Showing papers on "Coherent states published in 1981"
TL;DR: In this paper, a model consisting of a single two-level atom or spin interacting with a single mode of the quantized radiation field in the dipole approximation, the mode being initially in an arbitrary coherent state of excitation, was described.
Abstract: We describe the temporal behavior of the dynamic elements of an exactly soluble quantum model The model consists of a single two-level atom or spin interacting with a single mode of the quantized radiation field in the dipole approximation, the mode being initially in an arbitrary coherent state of excitation We give new long-time numerical and closed-form approximate analytic solutions for the expectation values of the atomic dipole moment and the difference in population of the two atomic levels in the rotating wave approximation The atomic dipole-dipole correlation function is calculated All of the results are obtained without semiclassical or decorrelation approximations Unusual features found in the temporal behavior of this lossless model problem are ''collapse,'' ie, episodic nonexponential damping of both the atomic inversion and dipole moment, and two kinds of ''revival'' or partial recorrelation, in the dynamic evolution, during which the initial state is nearly recovered We give analytic formulas for the collapse function, for both of the revival times, and for the envelope of the revival maxima Some remarks are made about the nature of irreversibility in this exactly soluble and loss-free model
469 citations
TL;DR: The relationship between the atomic coherent-state representation of Arecchi et al. as mentioned in this paper and the state multipoles is established, and a theory of generalized phase-space distributions for angular momentum (collective atomic) systems is developed.
Abstract: The relationship between the atomic coherent-state representation of Arecchi et al. [Phys. Rev. A 6, 2211 (1972)] and the state multipoles is established. The state multipoles are used to develop a theory of generalized phase-space distributions for angular momentum (collective atomic) systems. The general theory for angular momentum systems is shown to have many features in common with the general theory for boson systems [Phys. Rev. D 2, 2161 (1970)]. These generalized phase-space distributions contain as a special case the coherent-state representation of Arecchi et al. The applications of the generalized phase-space distributions and state multipoles to the dynamical problems and to the calculation of multitime correlations are given. State-multipole techniques are used to give a brief discussion of the master equation describing cooperative resonance fluorescence.
257 citations
TL;DR: In this article, a nonlinear dissipative evolution model was proposed for the spin-1/2 and damped harmonic oscillator, and it was shown that the coherent states remain coherent and evolve as in the corresponding classical problem.
Abstract: The author has considered a nonlinear dissipative evolution equation that generalises the Schrodinger equation. In the corresponding evolution all the stationary states of the usual Schrodinger equation have a behaviour of semistable limit cycles, except the ground state which is stable. The model is applied to the spin-1/2 and to the damped harmonic oscillator. For the latter it is shown that the coherent states remain coherent and evolve as in the corresponding classical problem.
129 citations
TL;DR: In this article, a new technique was developed to generate semiclassical wave functions using only information already available from a standard SDF quantization of a system using linear superpositions of Gaussian coherent states that lie along quantizing classical trajectories.
Abstract: A new technique is developed to generate semiclassical wave functions The method uses only information already available from a standard semiclassical quantization of a system Linear superpositions of Gaussian coherent states that lie along quantizing classical trajectories are used, with phases given by the action integrals plus a Maslov‐type correction Wave functions generated in this way suffer from none of the problems with caustics that primitive semiclassical wave functions encounter The semiclassical wave functions are convenient for subsequent use in applications, eg, molecular spectra By generating wave functions for several simple systems, we show that under most circumstances these wave functions are very accurate approximations to the true quantum states
74 citations
TL;DR: In this paper, the problem of a harmonic oscillator with varying mass parameter is reduced by canonical transformation to the corresponding constant mass problem and is solved in the case of an exponentially decaying mass.
