Quench Dynamics And Thermalization In The 1D Jaynes-Cummings-Hubbard Model

Fueled by enormous improvements in experimental techniques and supercomputers,the study of interacting quantum many-body systems has become an active field,because it is feasible to control and calculate quantum systems with many degrees of freedom.The experimental realization of cooling and trapping ultracold atoms in optical lattices and trapping ion systems as well as hybrid systems allow us to precisely study the interacting systems in the laboratory.In this highly controlled situation,non-equilibrium dynamics and thermalization have advanced.Theoretical work on non-equilibrium dynamics and thermalization in closed quantum systems is also flourishes with the development of massive parallelization and novel numerical methods.The thermalization has been studied for a wide number of lattice models such as Bose-Hubbard,Fermi-Hubbard and spin-1/2 chains,in which the validity of the eigenstate thermalization hypothesis has been observed,and the conditions that cannot be thermalized are obtained in some systems.However,the explorations of the thermalization properties in light-matter coupled systems are lacking.By the exact diagonalization,we focus on the quantum quench dynamics and thermalization in the JCH model.The JCH system is an important many-body model to understand light-matter interactions.The coupling between atoms and photons leads to optical nonlinearities and photon blocking effects,which exhibits rich phase diagrams in the quantum phase transitions.In addition,recent experimental progress in coupled-cavity arrays may provide a good idea for studying the non-equilibrium dynamics.In this thesis,we first illustrate exact diagonalization techniques in the JCH model.When the periodic boundary condition is imposed,we study the quench dynamics of the JCH model with a weak hopping strength by the fermionic approximation.The results show that the canonical ensemble fails to describe the JCH system with the weak hopping strength after the quantum quench.We believe that in the fermionic approximation,the JCH model is close to an integrable model.Thus,we perform the level spacing distribution of the system and find that they conform with the characteristics of the Poisson distribution.And we demonstrate that the JCH model cannot be thermalized through the evolution of the physical observables cannot be relaxed to the predicted values of the canonical ensemble.Finally,we also show that the eigenstate thermalization hypothesis is invalid in the system.In most lattice systems,the emergences of quantum chaos are contributed by the two-body interactions.However,there is no two-body interaction in the JCH model,so exploring quantum chaos in the JCH model arouses our interest.We find that when the hopping strength of photons and the coupling strength between photons and atoms are of the same order,the JCH system exhibits quantum chaos and obeys the eigenstate thermalization hypothesis in resonance,which proves that the competition between the hopping and the coupling is the new mechanism that leads to the emergence of quantum chaos.In addition,we find that the chiral symmetry of the Hamiltonian leads symmetric distributions of the diagonal elements.Subsequently,we also demonstrate that the detuning between photon and atom breaks the quantum chaos.Inspired by the integrability of the one-dimensional hard-core Bose-Hubbard model,we study the thermalization and the symmetry of the Hamiltonian in the low-density JCH model,and discuss the effects of the dipole interactions between atoms.The numerical results show that when the hopping strength and the coupling strength are of the same order,quantum chaos still appears in the lowdensity JCH model.In addition,when the hopping strength is much smaller than the coupling strength,the system exhibits an intermediate state that is neither a Poisson nor a Gaussian orthogonal ensemble,but the most characteristics of the matrix elements show it is close to the behavior of a nonintegrable system,and this result is quite different from that of the soft-core JCH model with the weak hopping strength limit.Finally,the dipole-dipole interaction can lead the intermediate states to be closer to the integrable point with the weak hopping strength limit,and the quantum chaos properties are not be affected when the hopping strength is of the same order of the coupling strength.In this thesis,we discuss in detail the thermalization properties of the JCH model with different conditions.These results provide a deep understanding about the relationship between eigenstates and macroscopic phenomena in the light-matter coupled system,which will provide insights theoretical support for thermalization studies in the coupled-cavity arrays.