Extended Hubbard Models Of Ultracold Bosonic Gases In A Light-Cavity

The system of ultracold atoms in optical lattices have been an important platform for study-ing low-temperature physics.Also,the Bose–Einstein condensate(BEC)plays a vital role in frontier fields like quantum simulation,quantum information and precise measurement.The widely-studied Hubbard model is effective to describe cold atom systems with strong corre-lation.With the progress of experimental research,people finally achieve the BEC in exter-nal field produced by optical lattice and optical cavity.By varying the short- and long-range interactions among particles in lattices,one can reach some new phase beyond superfluidity and Mott insulator.In this work,we investigate a extended Hubbard model containing both short- and long-range interactions.With perturbation method and self-consistent mean-field approach,we analyse physical properties of the system at different temperatures.At zero temperature,we firstly analyse the case of system without the particle transition.By examining the Hamiltonian,we map out the phase diagram of ground state,which show that the existence of long-range interactions may cause the CDW state.Then we analyse the case of system with particle transition.By applying self-consistent mean-field approach to transition kinetic energy terms in Hamiltonian,and numerically stimulating,we can obtain impact of transition kinetic energy on superfluid order parameter and particle density.With the existences of both transition kinetic energy and long-range intraction,we find that there is not only the CDW state,but also supersolid state.At finite temperature,we firstly analyse the impact of temperature on superfluid order parameter and particle density.We can obtain the critical temperatures where phase transition occurs with respect to different parameters,and find that long-range order come to vanish as temperature raising.Furthermore,by using the related thermodynamic theory,we map out the curves of various thermodynamic properties like internal energy,heat capacity and entropy with respect to temperature under different phase.We find that the variation of thermodynamic properties are obviously different between the situations when system temperature is above and below critical temperature.