Abstract: The problem of a harmonic oscillator with varying mass parameter is reduced by canonical transformation to the corresponding constant mass problem and is solved in the case of an exponentially decaying mass. The constructed canonical Hamiltonian has time-independent eigenvalues and eigenvectors. The cases of undercritical and overcritical damping are considered in detail. The Green function is calculated and the behaviour of coherent states is discussed. The theory is related to the case of a cavity oscillator with a decaying field as in threshold laser operation. In particular, the energy of the field is considered.
73 citations
TL;DR: In this paper, the authors apply the techniques of canonical transforms to equations of the type (A(t)P2 +B(t){IPQ + UPI+ C(t),02 +D(t,Q +E(t)/P +F(t))I)f(q, t) = -iat,(q, t), where 0 and P are the quantum position and momentum operators.
Abstract: We apply the techniques of canonical transforms to equations of the type (A(t)P2 +B(t){IPQ + UPI+ C(t)02 +D(t)Q +E(t)P +F(t)I)f(q, t) = -iat,(q, t), where 0 and P are the quantum position and momentum operators. The time-dependent parameters of the W A SL (2, R) evolution operator are found through linear differential equations. In terms of these we give explicitly the Green's function, all separating coordinates and similarity solutions of the equation. We analyze the behavior of Gaussian and coherent-state initial conditions in closed form and present a new interpretation of all the Lewis-Riesenfeld constants of motion. 1. Introduction. There has been sustained interest in the description of quantum systems with time-dependent Hamiltonians. These systems have been used to model, for example, the motion of charged particles in time-dependent electromagnetic fields and coherent states in lasers. (See the list of references given in (3) and (11).) Gunther (5), (6) and Leach (9)-(14) have used time-dependent canonical trans- formations to reduce some of the above problems to time-independent ones, mainly for classical mechanics. They have been able to extend their methods to quantum systems for the cases when the canonical transformation is linear and real. In quantum mechanics, one has to be aware (9), (10) that not all Hamiltonians can be mapped meaningfully into each other, not even all quadratic ones: there exist distinct orbits in the vector space of the latter under the action of real linear canonical transformations. These orbits are characterized by (among other things) the spectrum of the operators in each equivalence class. Here, we take up their suggestion that the techniques of canonical transforms which we developed in (19), (20), (22), (24), (25) can be used to extend and simplify the analysis of differential equations of the type (l.l1a) H(t)o(q, t) =-iato(q, t), q, t (- ,
67 citations
TL;DR: In this article, the authors considered the Bargmann or analytic function description of the Bose system and derived the transformation functions relating this description to the energy, position, and momentum eigenstates.
Abstract: The energy, position, and momentum eigenstates of a para‐Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para‐Bose system. This brings in, in a natural way, the coherent states ‖z;α〉 defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ‖z;α〉〈z;α‖ and the other containing the pseudodiagonal basis ‖z;α〉〈−z;α‖. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible α dependence of this minimum value is considered.
58 citations
TL;DR: In this article, a boson model for the major collective bands based on the coherent state formalism is applied to the shape transitional Pt isotopes 190 and 192, and a very reasonable description of both spectra and the electromagnetic quadrupole transition rates is obtained.
47 citations
TL;DR: The time evolution of harmonic oscillator coherent states (HOCSs) in symmetrical and nonsymmetrical nonharmonic potentials was studied numerically in this article, where the potentials were modeled with an ansatz V(e, q) = (1−e) VHO+e+e, vNH, where VHO is the harmonic oscillators potential and VNH is chosen as a convenient Morse oscillator (nonsymmetrical) or as a negative Gaussian (symmetrical) so that the potential near the minimum is not
Abstract: The time evolution of harmonic oscillator coherent states (HOCS’s) (displaced ground state wave functions) in symmetrical and nonsymmetrical nonharmonic potentials is studied numerically. The potentials were modeled with an ansatz V(e, q) = (1−e) VHO+e VNH, where VHO is the harmonic oscillator potential and VNH is chosen as a convenient Morse oscillator (nonsymmetrical) or as a negative Gaussian (symmetrical) so that the potential near the minimum is not distorted. The initially well located HOCS’s decay within a medium time scale of 5–100 classical oscillations to a wave packet which is delocalized in the position area of the potential well between the classical turning points. The time period up to this delocalization is designed as quasidecay time τQ, and it is demonstrated with some examples that in the symmetrical potentials the HOCS is refocused after a period of τR = 8τQ, while, as a rule, in the nonsymmetrical potential the recurrences need much longer time and could not be observed in the time sc...
