Showing papers on "Coherent states published in 1978"
TL;DR: The quantum analog of the classical paraxial diffraction theory for quasimonochromatic scalar waves is developed, which describes the propagation of arbitrary quantum states as a boundary-value problem suitable for communication system analysis.
Abstract: Recent theoretical work has shown that novel quantum states, called two-photon coherent states (TCS), have significant potential for improving free-space optical communications. The first part of a three-part study of the communication theory of TCS radiation is presented. The issues of quantum-field propagation and optimum quantum-state generation are addressed. In particular, the quantum analog of the classical paraxial diffraction theory for quasimonochromatic scalar waves is developed. This result, which describes the propagation of arbitrary quantum states as a boundary-value problem suitable for communication system analysis, is used to treat a number of quantum transmitter optimization problems. It is shown that, under near-field propagation conditions, a TCS transmitter maximizes field-measurement signal-to-noise ratio among all transmitter quantum states; the performance of the TCS system exceeds that for a conventional (coherent state) transmitter by a factor of N_{s} + 1 , where N_{s} is the average number of signal photons (transmitter energy constraint). Under far-field propagation conditions, it is shown that use of a TCS local oscillator in the receiver can, in principle, attenuate field-measurement quantum noise by a factor equal to the diffraction loss of the channel, if appropriate spatial mode mixing can be achieved. These communcation results are derived by assuming that field-quadrature quantum measurement is performed. In part II of this study, photoemissive reception of TCS radiation will be considered; it will be shown therein that homodyne detection of TCS fields can realize the field-quadrature signal - to-noise ratio performance of part I. In part III, the relationships between photoemissive detection and general quantum measurements will be explored. In particular, a synthesis procedure will be obtained for realizing all the measurements described by arbitrary TCS.
403 citations
TL;DR: In this paper, the authors define coherent states for general potentials, requiring that they have the physically interesting properties of the harmonic-oscillator coherent states, and show that they obey a quantum approximation to the classical motion.
Abstract: We define coherent states for general potentials, requiring that they have the physically interesting properties of the harmonic-oscillator coherent states. We exhibit these states for several solvable examples and show that they obey a quantum approximation to the classical motion.
212 citations
TL;DR: The transition from dynamical (regular) to stochastical behaviour in nonlinear quantum systems is considered in this paper, based on the determination of a discrete time mapping of the creation and annihilation operators in the Heisenberg picture and the projection of this mapping on the phase space of coherent states.
Abstract: The transition from dynamical (regular) to stochastical behaviour in nonlinear quantum systems is considered. A method of describing the stochastical instability is proposed for quantum systems. The method is based on the determination of a discrete time mapping of the creation and annihilation operators in the Heisenberg picture and the projection of this mapping on the phase space of coherent states. The condition that the phase correlation vanishes is found for a nonlinear quantum oscillator perturbed by the external periodical force, which is a linear combination of delta pulses. The kinetic equation describing the relaxation of the system in the space of c-numbers formed by the projections of the operators is derived.
204 citations
162 citations
TL;DR: In this paper, the authors derived reduced equations of motion for simple quantum systems which are strongly driven by an external field and are modulated stochastically by a coupling to a bath.
Abstract: We derive reduced equations of motion for simple quantum systems which are strongly driven by an external field and are modulated stochastically by a coupling to a bath. In the derivation we make use of the cumulant-expansion method of Kubo using two different time-ordering prescriptions. We demonstrate how the choice of the ordering prescription is related to the statistical properties of the bath, once the cumulant expansion is truncated. Our equations of motion are valid for arbitrary time scale for the motions of the bath relative to those of the system, and they change smoothly from the static to the Markov (motional narrowing) limit. As examples, we consider the problems of a randomly modulated and driven harmonic oscillator and a modulated and damped two-level system. In the Markovian limit both ordering prescriptions yield Bloch-type equations of motion; in general, however, the driving and modulation interfere and the different statistical properties of the bath, as determined by the two truncated ordering prescriptions, lead to different results.
124 citations
TL;DR: In this article, the master equation for cooperative fluorescence was solved in the limit J → ∞ without operator factorisation assumptions, using the atomic coherent state representation, in the special case of only collective damping.
59 citations
TL;DR: In this paper, the concept of loss energy states is introduced and the method of constructing the energy states for general multidimensional quadratic nonstationary quantum systems is briefly discussed.
Abstract: The concept of loss energy states is introduced. The loss energy states of the quantum harmonic damping oscillator are considered in detail. The method of constructing the loss energy states for general multidimensional quadratic nonstationary quantum systems is briefly discussed.
57 citations
TL;DR: The ground-state energy of the Lipkin-Meshkov-Glick hamiltonian was estimated by the Bogoliubov-Lieb inequalities which involve the atomic coherent states.
