Quantum phase transition and geometric phase in a coupled cavity-BEC system

摘要

We investigate the quantum phase transition and geometric phase of a model that describes a two-level atomic Bose-Einstein condensate coupled to a high-finesse optical cavity with considering the interactions between the coherent atoms. Using the Holstein-Primakoff transformation and the boson expansion approach, we identify a threshold coupling line separating the normal phase and the superradiant phase. We find that this phase transition is characterized by the nonanalyticity of the second-order derivative of the ground-state energy and the divergency of the first-order derivative of the geometric phase. In particular, we show that the atom-atom interactions can strongly affect the phase transition point and slightly modify the scaling behavior of the geometric phase in the vicinity of the critical point. The repulsive interaction can reduce the threshold and thus is favorable for observing the phase transition.