39 citations
TL;DR: In this paper, a relationship between the WKB approximation and the definition of the minimum-uncertainty coherent states is established, in terms of the ''natural'' quantum operators, which connect only adjacent energy eigenstates.
Abstract: The minimum-uncertainty coherent states empirically provide an approximation to the motion of a classical particle. This can be understood conceptually. One can obtain a relationship between the WKB approximation and the definition of the minimum-uncertainty coherent states. This definition is in terms of the ''natural'' quantum operators, which connect only adjacent energy eigenstates. The classical form of these operators is also related to the WKB approximation. In the Appendix we comment on the origin of ''exact'' WKB results.
39 citations
TL;DR: In this article, a method of deriving the equations for physical average values is proposed in the form of ħ orders expansion, based on c -number projection of Heisenberg equations on a coherent states basis.
TL;DR: In this paper, the semiclassical approximation of the propagator for the spin system is investigated, and a closed form for the propagators in the curved phase space is obtained.
Abstract: Starting with path integrals in the SU(2) coherent state representation, the semiclassical approximation of the propagator for the spin system is investigated. By extending the idea of the semiclassical expansion method, which was developed in the usual phase‐space path integrals, to the path integrals in the curved phase space, which is characteristic of the SU(2) coherent states, we obtain a closed form for the semiclassical propagator. As an application, we discuss the semiclassical quantization condition for the spin system.
TL;DR: In this article, a coherent state representation valid even near the singularity is constructed for each mode of a quantized scalar field in a classical spatially homogeneous anisotropic background cosmology.
Abstract: A coherent-state representation valid even near the singularity is constructed for each mode of a quantized scalar field in a classical spatially homogeneous anisotropic background cosmology. The stress-energy tensor expectation values are computed in a coherent state and shown to be classical except for zero-point-energy terms. The self-consistent problem of a quantized scalar field in a changing background metric is discussed. The scalar field can also be described by a density matrix rather than a pure state. The density matrix is then used to determine expectation values. The density matrix need not be a thermal distribution although such a choice is reasonable in a realistic model. Temperature estimates are made using dimensional analysis.
TL;DR: In this article, it was shown that the counter-example to the non-abelian Bloch-Nordsieck conjecture in order α s 2 is avoided at the cross section level if the initial st prepared according to the coherent state approach for treatment of the infrared region of nonabelian gauge theories.
TL;DR: In this paper, the authors extended the idea of Kulish and Faddeev for treating asymptotic dynamics in QED by a deductive construction of asymPTotic states corresponding to the asymptic behavior of the hamiltonian operator for | t |→∞, in the interaction representation, to provide a more complete analysis of the combinatorial structure of the approximate structure obtained by the analogous construction in QCD.
TL;DR: In this paper, a formula connecting any wave function in the kq representation with the corresponding amplitudes of the state on von Neumann lattices of states is derived, which is used for establishing a possible interpretation for these amplitudes, for obtaining linear relationships between them, and for finding sum rules for the squares of their absolute values.
Abstract: A formula is derived connecting any wave function 〈k,q‖f〉 in the kq‐representation with the corresponding amplitudes of the state ‖f〉 on von Neumann lattices of states. The formula is used for establishing a possible interpretation for these amplitudes, for obtaining linear relationships between them, and for finding sum rules for the squares of their absolute values, and other related sum rules. It can also be used for establishing completeness criteria for the lattices of states and for defining a modified Hilbert space in which they become strictly complete. Particular attention is given to the coherent state lattice, but the discussion is extended to von Neumann lattices generated from an arbitrary state. Lattices generated from harmonic oscillator states are studied explicitly, and shown incidentally to lead to a wealth of summation expressions for Laguerre polynomials.
