The Ground-state Properties And The Dynamics Properties Of Binary Spin-orbit Coupled Bose-Einstein Condensates

Bose-Einstein condensation(BEC),as the fifth matter form in nature,is one of the research hot spots of contemporary physics.Great progress in both the theoretical and experimental aspects of Bose-Einstein condensates(BECs)has been achieved in recent years due to their good purity,excellent quantum coherence and a high degree of artificial controllability.Especially,scientists have realized spin-orbit coupled quantum gases since 2011,which has greatly stimulated research interest concerning the spin-orbit coupled BECs and has provided a new way to explore novel quantum states and dynamic properties of quantum many-body systems.This thesis mainly includes two aspects of work.First,we have investigated the ground-state properties of binary Bose-Einstein condensates(BECs)with Dresselhaus spin-orbit coupling(D-SOC)in a rotating anharmonic trap by using the mean-field theory and numerical calculation methods.In different initial states,we have analyzed the effects of the SOC and rotation frequency on the ground-state structure.For initially mixed BECs without SOC,increasing rotation frequency can lead to the structural phase transition of the system.In the presence of isotropic D-SOC,the system sustains Anderson–Toulouse coreless vortices,circular vortex sheets,and combined vortex structures.In particular,when the rotation frequency is fixed above the radial trapping frequency the strong D-SOC results in a peculiar topological structure.In addition,the system exhibits rich spin textures including basic skyrmion,half-skyrmion cluster and various skyrmion lattices.The skyrmions will be destroyed in the limit of large D-SOC or rotation frequency.Furthermore,the effects of anisotropic D-SOC and Rashba-Dresselhaus SOC on the topological structures of the system are discussed.Second,in the field of quantum physics,the periodically kicked BECs present an ideal platform to study novel quantum dynamic behaviors including quantum resonance,quantum chaos,dynamical localization,quantum rachet,and so on.In this context,we have investigated the dynamic properties of the double-kicked and spin-orbit coupled BECs.It is shown that when the kick period the system exhibits interesting quasi quantum resonance and quasi quantum anti-resonance by regulating the relevant experimental parameters.For the quasi quantum resonance,the energy of the system displays an oscillatory growth and there are two resonance curves.By comparison,for the quasi quantum anti-resonance,three stationary states contribute to the energy evolution of the system which oscillates with two different energy amplitudes.At the same time,the system can show quantum beating,Rabi oscillation,and high order quantum resonance.In addition,the SOC makes the system occupy the narrower regime in the momentum space.Furthermore,the relation between the kick period,kick strength as well as the SOC strength and the average energy,fidelity as well as the state density in momentum space is revealed and discussed.