Dissipative Phase Transition And Two-photon Statistics In Several Typical Qubit-cavity Coupling Systems

Light-matter interaction systems are ubiquitous in various fields ranging from condensedmatter physics,quantum optics and quantum dissipative systems,and have been attracted a lot of interests for a few decades.In recent years,with the tremendous progresses of various solid state quantum platforms,the parameters of the light-matter interaction can be largely manipulated,and the system can enter ultrastrong and deep-strong coupling regime,and the strong-coupling physics can be explored.In this Ph.D thesis,we study dissipative phase transitions,quantum phase transitions,and two-photon statistics in several typical light-matter interaction systems.Since a quantum system inevitably interacts with its environment,we mostly consider the dissipative steady states.In the ultrastrong coupling regime,the traditional description of the dissipation with the Lindblad master equation becomes invalid.Therefore,we deal with the quantum dissipation by the dressed master equation,which is compatible with the strong coupling regime.The major results are described as follows.1)The Rabi-Hubbard model is composed by a lattice of interlinked cavities where a cavity photon is coupled to a two-level atom in each cavity and can hop to the nearest neighboring cavity.Recently the localization-delocalization quantum phase transition is observed in this model.Localization means the photon is confined in each cavity due to the coupling to the two-level atom.We present a new steady-state phase diagram by using the mean-field theory and the dressed master equation,and derive the analytically approximate results for the order parameter in the steady state.The analytical prediction for the phase boundary is excellently consistent with the numerical one.Especially,the analytical scheme correctly capture the key characteristics of the phase diagram,that is,no matter how weak the dissipation is,the critical tunneling strength approaches zero monotonously as the light-matter coupling increases.This result is quite different from the previous one using the Lindblad master equation,where the critical tunneling strength does not vanish with the increasing coupling.The present analytical solution can address such a remarkable difference.The present dressed master equation scheme can describe the Ohmic spectral function of the bath,while the white-noise type spectral function in the Lindblad master equation is obviously oversimplified,which overestimates the influence of the low-frequency component in system-environment interactions.2)We investigate the effect of the counter-rotating-wave interaction in the anisotropic Rabi model where the strengths of the rotating-wave and counter-rotating-wave terms are relaxed to be independent.We calculate the two-photon correlation function in the dissipative anisotropic Rabi model in the framework of the dressed master equation and the modified expression of the two-photon correlation function.Thus we can reveal not only the nonclassical property of the radiation field(e.g.,photon anti-bunching)but also the intrinsic behavior of a quantum system(e.g.,the first-order phase transition).Specifically,we find multiple photon antibunching-to-bunching transitions,in contrast to the single photon antibunching-to-bunching transition in the isotropic model.The emerged additional region of photon antibunching occurs in a wide parameter range of the system.Therefore,this model system provides an alternative platform for the photon blockade effect and single photon source which characterized by photon antibunching.Furthermore,we derive an analytical expression using a few low energy levels in the low temperature regime,which quantitatively agrees with the numerical results.The origin of the photon antibunching is also explained analytically.Very interestingly,we observe that the giant peaks of photon bunching are highly related to the first-order quantum phase transition of this model.This phenomenon has also been found in the dissipative Rabi-Stark model.It is therefore proposed that the measured photon bunching could detect the first-order quantum phase transition in the light-matter interaction system and hopefully also in the other quantum systems.3)The symmetric quantum Rabi model shows a quantum phase transition in the infinite ratio of the qubit and cavity field frequencies,while the asymmetry quantum Rabi model does not show any symmetry-breaking phase transition.If the parity symmetry is recovered in a two-qubit Rabi model with the opposite qubit biases,namely staggered fields,the quantum phase transition may reappear.It should be noted that such a model system can be easily realized in the modern solidstate quantum devices.In the infinite frequency ratio,equivalently in the thermodynamic limit,we derive the mean-field Hamiltonian and further the order parameter dependent energy density function.With given parameters of system,the ground state energy is just the minimum of the energy density function,meanwhile,its location corresponds to the actual order parameter.We numerically obtain the phase diagram and find that the phase transition varies from the secondorder type to the first-order one right at a tricritical point.Then based on the Landau theory for the second-order phase transition,we derive the analytical expression of both the second order phase transition point and the tricritical point.We also find the analytical equation for the first-order phase transition point.Finally,we perform the finite-size-scaling analysis for the ground-state fidelity susceptibility and surprisingly find the different critical exponents of correlation length for the second-order quantum phase transition and the tricritical point.It is suggested that the continuous phase transitions of the second-order quantum phase transition and at the tricritical point of the staggered field two-qubit quantum Rabi model belong to different universality classes.