in two-level atoms, and in the case of spectra, for the same choice of the phase, instead of a three-peaked symmetric spectrum, the authors have an asymmetric two- peaked spectrum.
Abstract: Considering a system consisting of a two-level atom, initially prepared in a coherent superposition of upper and lower levels, interacting with a coherent state of the field, we show that the dynamics of the atom as well as the spectrum of the field are sensitive to the relative phase between the atomic dipole and the cavity field. It is shown that, for a certain choice of this phase, ``coherent trapping'' occurs in two-level atoms. In the case of spectra, for the same choice of the phase, instead of a three-peaked symmetric spectrum, we have an asymmetric two-peaked spectrum.
TL;DR: In this article, a method for calculating the s-parametrized quasiprobability distributions W (α, s ) of Cahill and Glauber for the damped Jaynes-Cummings model is outlined.
TL;DR: A lower bound for the total noise is derived that is an increasing function of nonclassical distance and can conclude that highly non classical states have large amplitude fluctuations.
Abstract: The total noise of a field state is a measure of the fluctuations of the field amplitude. It is a minimum for coherent states. As the behavior of a state becomes more nonclassical, its total noise increases. This is shown first for several specific types of nonclassical states, among them squeezed and sub-Poissonian states. These results are generalized by using nonclassical distance to measure how nonclassical a field state is. A lower bound for the total noise is derived that is an increasing function of nonclassical distance. From it one can conclude that highly nonclassical states have large amplitude fluctuations.
TL;DR: In this article, the authors introduced the concept of two-mode squeezing, in which the fluctuations in a system of two oscillators are tightly correlated, and showed that the existence of squeezing is demonstrated in normal mode coordinates representing motion of superpositions of the motion of the oscillators.
Abstract: In a squeezed state, the variance in one canonical variable may be suppressed below that normally associated with either the ground state or a coherent state, at the expense of an expansion in the variance of the conjugate variable. Squeezed states are usually discussed in the context of quantized light fields. The principal properties of squeezed states are demonstrated using the motion of quantum mechanical simple harmonic oscillators. The motion of a single oscillator is discussed to introduce the key concepts of squeezing, including quadrature operators, and the error contours of the Wigner function describing the quantum quasiprobability distributions in phase space of the oscillator motion. The main topic of two‐mode squeezing is then addressed, in which the fluctuations in a system of two oscillators are tightly correlated. The existence of squeezing is demonstrated in normal mode coordinates representing motion of superpositions of the motion of the two oscillators. The fluctuations within a single oscillator are shown to increase when squeezing increases in the normal modes, generating thermal noise in individual mode subsystems.
TL;DR: In this article, the formalism of thermo field dynamics is used to define a thermal coherent state, and thus calculate some correlation functions, and the relation of the thermal coherent states so defined to earlier definitions is briefly discussed.
TL;DR: These elliptic states are uniquely defined from symmetry considerations and are the coherent states of the SO(4) symmetry group of the Coulomb interaction in three dimensions and are superpositions of the usual spherical states with well-defined weights and phases.
Abstract: We show how to build atomic states that mimic the classical Bohr-Sommerfeld elliptic orbits with minimum quantum fluctuations. These elliptic states are uniquely defined from symmetry considerations. They are the coherent states of the SO(4) symmetry group of the Coulomb interaction in three dimensions and are superpositions of the usual spherical states with well-defined weights and phases. They can be experimentally produced from laser excitation of Rydberg atoms in crossed electric and magnetic fields. We finally indicate how to build Coulomb wave packets localized both in space and time.
TL;DR: In this article, the authors evaluated the coherent state path integral developed by Klauder for a chaotic system (the kicked rotator) and found that it provides an accurate time evolution of a wave function over a finite time period even for the chaotic system.
TL;DR: In this article, three characteristic functions are reviewed along with the quantum theory of linear systems and used to derive the P-representation, Wigner distribution and quasi-probability density of coherent states and squeezed states.
