Research On Bose Gas From Long-range Interaction

Ultracold atomic system is a clean and versatile platform as a many-body quan-tum system.The research on its novel quantum states and exotic phases leads a advancing and challenging frontier in the world.With the development of experi-ment technologies and applications of new concepts and new methods,cold atomic physics is developing rapidly.For example,one can do some basic research and appli-cation by combining the cold atomic system with some quantum manipulation such as spin-orbit coupling,optical lattices,Feshbach resonance,synthetic gauge field.Spin-orbit coupling plays a crucial role in many new quantum phases in the solid state.We consider two-component Bose-Einstein condensates subject to Weyl spin-orbit cou-pling.We obtain mean-field ground state phase diagram by the methods such as vari-ational calculation,functional integrals.We study the excitation spectrum,the sound velocity,the quantum depletion of condensates,the shift of ground state energy,and the static structure factor.The application of optical lattice brings new research direction to cold atomic quantum simulation,which is relevant for simulation of con-densed matter physics phenomena.In order to explore the novel quantum phenom-ena and further study superfluid-Mott insulator transition,it is an innovation to change the geometric parameters of the optical lattice,the strength of tunneling and the interaction between atoms in the lattice and the potential barrier height of optical lattice.We further consider bosonic atoms loaded into optical lattices with cavity-mediated short-and global-range interactions.We obtain global ground-state phase diagram,the variation of particle number and the isothermal compressibility at atomic limit.With finite hopping amplitude,we study the property of the system by examining the excitation spectrum,phase diagram,order parameters and so on.