No abstract

In the mean-field theory of atom-molecule systems, where the bosonic atoms combine to form molecules, there is no usual U (1) symmetry, which presents an apparent hurdle for calculating the Berry connection in these systems. We develop a perturbation expansion method of Hannay's angle suitable for calculating the Berry curvature in the atommolecule systems. With this Berry curvature, the Berry connection can be computed naturally. We use a three-level atom-molecule system to illustrate our results. In particular, with this method, we compute the curvature for Hannay's angle analytically, and compare it to the Berry curvature obtained with the second-quantized model of the same system. An excellent agreement is found, indicating the validity of our method.

We investigate the nonlinear dynamics of a system composed of a cigar-shaped Bose—Einstein condensate and an optical cavity with the two sides coupled dispersively. By adopting discrete-mode approximation for the condensate, taking atom loss as a necessary part of the model to analyze the evolution of the system, while using trial and error method to find out steady states of the system as a reference, numerical simulation demonstrates that with a constant pump, atom loss will trigger a quantum optical bi-stability switch, which predicts a new interesting phenomenon for experiments to verify.