Nonadiabatic geometric phase and hannay angle: A squeezed state approach

The geometric phases of the cyclic states of a generalized harmonic oscillator with nonadiabatic time-periodic parameters are discussed in the framework of a squeezed state. A class of cyclic states is expressed as a superposition of an infinite number of squeezed states. Then their geometric phases are obtained explicitly and found to be -(n + 1/2) times the classical nonadiabatic Hannay angle. It is shown that the analysis based on the squeezed state approach provides a clear picture of the geometric meaning of the quantal phase.