Jaynes-Cummings晶格模型和Rabi晶格模型的量子相变  

The quantum phase transition in the Jaynes-Cummings lattice model and the Rabi lattice model

作　　者：尤冰凌 刘雪莹 成书杰 王晨 高先龙[1] You Bing-Ling;Liu Xue-Ying;Cheng Shu-Jie;Wang Chen;Gao Xian-Long(Department of Physics,Zhejiang Normal University,Jinhua 321004,China)

机构地区：[1]浙江师范大学物理系,金华321004

出　　处：《物理学报》2021年第10期1-7,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11774316,11704093)资助的课题.

摘　　要：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,研究了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-超流体相相变,但促进了光子聚束与反聚束之间的转变.We use the mean field approximation method to study the quantum phase transitions of the JaynesCummings lattice model and the Rabi lattice model. The effective Hamiltonians are obtained for the JC and Rabi model including the Kerr nonlinear term. Numerically we diagonalized the Hamiltonian matrix and calculated the superfluidity order parameter and the two-photon correlation function by solving the iteration equations.We have explored the Mott insulating-superfluid quantum phase transition, the bunching-antibunching behavior of light, and the effect of Kerr nonlinear term on the quantum phase transition and photon statistical characteristics. Our results show that in the JC lattice model, by increasing J, a quantum phase transition takes place and the system is driven to a superfluid phase. The phase boundaries of the Mott lobes are N-dependent.However the photon will always be in a bunching statistical behavior irrelevant of the coupling strength between the two-level atom and the phonton and the nonlinear Kerr effect.In the Rabi lattice model, the anti-rotating wave term breaks Mott-lobe structure of the phase diagram and 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. The photon statistical behavior changes from the bunching to the antibunching one when considering the anti-rotating wave term, which is important in the strongly coupled systems. Most interestingly, the increase of the Kerr nonlinear coefficient will inhibit the Mott insulating phase-superfluid phase transition, but favor the superfluid phase and the transition from the bunching to anti-bunching statistics.

关 键 词：JAYNES-CUMMINGS 晶格模型 RABI 晶格模型 量子相变 光子统计 

分 类 号：O469[理学—凝聚态物理]