We investigate the geometric phase in a model of a Bose-Einstein condensate coupled to an optical cavity in which both the condensate and the cavity are described with coherent states. When the argument of the atom-cavity coupling term varies in time slowly from zero to $2\pi$, we calculate the geometric phase accumulated by the ground state and obtain its analytic expression in explicit form. We find that the adiabatic geometric phase jumps from zero to nontrivial $\pi$ at a critical value that corresponds to the normal-superradiant phase-transition point. The magneticlike flux interpretation of the geometric phase is also discussed.

• Received 10 August 2011

DOI:https://doi.org/10.1103/PhysRevA.84.053610