Study On Thermalization Dynamics Of Fermi Superradiation Phase Transition With An Optical Cavity

In both classical and quantum many-body systems,the study of non-equilibrium dynamics far from equilibrium is of great importance,and the study of the evo- lution of an isolated system under non-equilibrium conditions also represents a major challenge.In recent decades,with the rapid development of laser cool-ing technology,experimental almost isolated cold atom systems can be obtained.Compared to many physical systems in condensed matter,the experimental plat-form of the ultracold atom has simpler degrees of freedom.Especially in recent years,such as the emergence of quantum control technologies such as Feshbach resonance,optical lattice and artificial standard potential,the potential energy,kinetic energy and interaction between atoms can be accurately controlled exper-imentally,which makes the ultracold atom system a good platform for quantum simulation.Long-range interactions exist widely in systems at all scales in nature,re-search fields from astrophysics,two-dimensional fluids,free electron lasers to nu-clear physics.Due to the non-additivity of long-range interacting systems,such systems exhibit many exotic properties in nonequilibrium dynamics,such as er-godic breaking,slow relaxation,etc.One striking feature among these dynamics is that there exists a prethermalizing behavior,associated to the emergence of a long-lifetime quasistationary state（QSS）,before relaxing to the final steady states.With the rapid development of ultracold quantum gas,the quantum evo-lution can be observed on the experimental time scale.The placement of the degenerate quantum gas in the optical cavity is an ideal experimental platform to study the relaxation behavior of the system.When the coupling strength of the atomic gas and the cavity field is higher than a certain critical value,the sym-metry of the system spontaneously breaks and a superradiation phase transition occurs.After the phase transition,a reciprocal feedback interaction occurs be-tween the atoms and the light field,and the two are coherently coupled,creating an equivalent long-range interaction.Based on this quantum phase transition process,a quantum quenching scheme can be adopted to study the nonequi-librium dynamic evolution of a second-order driven-dissipative quantum phase transition system.The light field in the optical cavity is coupled with the exter-nal environment due to the dissipation of the cavity,and the system reaches a non-equilibrium steady state after a sufficiently long time.This provides an ideal prerequisite for studying the non-equilibrium dynamics of long-range interacting systems.This thesis discusses the preparation of⁶Li degenerate non-interacting Fermi gas and the measurement of relevant parameters.Besides,the strong coupling of Fermi degenerate gas and optical cavity is realized.In this coupling system,the atom scattering pump photon is coupled to the cavity field,when the number of photons in the optical cavity reaches a certain critical value,the system will undergo a Fermi superradiation phase transition.The dependence of the critical threshold P_thon the atomic number N was investigated.At low temperature P_th∝N^-1/2,which is different from BEC.At the same time,the steady-state phase diagram was measured.And we next studied the dynamic response of the self-organization of fermionic superradiance by measuring the atom fraction at different momentum states after ramping the pumping lattice power to zero within a time constantd t_r.Based on the insight of the superradiation phase transition,the thesis also studies the evolution of the nonequilibrium dynamics of the system,uses the quantum quenching scheme to drive the system far away from the equilibrium state,and investigates the complex relaxation behavior of the system through real-time non-destructive measurement of the evolution in the light field of the cavity combined with the recording of the evolution of the atomic momentum distribution.The evolution can be divided into five stages,the impressive delay stage,the violent relaxation stage,the oscillation stage,the quasistationary state and the final thermalization stage,each stage has its own distinctive properties.An important result is that the scaling rates of the lifetime of quasistationary state（QSS）and atomic number of the degenerate Fermi gas coupled to the optical cavity are measured to be close to the values predicted by numerical theory.Another interesting result is that during the oscillation phase of system evolution,the light field acts on the atoms,leading to the exchange of the atoms in the normal state and the superradiation state,and finally inducing the emergence of the prethermalized state.Finally,the parameter dependence of the relevant features in each stage is examined and the corresponding scaling rate is given.In this thesis,the effect of Fermi-Dirac statistics on the phase transition of superradiation in the optical cavity is investigated and the non-equilibrium dynamic behavior of the system is investigated using quantum quenching.