Berry phase of two atoms in the same quantized light field

The Berry phase of two atoms exposed to the same quantized light field has been studied. The interaction between each atom and the light field obeys the Jaynes-Cummings model. Due to the quantization of the light field, the interaction Hamiltonians for the two atoms interacting with the field do not commute with each other, which induces new parts in the Berry phase. Meanwhile, there appears a phase which doesn't exist in the classical regime and is purely induced by the field quantization. (Abstract Copyright [2007], Wiley Periodicals, Inc.)