55 citations
TL;DR: In this article, the eigenfunctions of the harmonic quadrupole collective Hamiltonian were studied in both the lab and intrinsic systems of references, using the technique of projective coherent states and the theory of harmonic polynomials in collective coordinates.
40 citations
39 citations
TL;DR: In this article, a consistent formalism for the treatment of temporal atomic or molecular coherence in multiphoton absorption was developed, which is fully quantum mechanical under the assumption that the exciting laser fields are well described by coherent states.
Abstract: We develop a consistent formalism for the treatment of temporal atomic or molecular coherence in multiphoton absorption. The formalism is fully quantum mechanical under the assumption that the exciting laser fields are well described by coherent states. We make use of the language and methodology of resonance physics to the extent possible, but deliberately avoid the rotating‐wave approximation, and do not restrict the allowed atomic states to be finite in number or the electric field strengths to be small in magnitude. For compactness in the presentation only electric dipole transitions are considered. As all of the transitions, both stimulated and spontaneous, are due to the activation of quantum mechanical dipoles, it is most efficient to construct the formalism so that it emphasizes the role of dipole operators, and we do this. The one strong restriction imposed here, but avoided in a following paper, is to consider only multiphoton transitions that have one resonance between initial and final states and no intermediate resonance. We describe, in effect, the time dependences associated with the early multiphoton absorption calculations of Bebb and Gold.
CERN1
TL;DR: In this paper, the problem of mass singularities was studied using the formalism of coherent states and the introduction of new states which account for both soft and hard radiation effects provided one with matrix elements which are free from infra-red and mass singularity at the leading logarithmic approximation.
01 Jan 1978
TL;DR: The relation of classical and quantum theories, and the use of semi-classical approximations in quantum problems are topics that pervade all branches of physics Continuous representations, which are generalizations of coherent states, are ideally suited for the formulation of quantum theory, especially for phase-space, and related, formulations.
Abstract: The relation of classical and quantum theories, and the use of semi-classical approximations in quantum problems are topics that pervade all branches of physics Continuous representations, which are generalizations of coherent states, are ideally suited for the formulation of quantum theory, especially for phase-space, and related, formulations In addition, it is particularly natural to formulate the path integral in terms of continuous representations Examples and applications of this approach are presented
TL;DR: In this article, the authors construct soliton states as quantum corrections to the coherent states constructed from classical solutions of nonlinear field equations, and apply the corresponding field operator applied to the vacuum state to discuss physical features of the (one soliton plus various mesons) states.
TL;DR: In this paper, the second harmonic and subharmonic properties of the Fokker-planck equation are investigated on the basis of the coherent state technique, making use of coherent state techniques.
Abstract: The statistical properties of the second harmonic and subharmonic are investigated on the basis of the generalized Fokker-Planck equation making use of the coherent state technique. An iterative procedure of solving the Fokker-Planck equation is adopted making it possible to obtain some recursion equations, particularly two iterations are explicitly performed providing approximate solutions for the normal and antinormal characteristic functions. Higher-order corrections to the superposition of coherent and chaotic fields are found in the subharmonic mode or if the coupling of modes is taken into account. Earlier results for the anticorrelation effect are rederived, the reservoir effect is obtained and the related problems of the existence of the Glauber-Sudarshan quasidistribution are discussed.
TL;DR: In this paper, the authors sketch the proof of a rigorous master equation for a model of optical bistability and obtain its Fokker Planck equation in the coherent state representation.
TL;DR: In this paper, the construction of coherent states which are diagonal in a conserved charge and their unique characterization are discussed, and it is shown that a condition given by Glauber for a state to remain coherent with the time development can be extended to the present case.
TL;DR: In this paper, the two-photon coherent states described by Yuen are studied with respect to their spatial behavior. And the fluctuations of the field strength and the minimum uncertainty state character are analyzed.
TL;DR: In this article, it was shown that the expansion of harmonic oscillator states in discrete coherent states on a von Neumann lattice leads to relationships between lattice sums and expansion coefficients of the Weierstrass σ function.
Abstract: The expansion of harmonic oscillator states in discrete coherent states on a von Neumann lattice leads to relationships between lattice sums and expansion coefficients of the Weierstrass σ function. It is shown that these relationships can be generalized to arbitrary lattices. Some interesting identities are obtained between infinite sums of different convergence rates.
TL;DR: In this paper, the dynamics of the Dickemaser model is considered when the phase transition to a spontaneous coherent state takes place and an expression for the atomic correlation function is found which shows dynamic peculiarities of the spontaneous coherent states in the form of a Goldstone mode and a temperature dependence of the resonance frequency of the system.
