Geometric phases for two-mode squeezed state

TL;DR

This paper explicitly evaluates the geometric phase for two-mode squeezed states, revealing its elegant form, its relation to one-mode phases, and its connection to entanglement during cyclic evolutions.

Contribution

It provides the first explicit calculation of the geometric phase for two-mode squeezed states and explores its relation to entanglement and cyclic evolution.

Findings

The total phase factor is an elegant product of two squeezed operators.

The geometric phase for cyclic evolution equals the sum of two one-mode phases.

A relationship between geometric phase and entanglement is established.

Abstract

Although the geometric phase for one-mode squeezed state had been studied in detail, the counterpart for two-mode squeezed state is vacant. It is be evaluated explicitly in this paper. Furthermore, the total phase factor is in an elegent form, which is just identical to one term of product of two squeezed operators. In addition, when this system undergoes cyclic evolutions, the corresponding geometric phase is obtained, which is just the sum of the counterparts of two isolated one-mode squeezed state. Finally, the relationship between the cyclic geomtric phase and entanglement of two-mode squeezed state is established.