Quantum Phase Transitions And Dynamic Properties In Novel Spin-Orbit-Coupled Bose Condensates

Ultra-cold atomic Bose-Einstein condensates(BEC)are always considered as promising platforms of quantum simulations drawing wide attentions of researchers,because they are not only capable to present many significant properties of solids and liquids,but also are more experimentally controllable comparing with solid materials.As is known to all,cold atoms are neutral particles,and how to use such neutral atoms to simulate the quantum features of charged particles like electrons have been a key point in the relavant field.In 2011,Spielman's group from NIST experimentally realized the first synthetic spin-orbit(SO)coupled BEC with the help of a pair of counter-propagating Raman beams.The significance of the experiment of NIST is showing that cold atoms are able to present the gauge properties of the charged particles,hence readily being used to simulate quantum Hall effects,topological super-conductors and insulators.NIST SO coupling,which is also called Raman induced SO coupling,is perhaps the simplest coupling model,since it only considered the lowest spin?_z(spin 1/2)being coupled with 1D linear momentum k_x,i.e.?_zk_x.Due to the SO coupling,single-particle spectrum of the BEC system presented a novel double-minima structure.When two-body interactions are included,cold atoms can choose to condensate into one of the two minima or into two minima simultaneously,presenting many novel mean-field phases,such as striped phase and plane-wave phase,which do not exist in conventional spinor BEC systems.Moreover,on the level beyond mean-field theory,SO coupled BECs also give rise to exotic properties of collective excitations,such as increased low-energy density-of-state,roton,as well as softening of collective modes.Recently,researchers have proposed many novel SO coupled models that greatly enriched the relevant research field.Some models generalized NIST's scheme into higher spin systems,higher dimensional systems like Rashba and Weyl.Some models even give rise to new coupling forms such as spin-tensor coupling and angular momentum coupling.In these schemes,researchers have found many novel ground-state density distributions like annular stripes and lattice pattern,exotic spin textures like spin-density wave and topological skyrmions,and interesting dynamic phenomena like k-space Josephson tunneling.Motivated by the above investigations,we present our recent works in this thesis.We first study the collective excitations of a trapped BEC with NIST SO coupling by solving Bose Bogoliubov-de-Gennes equations.Then,we investigate the angular spin vector and spin tensor coupling models in quasi-2D spin-1 BEC systems.Moreover,we generalize the concept of SO coupling into a spinor mixture,and show that the inter-species spin-exchange interaction provides a new way in inducing SO coupling.Our work are presents as follows.1.Collective excitations of a trapped BEC with SO coupling.We investigate the collective excitations of a Raman-induced spin-orbit coupled Bose-Einstein condensate confined in a quasi-one-dimensional harmonic trap using the Bogoliubov method.By calculating the transition strength,we are able to classify various low-lying excitation modes that are experimentally relevant.We show that the dipole and the breathing modes become soft at the boundary between the PW and the ZM phases,but are smooth across the boundary between the ST and the PW phases.By contrast,the spin dipole and the spin breathing modes have distinct features in all three phases.These features therefore be useful to experimentally distinguish various phases.2.Spin vector,spin-tensor and angular momentum coupled BECs.We propose two simple models in spin-1 Bose-Einstein condensates with the help of Laguerre-Gaussian beams.One model possesses a spin vector and orbit angular momentum coupling,whereas the other is with a spin tensor and orbit angular momentum coupling.We study the single-particle spectra and symmetries of these models,and then calculate the many-body ground-state phase digram by using both a variational method and numerical simulation of Gross-Pitaevskii equations.Various exotic annularly striped phases as well as spin textures are predicted to exist in these systems.Furthermore,we show that a many-body Rabi oscillation between two quantum phases can be induced by a sudden quench of the quadratic Zeeman shift.3.Spin-exchange-induced spin-orbit in a superfluid mixture.We investigate the ground-state properties of a dual-species spin-1/2 Bose-Einstein condensate.One of the species is subjected to a pair of Raman laser beams that induces SO coupling,whereas the other species is not coupled to the Raman laser.In certain limits,analytical results can be obtained.It is clearly shown that,through the interspecies spin-exchange interaction,the second species also exhibits SO coupling.Our work provides a way of creating SO coupling in atomic quantum gases,and opens up an avenue of research in SO-coupled superfluid mixtures.From a practical point of view,the spin-exchange-induced SO coupling may overcome the heating issue for certain atomic species when subjected to Raman beams.