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Journal of Modern Optics

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

Ts. Gantsog, R. Tanaś

Published Jun 1, 1991• 19 citations
Publisher

Abstract

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.

DOI
10.1080/09500349114551071

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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.
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 squeezed number states have been studied from the lower order to the higher order via the measured phase operators (MPO) introduced by Barnett and Pegg and compared with those obtained via the Hermitian and Susskind-Glogower phase operators. We have found many new, interesting results. For the lower order, the phase fluctuations of the MPO are exactly independent of the photon number n. For the higher order, the corresponding fluctuations are a decreasing function of n.
WT5BZ]We consider the generalized Jaynes-Cummings model with intensity - dependent coupling interacting with a squeezed vacuum. From the point of view of the new phase formalism of Pegg and Barnett, we have not only found the exact general expressions of the phase distribution and the associated expectation value and variance of the phase of the squeezed vacuum field and their evolution illustrated graphically, but also derived approximately analytic formulas of that for the weakly and strongly squeezed vacuum. The relation between squeezing and the phase properties of the squeezed vacuum is discussed briefly.