The Study Of Analytical Solution And QPT On Strong Coupling Between Light And Two-level System

In recent years,the experimental coupling strength of the interaction between light and two-level system reaches the ultrastrong coupling region or even the deep strong coupling region,which lead to many physical phenomena that cannot be observed by weak coupling,such as bloch-siegert shft under resonance,quantum phase transition and quantum chaos.The interaction between single-mode cavity and two-level atom can be described by Rabi model.The rotating wave approximation failed to describe the utrastrong coupling mechanism,which motive us to develop the analytic solution without rotating-wave approximation.Among them,the generalized rotating-wave approximation by taking into account the coherent state wave function provides a valid analytic approximate solution for the Rabi model under the ultrastrong coupling regime.In this thesis,we use the generalized rotating-wave approximation method to study the coupling system of few qubits and oscillator,and an effective analytical approximate solution is obtained.The dynamics of the atom population in the two-qubit Rabi model and the quantum entanglement in three qubits are studied by using the analytical approximate solution above.In addition,the generalized variational method by coherent state improved the generalized rotating-wave approximation but there is still a lack of nonperturbative deep strong coupling region between ultra-strong coupling and deep coupling.Therefore,we put forward generalized squeezing rotating-wave approximation(GSRWA)method,which provides and effectively solutions for Rabi model in nonperturbative deep strong coupling region,both for ground state and low excited states as well as isotropic and anisotropic Rabi model,providing the possibility for the experimental exploration of interesting phenomena in this partially coupling region.However,with increasing of the ratio Δ/ω,The phase transition trend to happen in Rabi model,there need more than one coherent-squeezing state to describe the wave function in this case.For this reason,we develop two coherent-squeezing state(2CSS)method,which provides effective ground state wave function for isotropic and anisotropic Rabi model with finite large Δ/ω。There exist a quantum phase transition(QPT)when Δ/ω tends to infinity in quantum Rabi model,which equivalent to the thermodynamic limit of tends to infinity in the Dicke model.A lot of related work has been done to study the superradiant phase transition and finite-size scaling behavior in Rabi model and Dicke model.However,compared with the Dicke model,the two-photon Dicke model will show some different properties,such as,due to the interaction of two-photon process,the energy spectrum of two-photon Dicke model inevitably collapses into continuous spectrum with the increase of coupling strength.However,there still be existence superradiant phase transition under the thermodynamic limit before the collapse point in two-photon Dicke model.In this thesis,the excitation energy spectrum,superradiant phase transition point and energy spectrum collapse point of the two-photon Dicke model under the thermodynamics limit are given by our proper analytical method.The observables’ analytical finite-scaling function and finite-scaling exponents of the two-photon Dicke model are given by using the effective scaling transformation,and the scaling exponents of the observables are the same as those in the standard Dicke model,indicating they are in the same universality class.