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 squeezed state. A class of cyclic states are expressed as a superposition of an infinte number of squeezed states. Then, their geometric phases are obtained explicitly and found to be $-(n+1\mathrm{/}2)$ times the classical nonadiabatic Hannay angle. It is shown that the analysis based on squeezed state approach provide a clear picture of the geometric meaning of the quantal phase.