Nonadiabatic Geometric Phase and Hannay Angle: A Squeezed State Approach
Jie Liu, Bambi Hu, and Baowen Li (Centre for Nonlinear Studies, Hong, Kong Baptist University, China)
TL;DR
This paper explores the geometric phases of cyclic states in a generalized harmonic oscillator with nonadiabatic, time-periodic parameters, using a squeezed state approach to clarify their geometric and quantum significance.
Contribution
It introduces a squeezed state framework to explicitly compute geometric phases and relate them to classical Hannay angles in nonadiabatic quantum systems.
Findings
Geometric phases are proportional to classical Hannay angles.
Cyclic states are expressed as superpositions of infinite squeezed states.
The squeezed state approach clarifies the geometric meaning of quantum phases.
Abstract
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 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.
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