Dicke Phase Transition And Multiple Stable States For Two-Level Atoms In An Optical Cavity

In 1963,Edwin Jaynes and Fred Cummings firstly proposed JaynesCummings model(J-C model),which is the beginning of research in the material structure.Tavis-Cummings model(T-C model)is an extension of J-C model which describes the interaction between two two-level atoms and a single-mode quantized electromagnetic field without the interaction between two atoms.In recent years,many scholars have done a lot of research on the quantum properties of J-C model and T-C model.In terms of the continuity of chemical potential,P.Ehrenfest proposed that the phase transition can be divided into first-order phase transition and continuous or second-order phase transition,which can be obtained by the continuity of first and second derivatives.Quantum fluctuations play a major role in the quantum multi-body system at zero temperature,the system experiences a continuous change from a disordered status to another an ordered status by changing some other parameters of the multi particle system,such as the coupling strength between the particles and the external magnetic field's strength.This phase transition driven by the quantum fluctuations is called quantum phase transition.Dicke quantum phase transition refers to the second-order phase transition from the normal phase to the superradiant phase,which is related to the excitation of the photon number.Based on the discussion of Dicke phase transition,it is found that in addition to the normal phase and the superradiant phase,the system also has a multistable macroscopic quantum state.The stimulated radiation is generated from one of the atoms,and the other atom is still in the usual super radiation state.By adjusting the relative atom field coupling strength and atomic frequency detuning,the super radiation state and stimulated radiation state can be exchanged between the two atoms.This paper mainly discusses from the following aspects:In the first part,Jaynes-Cummings model and Tavis-Cummings model are briefly introduced,as well as the background of classical phase transition and quantum phase transition.Finally,spin squeezing is introduced.In the second part,we discuss the Dicke phase transition and multistability of two two-level atoms in a single-mode cavity by using the coherent state variational method.We can get the eigenstates and eigenenergies of the system,and solve different photon number solutions and boundary conditions by variational method.Through abundant phase diagrams,the multistable excited states and the phase transition of atomic number inversion can be shown directly.In addition to the Dicke phase transition from the normal phase to the superradiant phase,there is also a phase transition from the normal state to the stimulated radiative state,and the normal state in which both of the components are reversed is stable in the whole space.In addition,considering that the application of J-C model in quantum optics generally discusses the existence of external field drive,the last section introduces external field drive from Hamiltonian,and finally discusses the specific effect of external field drive on phase transitionIn the third part,the related theories and common models of spin squeezing are briefly introduced,and the spin squeezing coefficients of T-C model are derived and discussed.