Journal of Quantum Optics, Volume. 27, Issue 2, 87(2021)
Multiple Stable States and Dicke Phase Transition of T-C Model
In this paper, the multiple stable states and Dicke phase transition of two two-level atoms in a single mode optical cavity are studied by using the coherent state variational method in the rotating wave approximation. There is no interaction between two atoms for the distance. Firstly, we obtain the eigenstates and eigenenergies of the system, meanwhile, we solve different photon number solutions and boundary conditions by variational method. Figure 1 gives the the limit case that the second atom does not exist and T-C model degrades into J-C model, in which a second-order Dicke quantum phase transition from the normal phase to the superadiant phase occurs. Meanwhile, the completely reversed atomic population exists with the increase of the atom-field coupling strength. The effects of the detuning between the cavity’s frequency and the atomic frequencies on Dicke phase transition are characterized by numerical calculation. Rich phase diagrams are presented by adjusting the parameters, such as the atom-field coupling strengths, the frequency detuning and the non-equilibrium parameter. These phase diagrams visually show Dicke phase transitions. Interestingly, multi-stable excited states are induced by the atomic inversion. Apart from Dicke phase transition from normal phase to superradiant phase, the system shows a new phase transition from the revised normal state by just one atom to stimulated radiation state, while the completely revised normal state by both atoms exists stably in the whole space. In addition, the application of J-C model or T-C model in quantum optics generally considers the driven field, which can at least make the critical quantum phase point or boundary shift. In the future we can add the driven field in Hamiltonian and discuss the effect on Dicke phase transition.
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LIU Ni, LING Ming-xia, CUI Xin-lin, LIANG Jiu-qing. Multiple Stable States and Dicke Phase Transition of T-C Model[J]. Journal of Quantum Optics, 2021, 27(2): 87
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Received: Dec. 24, 2020
Accepted: --
Published Online: Sep. 13, 2021
The Author Email: LIU Ni (317446484@qq.com)