Aharonov-Anandan Phase in the Degenerate Parametric Amplifier

As a non-adiabatic generalization of a recent work of Gerry, the manifestation of the Aharonov-Anandan phase in the degenerate parametric amplifier of quantum optics is discussed by making use of the Lewis-Riesenfeld quantum theory. We find the Lewis invariant for the system and study its evolution. The Aharonov-Anandan phase is then calculated and the connection between the Aharonov-Anandan phase difference and the average photon-number of the output field is obtained. Finally, the observable effect of the phase difference is investigated.