Coupling effect on the Berry phase

Abstract

The Berry phase has universal applications in various fields. Here, we explore the coupling effect on the Berry phase of a two-level system adiabatically driven by a rotating classical field and interacting with a single quantized mode. Our simulations clearly reveal that the Berry phase change is quadratic proportional to the coupling constant if it is less than the level spacing between neighboring instantaneous eigenstates. Remarkably, if the nearest neighbouring level spacing is comparable with the coupling constant, this simple quadratic dependence is lost. Around this resonance, the Berry phase can be significantly tuned by slightly adjusting the parameters, such as the coupling constant, the frequency of the quantized mode, and the transition frequency. These numerical results, agreeing well with the perturbation theory calculations, provide an alternative approach to tune the Berry phase near the resonance, which is useful in quantum information science, i.e. designing quantum logic gates.