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Physical Review A

Creating multiphase coherent states in a damped anharmonic oscillator

Martina Brisudová

Published Aug 1, 1992• 5 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.46.1696

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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.
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.
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The present review is devoted to the study of the problem of coupled anharmonic oscillators. A perturbative solution is obtained for the system of an undamped and the damped coupled anharmonic oscillators in the coherent state representation. The solution does not contain the vicious secular terms and shows, explicitly, the anharmonic effects of a coupled system. In order to derive the perturbative solution of a damped coupled system a new frame of time, called quasi time τ, has been exploited. The large quantum number behaviour of coupled anharmonic oscillators has been derived using the path integral method.
In the preceding paper (arXiv: 0710.2724 [quant-ph]) we have constructed the general solution for the master equation of quantum damped harmonic oscillator, which is given by the complicated infinite series in the operator algebra level. In this paper we give the explicit and compact forms to solutions (density operators) for some initial values. In particular, the compact one for the initial value based on a coherent state is given, which has not been given as far as we know. Moreover, some related problems are presented.
For the model of a linearly driven quantum anharmonic oscillator, the role of damping is investigated. We compare the position of the stable points in phase space obtained from a classical analysis to the result of a quantum mechanical analysis. The solution of the full master equation shows that the stable points behave qualitatively similar to the classical solution but with small modifications. Both the quantum effects and additional effects of temperature can be described by renormalizing the damping.