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Phys. Rev. A 59, 1777 - 1780 (1999)

Unitary equivalence and phase properties of the quantum parametric and generalized harmonic oscillators

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M. Maamache1, J.-P. Provost2, and G. Vallée3
1Institut de Physique, Université de Sétif, Sétif 19000, Algeria
2Institut Non Linéaire de Nice, UMR CNRS 129, 1361 Route des Lucioles, Sophia Antipolis, 06500 Valbonne, France
3Laboratoire, J.A. Dieudonné, UMR CNRS 6621, Université de Nice Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 2, France

Received 15 May 1997; revised 8 October 1997

A quantum parametric harmonic oscillator with a unitary evolution but not invariant under time reversal, is shown to be unitarily equivalent to a quantum generalized harmonic oscillator. As a consequence the phase properties of the two systems, in particular their geometric phases, are identical. Equivalent results for the corresponding classical systems are deduced from the study of the time evolution of the appropriate squeezed coherent states.


©1999 The American Physical Society

URL: http://link.aps.org/abstract/PRA/v59/p1777
DOI: 10.1103/PhysRevA.59.1777
PACS: 03.65.Bz, 03.65.Sq

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