Berry’ Phase In The Degenerate Parametric Amplifier

We discuss the manifestation of Berry’s phase in the degenerate parametric amplifier of quantum optics. Mainly we derive the Berry phase in the simplest case when the phase of the classical pump field varies adiabatically. Also we show that the effect of the phase may be discerned at all times in the photon-counting statistics of the output field.The main contents of this paper are as follows:first, we introduce the background of Berry phase as well as the significance of this research, and give a brief account of the structure of the paper. Then, the theory of the quantized adiabatic approximations is stated here, only by which can Berry phase be calculated. At the same time, we take a further step to contrast the new adiabatic approximations with the classical adiabatic approximations, which shows up some weaknesses of the latter and more importantly, some strengths of the former. Next, we give a brief introduction to Berry Topology phase as well as the calculation process of its basic theory. We also try to explore how to work out Berry Geometric phase under the precondition of the classical adiabatic approximations. Finally, we come to the conclusion and are hopeful for the prospects.