A New First-Order Phase Transition for an Extended Jaynes–Cummings–Dicke Model with a High-Finesse Optical Cavity in the BEC System†

Abstract

We present a two-level atomic Bose–Einstein condensate (BEC) with dispersion, which is coupled to a high-finesse optical cavity. We call this model the extended Jaynes–Cummings–Dicke (JC-Dicke) model and introduce an effective Hamiltonian for this system. From the direct product of Heisenberg–Weyl (HW) coherent states for the field and U(2) coherent states for the matter, we obtain the potential energy surface of the system. Within the framework of the mean-field approach, we evaluate the variational energy as the expectation value of the Hamiltonian for the considered state. We investigate numerically the quantum phase transition and the Berry phase for this system. We find the influence of the atom–atom interactions on the quantum phase transition point and obtain a new phase transition occurring when the microwave amplitude changes. Furthermore, we observe that the coherent atoms not only shift the phase transition point but also affect the macroscopic excitations in the superradiant phase.