Abstract: Three characteristic functions are reviewed along with the quantum theory of linear systems and used to derive the P-representation, Wigner distribution and quasi-probability density of coherent states and squeezed states. The quasiprobability density is interpreted as the outcome of measurements utilising a beamsplitter with homodyne detection. The quasiprobability density concept is generalised and its interpretation in terms of a measurement is presented. The measurement utilises a beam splitter with one of its inputs in a squeezed state followed by two homodyne detectors.
TL;DR: In this paper, the feasibility of exciting correlated and coherent states in a Josephson junction is suggested, and the influence of an external current and of parametric buildup on the junction is discussed.
Abstract: Coherent and correlated states of a Josephson junction are constructed. Quantum current and voltage noises are calculated. The influence of an external current and of parametric buildup on the Josephson junction is discussed. The feasibility in principle of exciting correlated and coherent states in a Josephson junction is suggested.
TL;DR: In this article, a simple physical picture of light beams generated by the degenerate optical parametric oscillator operating below threshold is analyzed in terms of photoelectron counting sequences, and the dependence of these distributions on mean photon number inside the cavity and efficiency of detection is studied.
Abstract: Nonclassical light beams generated by the degenerate optical parametric oscillator operating below threshold are analyzed in terms of photoelectron-counting sequences. The positive-P representation is used to calculate the generating function for photoelectron statistics in a closed form. This generating function is used to derive expressions for the photoelectron-counting and waiting-time distributions. The dependence of these distributions on mean photon number inside the cavity and efficiency of detection is studied. The relationship between photoelectron-counting sequence and the photon emission sequence is used to present a simple physical picture of light beams produced by the degenerate parametric oscillator.
TL;DR: In this paper, the authors considered quantum-mechanically partially polarized light propagating through a Kerr-like medium and formulated the theory in terms of an effective Hamiltonian which is quartic with respect to the operators for two orthogonally polarized modes.
Abstract: We consider quantum-mechanically partially polarized light propagating through a Kerr-like medium. Using the usual form of the induced polarization P=A(E.E)E+B(E.E)E, the theory is formulated in terms of an effective Hamiltonian which is quartic in terms of the operators for two orthogonally polarized modes. Exact solutions in closed form for the Heisenberg equations of motion are obtained. These solutions are used to evaluate the physical behavior of various observables as the field propagates through a nonlinear medium. We also present explicit results for the time evolution of the input coherent and Fock states of the field. We show the generation of states that are macroscopic superposition of coherent states. We also find that if the input field is completely polarized, then due to quantum effects the output field becomes partially polarized. This is in contrast to the classical prediction and can have an important bearing on questions like topological phases of light propagating through a nonlinear medium. Numerical results for the energy in each mode, the correlation between two modes, and the higher-order correlations are presented. The input photon statistics is found to make a considerable difference in the dynamics.
TL;DR: In this article, the effects of coherence between the states of a two-level atom on the phenomenon of collapses and revivals in an undamped binomial state of the electromagnetic field are investigated.
Abstract: The effects of the coherence between the states of a two-level atom on the phenomenon of collapses and revivals in an undamped binomial state of the electromagnetic field are investigated. It is found that the Rabi oscillations exhibit qualitatively different behaviour for different phases of coherence between the levels. This behaviour in the binomial state of the field is in contrast with that in a coherent state field, in which case the Rabi oscillations are qualitatively the same for all values of the coherence between the two atomic levels.
TL;DR: In this article, the effects of vibronic coherence transfer induced by the heat bath on ultrafast time-resolved resonant light scattering (RLS) spectra are theoretically investigated within the master equation approach.
Abstract: Effects of vibronic coherence transfer induced by the heat bath on ultrafast time‐resolved resonant light scattering (RLS) spectra are theoretically investigated within the master equation approach. The vibronic coherence initially created by a coherent optical excitation transfers to other vibronic coherent states due to inelastic interactions between the vibronic system concerned (the relevant system) and the heat bath. The vibronic coherence transfer results in the quantum beats in the time‐resolved RLS spectra. The bath‐induced vibronic transition operator is derived in the double space representation of the density matrix theory. Model calculations of the femtosecond (fs) time‐resolved RLS spectra are performed to demonstrate the effects of the bath‐induced vibronic coherence transfer.