TL;DR: In this article, the authors have shown that phonon coherent states are involved in electronic absorption and emission of light and in non-radiative decay of molecules in gases and of centers in solids.
TL;DR: Quasicoherent states, previously defined for bosons with SU(2) gauge charge and no other degree of freedom, are now defined for the general (field-theoretical) case.
Abstract: Quasicoherent states, previously defined for bosons with SU(2) gauge charge (and no other degree of freedom), are now defined for the general (field-theoretical) case. The coherent states thus constructed form a complete basis in the Fock space. They transform according to irreducible representations of the SU(2) group and are at the same time eigenstates of isosinglet pair and isosinglet three-particle annihilation operators. Some physical applications are indicated in the contexts of multiple particle production and gluon bremsstrahlung by a quark line in ${e}^{+}{e}^{\ensuremath{-}}$ annihilation.
TL;DR: In this article, it was shown that for atoms and molecules the partition function of Thomas-Fermi theory becomes exact in the limit Z → ∞, in the appropriate scaling.
TL;DR: In this article, a quantum mechanical formalism of collective motion is proposed by using the idea of path integral method, where the propagator joins the many-body state vectors parametrized by complex collective parameters.
Abstract: A Quantum mechanical formalism of collective motion is proposed by using the idea of path integral method. Time evolution of many· body system is described by the propagator which joins the many-body state vectors parametrized by complex collective parameters. A general form of path integral representation for the propagator is derived in the complex parameter space. In particular the case of the coherent state representation is discussed in detail. It is pointed out that the time-dependent variation principle and especially the time dependent Hartree-Fock are naturally obtained as a classical limit.
TL;DR: In this article, a classical hamiltonian is constructed using coherent states parametrized in terms of five coordinates and their conjugate momenta using a Bohr-Sommerfeld type requantization condition.
TL;DR: In this article, the degenerate two-photon emission process is treated on the basis of quantum theory and solutions in short time approximation are given, neglecting relaxation mechanisms, and relevant quantities such as the mean photon number, second order correlation, field fluctuations and the uncertainty product are analyzed.
TL;DR: In this paper, the authors used the minimum uncertainty wave packet model to describe the relaxation of the initially prepared state of a material in the presence of a laser field, where the material states are expressed as wave packets formed from those special collective states that couple with the radiation field.
Abstract: The formalism of collective (Dicke‐like) states and operators is used to describe the relaxation of the initially prepared state of a material in the presence of a laser field. The material states are shown to be expressible as minimum uncertainty wave packets formed from those special collective states that couple with the radiation field. It is shown that these coherent states of matter exhibit all the features that are usually attributed to ensemble averages of two‐level molecules in a conventional statistical picture. However, there are new features in the quantum mechanical model when there are correlations among the molecules in the ensemble. The loss of minimum uncertainty characteristics of the wave packet correspnds to the transverse (T2) relaxation of the statistical model. Different types of T2 processes can be defined corresponding to the decay of different orders of coherence of the wave packet. Only for the case that the system decays in all orders of coherence do the quantum and statistical...
TL;DR: In this article, the statistics of pure quantum states of the harmonic oscillator are separated into a quantum mechanical and a classical part by associating a classical analog with each quantum state.
Abstract: The statistics of pure quantum states of the harmonic oscillator is separated into a quantum mechanical and a classical part by associating a classical analog with each quantum state. Several types of states are considered and it is shown that all pure states of the same average energy are equally close to their classical analogs.
TL;DR: In this paper, it was shown that unless the transmitted (input) state is a Glauber coherent state, the received (output) state will be a statistical mixture of states.