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摘要: 我们采用平均场近似的方法，分别研究了Jaynes-Cummings晶格模型和Rabi晶格模型的量子相变：Mott绝缘体相-超流体相量子相变，探索了光的聚束-反聚束行为，以及考虑Kerr非线性作用对量子相变与光子统计特征的影响。研究结果表明在Rabi晶格模型中二能级原子和光子相互作用强度$g$和格点之间光子跃迁强度$J$的增大会使晶格体系从Mott绝缘体相向超流体相转变，同时光子统计行为由聚束转变为反聚束，而Kerr非线性强度的增大抑制了Mott绝缘体相-超流体相变，但促进光子聚束-反聚束之间的转变。
Abstract: We use the mean field approximation method to study the quantum phase transitions of the Jaynes-Cummings lattice model and the Rabi lattice model: Mott insulating-superfluid quantum phase transition, and explore the bunching-antibunching behavior of light. And we consider the effect of Kerr nonlinear term on the quantum phase transition and photon statistical characteristics. Our results show that in the Rabi lattice model, the increase of the two-level atom and photon interaction strength $g$ and the photon transition strength $J$ between the lattices drive the system from the Mott insulating phase to the superfluid phase, and the photon statistical behavior changes from the bunching to the antibunching one. The increase of the Kerr nonlinear coefficient will inhibit the Mott insulating phase-superfluid phase transition, but promote the transition between photon bunching and anti-bunching.
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