Novel Quantum States Of Spinor Bose-einstein Condensates With Spin-orbit Coupling

The experimental realization of Bose-Einstein condensation(BEC)opened up the exploration of topological quantum state in a controlled environment.Atomic physics can provide the basic methods for creating and manipulating cold atom systems.Because interactions between atoms play a key role for many behaviour of ultracold atoms,the concepts and methods from condensed matter physics are used and extended.Investigations of spatial and temporal correlations of particles provide a link to quantum optics.Trapped atomic clouds have some similarities to atomic nuclei,and insights from nuclear physics have been helpful in understanding their properties.Due to the widely tunable and nearly disorder-free characteristic of the BEC,it is an ideal platform for the study of topological defect and quantum phase transition.Most of the atoms that realize BEC have internal degrees of freedom.The spin degrees of freedom of the atoms in optical trap are not frozen,the atoms can be condensed into each superfine quantum state,which is known as spinor BEC.This spin degree of freedom becomes a relevant dynamical variable,which gives rise to new quantum states,such as domain wall?fractional vortex?magnetic monopole and so on.For this reason,we will obtain the richer quantum states in the spinor BEC.In recent years,with the developments of topological insulators and the spin-Hall effect,the research of spin-orbit coupling has attracted more and more attention.In particular,the experimental realization of artificial spin-orbit coupling in ultracold atomic gases opens a new window for studying topological quantum states.The spin-orbit coupling in the BEC is high tunability and controllable,which provides an unprecedented opportunity to study the novel quantum states,including fractional skyrmion? quantum quasicrystals and supersolid state.With the developments and applications of new technologies and new methods in experiments,exploring the novel topological states in spinorbit coupled BEC,recently have been hot topic in the ultracold atomic physics.In chapter 1,we first give a brief review of history on the development of the research for the BEC.We then introduce the basic theory of the BEC.Furthermore,we introduce the experimental progress of spin-orbit coupling in the BEC,and theoretical derivation of the Hamiltonian with the spin-orbit coupling.Finally,we introduce the classification of topological defects based on knowledge of group theory.In chapter 2,we investigate the configuration of monopoles in the spin-orbit coupled BEC.By adjusting the spin-orbit coupling strength,it is found that the monopoles with polar-core vortex and the monopoles with the square lattice can occur in the present system.The influence of the anisotropic spin-orbit coupling,the anisotropic optical trap,and the magnetic field gradient on the properties of the monopoles have also been investigated.We further confirm that the monopoles with the polar-core vortex are a long-lived structure.Therefore,experimental observation of such the monopoles will be easier.Finally,we propose an experimental scheme for producing magnetic monopole in spin-orbit coupled spinor BEC.In chapter 3,we consider the spinor BEC with Weyl type spin-orbit coupling and rotation.When the spin-orbit coupling is strong,the ground state of the system exhibits square lattice phase for the non-rotation case;for the rotation case,two half-skyrmion chains can occur,which is perpendicular to each other.For the weak spin-orbit coupling case,half-skyrmion displays the symmetrical arrangement around the center of condensate as the rotation frequency is increased.In chapter 4,we first study phase separation and the corresponding phase diagram in the spin-orbit coupled BEC with rotation and Rabi coupling.The spin-orbit coupling can result in the hidden vortices in the presence of the rotation,which provides a method of creating the hidden vortices in the spinor BEC.Furthermore,we determine the entire phase diagrams of the hidden vortices,which shows the critical condition and phase boundary of the occurrence of such vortex states.In chapter 5,we study the ground state of a rotating two-component BEC with spin-orbit coupling and gradient magnetic field.We concentrate on the effects of the spin-orbit coupling and the gradient magnetic field on the ground state.In the presence of the gradient magnetic field,increasing the strength of the spin-orbit coupling can induce a phase transition from skyrmion lattice to skyrmion chain.The gradient magnetic field can induce a phase transition from a single plane-wave to half-skyrmion.The gradient magnetic field and spin orbit coupling,as the governing parameters of the system,can be used to control the transformation between different ground states.In chapter 6,we give a brief summary of the research contents of this paper.