Evolution of Extended JC-Dicke Quantum Phase Transition with a Coupled Optical Cavity in Bose-Einstein Condensate System

• Published in: International journal of theoretical physics 2017-11, Vol.56 (11), p.3655-3666
• Main Authors: Abdel-Rady, A. S., Hassan, Samia S. A., Osman, Abdel-Nasser A., Salah, Ahmed
• Format: Article
• Language: English
• Subjects: Bose-Einstein condensates; Coherence; Condensates; Elementary Particles; Mathematical and Computational Physics; Mathematical models; Phase transitions; Physics; Physics and Astronomy; Potential energy; Quantum Field Theory; Quantum mechanics; Quantum Physics; Theoretical
• ISSN: 0020-7748; 1572-9575
• DOI: 10.1007/s10773-017-3531-3

In this paper, the extended Jaynes-Cummings-Dicke (JC-Dicke) model which describes a two-level atomic Bose-Einstein condensate (BEC) dispersive coupled to a high-finesse optical cavity is considered. The theoretical description of an effective Hamiltonian for BEC is introduced. The potential energy surface of the system is obtained from the direct product Heisenberg-Weyl (HW1) coherent states for the field and U(2) coherent states for the matter. Also, the variational energy is evaluated as the expectation value of the Hamiltonian for this state in the framework of mean-field approach. The quantum phase transitions (QPTs) and the Berry phase for this model are investigated numerically. We observed that the atom-atom interactions can strongly affect the quantum phase transition point. Furthermore, we noticed that the coherent atoms not only shift the phase transition point but also affect the macroscopic excitations in the superradiant phase. Moreover, it is found that the new phase transition occurs when the microwave amplitude changes. Some of the numerical results in this paper are agreement precisely with the results of our paper which has published in Int. J. Mod. Phys. B when we studied the same model using a different coherent state.