TL;DR: In this article, exact phase calculations for general squeezed states are presented for different phase definitions, using number-state expansions, and it is shown that the calculations based on measured-phase operator formalism leads to contrasting behavior compared with those based on the Susskind-Glogower, Lerner-Lynch, and Hermitian-phase-operator formalisms.
Abstract: Exact phase calculations for general squeezed states are presented. Results are given for different phase definitions, using number-state expansions. It is shown that the calculations based on the measured-phase-operator formalism leads to contrasting behavior compared with those based on the Susskind–Glogower, Lerner–Lynch, and Hermitian-phase-operator formalisms.
TL;DR: In this paper, it was shown that the conventional squeezed states of quantum optics, which can be thought of as generalized coherent states for the algebra SU(1,1), are dynamically generated by single-mode hamiltonians characterized by two-photon process interactions.
Abstract: The conventional squeezed states of quantum optics, which can be thought of as generalized coherent states for the algebra SU(1,1), are dynamically generated by single-mode hamiltonians characterized by two-photon process interactions. By the explicit construction of a (highly non-linear) faithful realization of the group $\mathscr G$ of automorphisms of SU(1,1), such hamiltonians are shown to be equivalent — up just to elements of $\mathscr G$ — to that describing quantum mechanically a damped oscillator.
TL;DR: In this paper, a generalization of the Perelomov procedure for the construction of coherent states is proposed, which is used to construct coherent states in the carrier spaces of unitary irreducible representations of groups G =S∅V, where V is a vector space and S⊂GL(V).
Abstract: A generalization of the Perelomov procedure for the construction of coherent states is proposed. The new procedure is used to construct systems of coherent states in the carrier spaces of unitary irreducible representations of groups G=S∅V, where V is a vector space and S⊂GL(V). The coherent states are shown to be labeled by the points in cotangent bundles T*O* of orbits O* of S in V*, the dual of V; it is proven that T*O* is a symplectic homogeneous space of G. The generalized procedure for the construction of coherent states presented in this paper is shown to encompass as special cases the constructions known in the literature for the coherent states of the Weyl–Heisenberg, the ‘‘ax+b,’’ and the Galilei and Poincare groups. Moreover, completely new sets of coherent states are constructed for the Euclidean group E(n), where the Perelomov construction fails.
TL;DR: For a damped oscillator forced by a time-dependent field, the exact wave function is obtained by three different methods: Path-integral, Second quantization and Dynamical invariant.
Abstract: : For a damped oscillator forced by a time-dependent field, the exact wave function is obtained by three different methods: (i) Path-integral, (ii) Second quantization and (iii) Dynamical invariant. The explicit form of the dynamical invariant involves a solution to a corresponding auxiliary equation. The coherent states, defined as eigenstates of a new destruction operator, form a nonorthogonal, over complete set and correspond to the minimum uncertainty states. These coherent states give the exact classical motion of the damped driven harmonic oscillator.
TL;DR: By using coherent-state path integrals, this work provides a derivation of a two-dimensional chiral boson action which is equivalent to a free Weyl fermion.
Abstract: By using coherent-state path integrals I provide a derivation of a two-dimensional chiral boson action which is equivalent to a free Weyl fermion.
TL;DR: In this paper, the quantum dynamics of time-dependent Hamiltonians of the kind H(t)=U(t)H(0)U(T)° are studied in the framework of generalized coherent states.
Abstract: The quantum dynamics of time‐dependent Hamiltonians of the kind H(t)=U(t)H(0)U(t)° is studied in the framework of generalized coherent states. It is shown that the quantum and the classical dynamics are isomorphic and that the phase of ‖ψ(t)〉 is simply the classical action. In adiabatic approximation it is easy to extract Berry’s phase from this. A discussion of generalized coherent states (CS’s) necessary to deal with excited states is given; in particular for SU(2), SU(1,1) and E(2) their structure is completely characterized, showing that the deep connection with geometric quantization extends to these generalized CS’s. This technique may be employed to estimate higher‐order correction to the adiabatic approximation.