Novel Quantum States Of Ultra-cold Spinor Atomic Gases With Spin-orbit Coupling

The Bose-Einstein condensates(BEC)of ultracold atoms have been proven by more and more experiments to be unexceptionable platforms for studying interacting many-body quantum systems since the experimental discovery in 1995.The condensates can be controlled spatially and temporally with external lasers and magnetic fields conveniently.Theoretically,these low-temperature systems can be described starting from first principles,and their ground states and dynamical properties are accurately captured by the mean-field theory.In recent years,due to the possible existence of various types of new topological defects,including vector solitons,vortex lattice,Dirac monopole and skyrmions,etc.,ultracold atomic BECs with spin degrees of freedom have become one of the hot topics in this field.The accurate controllability by the external fields,especially including the spin-orbit coupling and the bizarre trapping potentials,greatly promoted the study for these novel topological configurations.Exploring their basic properties and finding effective ways to control them become into one of the hottest topics in this field.In this thesis,based on the latest research achievements in the fields of the spinor BECs and the spin-orbit coupling(SOC)effect,combining the theoretical analysis and numerical simulation method to solve the average Gross-Pitaeviskii equation,the novel quantum state and its properties in the spinor F =1 BEC with the spin-orbit coupling are investigated.we discussed the magnetized vector solitons in spinor BEC with the spin-orbit coupling and the Zeeman coupling,the exotic ground states of a spinor BEC trapped by a toroidal potential and the ground-state and rotational properties of a spin-1 BEC in a concentrically coupled toroidal trap.Reveals the roles played by the field parameters on the structure and property of the system state.From the density distribution,the phase distribution,magnetic susceptibility,topological charge density and spin texture show the transition of the novel quantum state and some innovative research results are obtained.Specific content is as follows:1.Magnetized vector solitons of spin-1 BEC with the spin-orbit couplingThe property of matter-wave vector solitons in a spin-1 BEC with the SOC and Zeeman coupling is investigated by multiscale perturbation method.The energy spectrum and the corresponding state vectors of the system are obtained analytically,and they can be adjusted by the parameters of the system.The bright and dark vector solitons are formulated by reducing the three-component coupled Gross-Pitaeviskii equations to a standard nonlinear Schr¨odinger equatoin,which has the solutions of the bright and dark solitons with positive or negative mass depending on the product of the effective dispersive and nonlinear coefficients.The moving vector solitons are demonstrated by adjusting specific momentum near the energy minimum.Finally,the magnetized features of the vector solitons are discussed by the spin polarization of the system.2.Ground state of spin-1 BEC with the spin-orbit coupling in a toroidal trapThe ground-state properties of a spin-orbit-coupled spin-1 BEC in a toroidal trap are investigated.The exotic states,such as the necklace state,the persistent flow and even the vortex state,for the three components in the system are induced by adjustable external parameters.It is found that the petal number of the necklace states increases with the intensity of the SOC,and the anisotropy of the SOC can be used to control the structure of the ground state.The rotation of the condensate induced by the external field makes the densities of the three components asymmetric and tends to transform the necklace state to the persistent flow.The radius of the toroidal potential is another degree of freedom for manipulating the necklace state.In addition,the transition between the necklace and vortex states,intermediated by the persistent flow,can be controlled by the ratio of the density-density and spin-exchange interactions.3.Novel state of spin-1 BEC with the spin-orbit coupling in a concentrically coupled toroidal trapWe investigate the exotic states of an antiferromagnetic spin-1 BEC with SOC in a concentrically coupled toroidal trap.It is found the necklace-type state with double-ring structure can be created in the system due to the interplay among SOC,external potential,and rotation.The petal number of the necklace state increases with increasing the strength of the SOC.When the rotation is included,the condensate is dragged into the outer trough of the trap by increasing the rotation frequency,which make it possible for realizing the ground state,where the inner trough is populated by the necklace sate and the outer one is the persistent flow.Once the two troughs of the toroidal trap are in the persistent flow state at specific effective interactions between atoms,the hidden vortices may occur at the central region of the trap and the barrier between the two troughs.In addition,the visible vortex with laminar structure can be generated under larger effective atomic interaction.All of these studies can help us to understand the superfluidity properties of the spinor BECs,illuminate the topological excitations in the such coupled complex nonlinear systems,and explain the roles played by the SOC,Raman coupling,Zeeman coupling and the interactions between atoms in the systems.The corresponding results may further enrich the state of the spinor BECs in the toroidal potentials and demonstrate the exotic properties of the superfluid.At the same time,the exploration and study of the novel state in these systems will lay theoretical foundations for the constructions of the new quantum devices based on the cold atomic systems such as supercurrent Josephson junctions and the atomic interferometers.