The Ground-state Properties Of Spin-orbit Coupled Dipolar Bose-einstein Condensates

Bose-Einstein condensation of ultra-cold atomic gases and molecular gases has attract-ed considerable interest both in experiment and theory since 1995.Especially in recent years,scientists have successively realized the dipolar Bose-Einstein condensates(BECs)and the spin-orbit-coupled quantum gases in experiment.Consequently,spin-orbit-coupled dipolar BECs have become one of frontier research hotspots in modern physics,and have provided new research topics and directions for exploring the exotic quantum phenomena and topo-logical quantum states in cold atom physics and condensed matter physics.In this thesis,the ground-state properties of Bose-Einstein condensates in the presence of spin-orbit coupling,dipole-dipole interaction,in-plane gradient magnetic field and rotation are investigated by using quantum many-body theory and numerical calculations.Specific work is as follows:First,we have investigated the ground-state properties of spin-orbit-coupled pseudo-spin-1/2 dipolar Bose-Einstein condensates(BECs)in a two-dimensional harmonic trap and an in-plane quadrupole field by using the mean-field theory and numerical calculation method The effects of spin-orbit coupling(SOC),dipole-dipole interaction(DDI)and the in-plane quadrupole field on the ground-state structures and spin textures of the system have been systematically analyzed and discussed.For fixed SOC and DDI strengths,the system shows a quadrupole stripe phase with a half-quantum vortex,or a quadrupole Thomas-Fermi phase with a half-quantum an-tivortex for small quadrupole field strength,depending on the ratio between inter-and intraspecies interaction.As the quadrupole field strength enhances,the system realizes a ring mixed phase with a hidden vortex-antivortex cluster rather than an ordinary giant vortex in each component.Of particular interest,when the strengths of DDI and quadrupole field are fixed,strong SOC leads to the formation of criss-crossed vortex string structure.For given SOC and quadrupole field,the system for strong DDI displays a sandwich-like structure,or a special delaminated structure with a prolate antivortex in the spin-up component.In addition,typical spin textures for the ground states of the system are analyzed.It is shown that the system sustains exotic topological structures,such as a hyper-bolic spin domain wall,skyrmion-half-antiskyrmion-antiskyrmion lattice,half-skyrmion-skyrmion-half-antiskyrmion lattice,and a drum-shaped half-antiskyrmion.Second,we have studied the ground-state structure of spin-orbit-coupled dipolar BECs in a rotating harmonic trap.We find that in the case of fixed SOC,quadrupole magnetic field and DDI,for initially mixed BECs and initially separated BECs,the increase of rota-tion frequency leads to the generation of a complex vortex structure composed of a triangular antivortex lattice and a hidden antivortex string,and that of an antivortex string,respective-ly.For fixed rotation frequency,DDI and quadrupole magnetic field,with the increase of SOC strength,the ground state of the system evolves from a half-quantum antivortex into a composite vortex structure consisting of an antivortex pair and a hidden vortex string,or into a pure antivortex string.In the case of fixed DDI,rotation frequency and SOC,the sys-tem exhibits a half-moon-shape density profile accompanied with an inhomogeneous hidden antivortex string when the strength of the gradient magnetic field is increased.In addition,when the DDI strength is changed,the system shows as a prolate antivorex string composed visible antivortices and hidden antivortices.These interesting topological structures have contributed to a new understanding of the physical properties of ultracold atomic systems.