New method for calculating the Berry connection in atom-molecule systems

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 atom-molecule 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.