Abstract: The dynamics of the Dicke-maser model is considered when the phase transition to a spontaneous coherent state takes place. In the molecular field approximation an expression for the atomic correlation function is found which shows dynamic peculiarities of the spontaneous coherent state (SCS) in the form of a Goldstone mode and a temperature dependence of the resonance frequency of the system. Also the photon correlation function is obtained which consists of two parts in the SCS. The first part, which is coherent and proportional to the number of the atoms, has a pole Ω = 0 . An ambiguity caused by this pole explains the SCS phase transition as the spontaneous appearance of the coherent state of the radiation field. The second uncoherent part is responsible for the dynamic properties of the radiation field into the resonance cavity. From a physical point of view the phase transition to the SCS is displayed by the spontaneous appearance of a constant transverse field with simultaneous transverse dipolar polarization of the atoms. By a simple decoupling of the equations of motion the existence of a soft mode is shown for T ⩾ Tinc
TL;DR: In this paper, a method for calculating the number generating function of a harmonic oscillator density matrix directly from the quantum characteristic function is presented, which is used to interpret thermal noise in a model for an optical detector.
Abstract: A method is found for calculating the number generating function of a harmonic oscillator density matrix directly from the quantum characteristic function. This technique is used to interpret thermal noise in a model for an optical detector. The results clearly reveal an earlier misinterpretation and emphasise that the terminal noise is a statistically independent amplitude in the detector/harmonic oscillator which is superposed with an amplitude having the same statistical nature as the incident optical field.
TL;DR: In this paper, a first order perturbation solution for a system of 2m, unequal mass, coupled oscillators perturbed by anharmonic terms of homogeneous power 4p of the position variables in the coherent state representation was obtained.
Abstract: We obtain a first order perturbation solution for a system of 2m, unequal mass, coupled oscillators perturbed by anharmonic terms of homogeneous power 4p of the position variables in the coherent state representation.
TL;DR: In this paper, the energies of the odd-spin negative parity bands are interpreted as the lowest eigenvalues of a quadrupole-octupole Hamiltonian in a space which is the direct product of the ground band and one octupole phonon spaces.
Abstract: The energies of the odd-spin negative parity bands are interpreted as the lowest eigenvalues of a quadrupole-octupole Hamiltonian in a space which is the direct product of the ground band and one octupole phonon spaces. The ground band states are obtained by the projection technique from a coherent state. Alternatively the negative parity levels are treated perturbatively. Applications to 150Sm, 152Gd and 238U show a good agreement with experiment. Also the BE1/BE2 ratios are estimated and compared with the available data.
TL;DR: In this article, the Compton scattering of electrons from a coherent photon beam is considered and it is shown that the electrons can scatter with only a small probability (per scattered electron) of disturbing the coherence of the ongoing incident beam.
TL;DR: In this article, a new approach to Heisenberg ferromagnet using the spin coherent state representation is developed, which has noad hoc assumptions and does not use any boson representation.
Abstract: A new approach to Heisenberg ferromagnet using the spin coherent state representation is developed. The differential operator representation of spin angular momentum operators is used to derive thec-number analogs of the basic quantum mechanical equations, viz., the Schrodinger, Bloch and Liouville equations for the Heisenberg ferromagnet. As an important illustration of our formulation, which has noad hoc assumptions and does not use any boson representation, the excitation spectrum for one, two and three spin waves is obtained. In these cases it is also shown that eigenvalue spectrum can be obtained by completely ignoring the kinematical interactions.
TL;DR: In this paper, it is shown that the dynamics of the time-dependent phase-space probability densities is again representable in the form of a stochastic process, and the correspondence rule relating quantum-mechanical observables to ordinary functions in phase space is obtained.
Abstract: For physical systems with Hamiltonians analytic in the position and momentum operators the diagonal matrix elements of the density operator in the coherent state representation may be considered as a phase‐space probability measure in the stochastic formulation of quantum mechanics. The correspondence rule relating quantum‐mechanical observables to ordinary functions in phase space is obtained. It is shown that the dynamics of the time‐dependent phase‐space probability densities is again representable in the form of a stochastic process.
TL;DR: In this paper, the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states was investigated and a new class of discrete diagonal representations was discovered.
Abstract: In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.
TL;DR: In this paper, it was shown that the condition given by Glauber for a state to remain coherent with time development is necessary and sufficient, and that it is not sufficient.
TL;DR: In this article, the energy level of an anharmonic oscillator with the anharmonicity lambda x2k was obtained by the coherent states method, and the asymptotic behavior of an energy level with the lambda x 2k was analyzed.
Abstract: The asymptotic behaviour of an energy level of the anharmonic oscillator with the anharmonicity lambda x2k was obtained by the coherent states method.