Berry connection in atom-molecule systems

In the mean-field theory of atom-molecule systems, where bosonic atoms combine to form molecules, there is no usual U(1) symmetry, presenting an apparent hurdle for defining the Berry phase and Berry curvature for these systems. We define a Berry connection for this system, with which the Berry phase and Berry curvature can be naturally computed. We use a three-level atom-molecule system to illustrate our results. In particular, we have computed the mean-field Berry curvature of this system analytically, and compared it to the Berry curvature computed with the second-quantized model of the same system. An excellent agreement is found, indicating the validity of our definition.