Theoretical Study Of Artificial Spin-orbit Coupling Effects In Cold Atom Systems

The spin-orbit coupling,known as SOC,plays an important role in quantum physics,which is derived from the nonrelativistic approximation of the Dirac equation.It is widely existed in the solid materials with asymmetric spatial inversion,and its strength is determined by the intrinsic properties of materials,which is difficult to control in the experiment.In recent years,the controllable synthetic SOC in neutral Bose-Einstein condensate has been successfully realized,which has aroused the research interest of many physicists.Researches show that when there is a SOC in the ultra-cold atom system,the system usually presents non-trivial topological properties,such as Topological state,Majorana fermion,etc.Meanwhile,with implementation of the synthetic SOC,people can use the highly adjustable experimental platform of cold atom systems to simulate the important quantum states in condensed matter physics,such as topological insulators and chiral superfluids.In addition,the cold atom system of the synthetic SOC has gradually become an important platform to realize topological quantum computing.In this paper,we use the Monte Carlo simulation method to study the synthetic SOC in cold atom system,especially the new phases with the synthetic SOC in 2D hexagonal optical lattice and the influence of the synthetic SOC on the topological properties of the system.In this paper,firstly,we introduce the concrete form of the synthetic SOC in cold atom systems.The research system is the synthetic SOC in cold atom systems on hexagonal lattice,the Hamiltonian is H=K+TSOC+HU,with K as kinetic energy said the kinetic energy of particle movement between the lattice,TSOC as the synthetic SOC,HU as the interaction between the two components boson on one lattice,with U and U' as the composition and the interaction between different components,respectively.At present,the main research method for this kind of system is to make classical approximation under the large U limit,and the system is equivalent to a spin model with Dzyaloshinsky-Moriya(DM)interaction.Secondly,we describe this kind of spin model in detail,and mainly study the classical case of this model.For the system containing DM interaction,the main research method is numerical method.Therefore,we use Monte Carlo simulation to calculate the ground state properties and topological magnetic configuration of the system.The main research results of this paper include the following two parts.Firstly,we calculate the ground state characteristics of the system under the U'/U=1,including ferromagnetism(FM)phase,spiral phase,meron phase and vortex phase,etc.The real space magnetic configuration of each phase and the spin structure factor of k space are calculated,respectively.We focus on the meron phase and vortex phase,two novel topological magnetic structures,analyze the geometric configuration and periodic properties of topological magnetic structures,and calculate their related topological Numbers.Secondly,we calculate the ground state properties of the U'/U?1,including FM phase,antiferromagnetism(AFM)phase,spiral phase and AFM-Vortex,and calculate the relevant real space magnetic configuration and spin structure factors,etc.It is found that by adding the interaction between different components,equivalent to the spin z direction anisotropy in the spin system,it would affect or even destroy the various phases obtained in the U'/U=1 case.AFM-Vortex phase is analyzed and compared with Vortex phase to analyze the similarities and differences of the geometric structure.Finally,the phase diagram of ground state is given.The summary of this paper is given.