Topological Excitation Of Multi-component Spin-orbit Coupled Rotating Bose-einstein Condensates

Since the experimental realization of spinor Bose-Einstein condensates(BECs)in optical dipole trap,multi-component BECs as a family of quantum fluids manifesting both magnetic order and superfluidity have opened a new research platform for ultracold atomic systems.In particular,the realization of artificial gauge potential such as spin-orbit coupling(SOC)in ultracold atomic gases makes the BECs with SOC become one of the frontier research hotspots in modern physics,and thus provides new subjects and direction for exploring novel quantum phenomena and topological quantum states in cold atom physics,condensed matter physics,optics and particle physics.The main research contents of this thesis are given as follows:First,we investigate the ground-state properties of Rashba spin-orbit coupled pseudospin-1/2 BECs in a rotating two-dimensional(2D)toroidal trap by using the mean field theory and numerical calculation methods.We show that in the absence of SOC the increasing rotation frequency enhances the creation of giant vortices for the initially miscible BECs while it can lead to the formation of semi-ring density patterns for the initially immiscible BECs.Without rotation,strong 2D isotropic SOC yields a heliciform-stripe phase for the initially immiscible BECs.Combined effects of rotation,SOC,and interatomic interactions on the vortex structures and typical spin textures of the ground state of the system are discussed systematically.In particular,for a fixed rotation frequency above the critical value,the increasing isotropic SOC favors a visible vortex necklace in each component which is accompanied by a hidden giant vortex plus a(several)hidden vortex necklace(s)in the central region.In the case of one dimensional anisotropic SOC,large SOC strength results in the generation of hidden linear vortex string and the phase transition.Furthermore,the peculiar spin textures including skyrmion lattice,skyrmion pair and skyrmion string are revealed in this system.Second,the ground-state structures of spin-1 BECs with different types of SOC in a rotating toroidal trap are studied systematically.We show that,in the case of antiferromagnetic phase,the SU(2)SOC and SU(3)SOC with the same strength result in the stripe phase and the doubly quantum vortex structure,respectively;for the fixed rotation frequency,the two different types of SOC lead to the generation of the central giant vortex structure and that of the triangular layered vortex lattice,respectively.In the case of ferromagnetic phase with fixed rotation frequency,SU(2)SOC tends to sustain the formation of giant vortex,while SU(3)SOC favors the creation of three chain vortex structures.When there is only a coupling along the x direction for the SU(3)SOC,a doubly quantum vortex string is generated along the x axis in the system.It is demonstrated that the competition among SU(3)SOC,rotation,and spin-exchange interactions leads to novel vortex structure and peculiar spin texture constituting of half skyrmion string.Furthermore,the effect of Zeeman magnetic field on the topological structure and the phase transition of spin-1 BECs with SOC is studied in detail,which provides an alternative effective method to control the spinor BECs.