Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Phase properties of a damped anharmonic oscillator

Ts. Gantsog, R. Tanaś

Published Aug 1, 1991• 40 citations
Publisher

Abstract

Phase properties of a damped anharmonic oscillator are studied within the Hermitian phase formalism of Pegg and Barnett. Exact analytical formulas for the phase distribution function, the expectation value and variance of the phase operator, and the expectation value and variance of the cosine of the phase operator are obtained assuming the zero-temperature reservoir and a coherent initial state of the system. It is shown that quantum periodicity in the evolution of phase quantities is destroyed by damping. The effect of damping on the formation of discrete superpositions of coherent states is discussed. A comparison is made between different phase approaches.

DOI
10.1103/physreva.44.2086

Related papers

Phase Properties of Self-squeezed States Generated by the Anharmonic Oscillator

Ts. Gantsog, R. Tanaś

The phase properties of the self-squeezed states generated during the evolution of the anharmonic oscillator are discussed from the point of view of the new phase formalism of Pegg and Barnett. The phase distribution, the expectation values and the variances of the Hermitian phase operator are obtained and their evolution illustrated graphically. The mean values for the phase cosine and sine functions as well as their variances are also calculated. The results are compared to the Susskind-Glogower formalism results and the results based on the measured phase concept. The relation between squeezing and the phase properties of the field is discussed briefly.

Journal of Modern Optics•Jun 1, 1991•19 citations

Discrete superpositions of coherent states and phase properties of the m-photon anharmonic oscillator

Małgorzata Paprzycka, R. Tanaś

The formation of discrete superpositions of coherent states via the unitary evolution of the m-photon anharmonic oscillator is studied. Exact analytical formulae for the superposition coefficients are obtained. It is shown that, in contrast to the two-photon anharmonic oscillator, for m>2 the superposition components enter the superposition with different amplitudes. The Pegg-Barnett phase formalism is used to calculate the phase distributions for the resulting states and to visualize their symmetry.

Quantum Optics Journal of the European Optical Society Part B•Oct 1, 1992•31 citations

Phase properties of excited coherent states

Ravinder Nath, Satish Kumar Muthu

The phase properties of states generated by excitations on a coherent state have been studied by evaluating the expression for the phase probability distribution, using the recent formalism of Pegg and Barnett in which the existence of a Hermitian optical phase operator has been shown. This distribution has been further used to evaluate the variance of the phase operator and the number - phase uncertainty product.

Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Aug 1, 1996•8 citations

Creating multiphase coherent states in a damped anharmonic oscillator

Martina Brisudová

We elicit an analytic approximation of the Q function of a damped anharmonic oscillator which is initially in a coherent state. We start with a Q function obtained by using a solution of the master equation. We find that multiphase coherent states can be observed in a damped anharmonic oscillator and determine the range of parameters for which it is possible.

Physical Review A•Aug 1, 1992•5 citations

Study of Certain Aspects of Anharmonic, Time-Dependent and Damped Harmonic Oscillator Systems

Subir Kumar Bose, U. B. Dubey, N. Varma

The present review is devoted to the study of certain aspects of anharmonic, time-dependent and damped oscillator(s) system using different theoretical techniques. A theoretical understanding of these systems is important for application in many problems in physics, mechanics and other fields. We discuss in detail the difficulties in the theoretical analysis of the problem. In particular we discuss here the regular, well-behaved perturbative solution, the large quantum number behaviour of anharmonic oscillator(s) using the technique of coherent states, exact solution of quantum anharmonic oscillators, the electromagnetic radiation emitted by a charged particle executing damped anharmonic oscillator motion using Krylov-Bogoliubov approximation method, use of invariants to obtain solution and coherent states of time-dependent oscillator(s), the derivation of perturbative frequencies of a damped coupled anharmonic oscillators system using suitable canonical transformation in the framework of Hamilton-Jacobi formalism and the quantisation and construction of coherent states of a damped oscillator using time-dependent operators.

Fortschritte der Physik/Progress of Physics•Jan 1, 1989•11 citations

Dissipative Quantum and Classical Liouville Mechanics of the Anharmonic Oscillator

Gerard J Milburn, Catherine A. Holmes

We present a solution for the dynamics of an anharmonic oscillator coupled to a zero-temperature heat bath. Comparison of observable properties in a classical and quantum description uses true joint phase-space probability densities. The time evolution of the density in the quantum case is rapidly "reduced" to that given in the classical description. The rate of reduction is proportional to the product of the damping rate and the oscillator's initial energy. Quite rapidly, typical quantum recurrence effects are destroyed and the classical "whorl" structure restored. We point out the close similarity with rapid destruction of quantum coherence through dissipation.

Physical Review Letters•May 26, 1986•307 citations
Phase properties of a damped anharmonic oscillator are studied within the Hermitian phase formalism of Pegg and Barnett. Exact analytical formulas for the phase distribution function, the expectation value and variance of the phase operator, and the expectation value and variance of the cosine of the phase operator are obtained assuming the zero-temperature reservoir and a coherent initial state of the system. It is shown that quantum periodicity in the evolution of phase quantities is destroyed by damping. The effect of damping on the formation of discrete superpositions of coherent states is discussed. A comparison is made between different phase approaches.
The phase properties of the self-squeezed states generated during the evolution of the anharmonic oscillator are discussed from the point of view of the new phase formalism of Pegg and Barnett. The phase distribution, the expectation values and the variances of the Hermitian phase operator are obtained and their evolution illustrated graphically. The mean values for the phase cosine and sine functions as well as their variances are also calculated. The results are compared to the Susskind-Glogower formalism results and the results based on the measured phase concept. The relation between squeezing and the phase properties of the field is discussed briefly.
The formation of discrete superpositions of coherent states via the unitary evolution of the m-photon anharmonic oscillator is studied. Exact analytical formulae for the superposition coefficients are obtained. It is shown that, in contrast to the two-photon anharmonic oscillator, for m>2 the superposition components enter the superposition with different amplitudes. The Pegg-Barnett phase formalism is used to calculate the phase distributions for the resulting states and to visualize their symmetry.
The present review is devoted to the study of certain aspects of anharmonic, time-dependent and damped oscillator(s) system using different theoretical techniques. A theoretical understanding of these systems is important for application in many problems in physics, mechanics and other fields. We discuss in detail the difficulties in the theoretical analysis of the problem. In particular we discuss here the regular, well-behaved perturbative solution, the large quantum number behaviour of anharmonic oscillator(s) using the technique of coherent states, exact solution of quantum anharmonic oscillators, the electromagnetic radiation emitted by a charged particle executing damped anharmonic oscillator motion using Krylov-Bogoliubov approximation method, use of invariants to obtain solution and coherent states of time-dependent oscillator(s), the derivation of perturbative frequencies of a damped coupled anharmonic oscillators system using suitable canonical transformation in the framework of Hamilton-Jacobi formalism and the quantisation and construction of coherent states of a damped oscillator using time-dependent operators.
We present a solution for the dynamics of an anharmonic oscillator coupled to a zero-temperature heat bath. Comparison of observable properties in a classical and quantum description uses true joint phase-space probability densities. The time evolution of the density in the quantum case is rapidly "reduced" to that given in the classical description. The rate of reduction is proportional to the product of the damping rate and the oscillator's initial energy. Quite rapidly, typical quantum recurrence effects are destroyed and the classical "whorl" structure restored. We point out the close similarity with rapid destruction of quantum coherence through dissipation.