Dynamic Properties Of BEC In Optical Lattices Under The Artificial Gauge Field

The dynamics properties of ultra-cold atoms in optical lattices under the artificial gauge field have attracted much attention both experimentally and theoretically,which provides an ideal platform for studying many fundamental phenomena of many-body physics.When a neutral atom subjected to an artificial gauge field,its center-of-mass can simulate the motion of an electron with Lorentz force in magnetic field.In particular,the cyclotron dynamics induced by the artificial gauge magnetic field can be observed experimentally.In this paper,we discussed the dynamics and stability of atoms in a two-dimensional square optical lattice under the action of the artificial magnetic field and the harmonic trap potential.It is found that there are rich cyclotron dynamics under the coupling effects of the optical lattice,harmonic trap potential and artificial gauge field.The main contents and structure of this paper are as follows:In the first chapter,the background knowledge related to this paper and some phenomena of ultra-cold atoms under the coupling and uncoupling effects of lattice potential,harmonic trap potential and the artificial gauge field are introduced briefly.In the second chapter,the collective dynamics and stability of ultra-cold atoms under the coupling effects of optical lattice,harmonic trap potential and artificial magnetic field are studied by using variational approach under the tight-binding approximation and numerical simulation.It is found that there are rich cyclotron dynamics in the system.The harmonic trap potential plays a key role in modifying the equilibrium state properties of the system and stabilizing the cyclotron orbits of the condensate.Meanwhile,the presence of the harmonic trap potential and lattice potential results in rich cyclotron dynamics of the condensate.The coupling effects of the lattice potential,artificial magnetic field,and harmonic trap potential lead to single periodic,multi-periodic or quasi-periodic cyclotron orbits of the condensate.So we can control the cyclotron dynamics of neutral atoms in optical lattice by manipulating the strength of harmonic confinement,artificial magnetic field,and initial conditions.Our results provide a direct theoretical evidence for the cyclotron dynamics of neutral atoms in optical lattices exposed to the artificial gauge magnetic field and harmonic trap potential.Finally,in the third chapter of this paper,we summarize the main results and give some outlooks in this field.