Study On Dynamics Of Ultracold Atoms With Spin-Orbit Coupling In A Double-Well Potential

Ultracold atomic gases afford unique opportunities to simulate quantum optical and condensed matter phenomena,many of which are difficult to observe in their original contexts.Over the past decade,much theoretical and experimental progress in implementing quantum simulations with ultracold atomic gases has been achieved,exploiting the flexibility and tunability of these systems.The recent generation of spin-orbit(SO)coupling in ultracold atomic gases has brought the simulation of a large class of gauge field related physics phenomena into reach.In condensed matter systems,SO coupling is crucial for the spin-Hall effect,topological insulators,topological superconductors/superfluids and so on.With such achievements,SO-coupled(SOC)ultracold atomic gases have emerged as excellent platforms to simulate and investigate interesting gauge field-related phenomena,which have important applications for the design of next generation spin based atomtronic devices and for topological quantum computation.One of the richest scenarios opens up when two internal hyperfine states of the same bosonic atom are coupled to each other by means of two counterpropagating laser beams and confined by a one-dimensional double-well potential.Quantum dynamics of a BEC with single-species and mixtures in a double-well potential has been widely investigated.In particular,the coherent atomic tunneling between two wells results in oscillatory exchange of the BEC,which is analogous to the Josephson effects and the weakly atomic interactions display nonlinear generalizations of typical macroscopic quantum self-trapping,all of which have been observed in experiments.SOC BEC in a double-well potential represents the ideal arena to analyze the spin-dependent phenomenon,and would be essential for engineering spin Hamiltonian models and spindependent atomtronic transistors.Based on the rich theory and the potential application value,in the present thesis,SOC BEC in a double-well potential is investigated theoretically.The thesis includes one introduction(see chapter 1)and four chapters,and the main contents are shown in chapters 2-5.In chapter 1,a brief introduction on the research background of this thesis is given.Mainly include the ultracold atomic physics,some important concepts closely related to the study including synthetic gauge fields and the neutral atoms spin-orbit coupling in the generated effective non-Abelian gauge fields.Moreover,the potential significance and value of the research SOC in ultracold atomic system are reviewed in detail.In chapter 2,the mean field energy levels associated with degeneracy and symmetry breaking of the SOC BEC in a double-well potential is investigated.The mean-field analysis shows that the energy levels of the system are modified significantly by the atomic interactions.Without atomic interactions,four energy levels change linearly with the tunneling amplitude,and the Raman coupling.However,whenever atomic interactions is considered,three more energy levels is appear,which have a nonlinear dependence on those parameters above.The analytical expressions of the mean-field energies are obtained,which are consistent with the numerical results.The degeneracy of the energy levels and the related symmetries of each stationary state are also investigated.The symmetry breaking induces the multi-degeneracy of the energy levels.Moreover,the macro-symmetry of the system,i.e.the symmetric properties between the stationary states of the degenerate energy levels is discussed in detail.In chapter 3,quantized energy spectrum and flat band of the SOC BEC in a doublewell potential are studied.The commutability between quantum energy spectrum and mean field energy levels is given,which show that the quantized energy spectrum are bounded by the mean-field energies.The single-particle quantized energy spectrum dependent on Raman laser intensity shows a high degeneracy flat band in the ground state,which remains stable against changes of the Raman laser intensity.Many-body interactions between atoms remove this high degeneracy.By using the perturbation theory with interactions as the perturbation,analytical results are obtained,which agree well with the numerical results.The results related to a huge degeneracy may lead to possible phases with non-trivial topological properties,and may have important applications in quantum information and quantum optics.In chapter 4,measure synchronization(MS)of the two atomic hyperfine states for the SOC BEC in a double-well potential is investigated.The transition from non-MS to MS dynamics is related to the energy exchange between the two atomic hyperfine states.Without considering interspin atomic interactions,the transition from non-MS to MS dynamics of two coupled atomic hyperfine states is determined by Raman laser intensity.When considering the interspin atomic interactions,the system displays MS breaking dynamics resulting from the competition between intraspin and interspin atomic interactions.The results provides an effective way for controlling the MS dynamics of two atomic hyperfine states,and may be helpful to investigate the collective coherent dynamical behavior.In chapter 5,we investigate dynamical coherent control of interwell tunneling and spinflipping by high-frequency driven spin-dependent oscillating gradient magnetic field.We consider a single spin-half particle with SO coupling in a double-well potential.The spin selectivity is provided by Zeeman shifts created with a magnetic field gradient.In the framework of the Floquet theory,we obtain the Floquet quasienergy spectrum dependent on the driving parameters.The Floquet quasienergy spectrum exhibits anticrossings and crossings for different types of strong driving gradient magnetic fields,which are associated with different types coherent control of spin-flipping and tunneling.By selective modulations parameters,we propose a switchlike effect scheme for control transport and spin-flipping of the system.The results can be exploited in optical-lattice setups so as to control the tunneling between lattice sites and spin-flipping between two spin states,and may offering a powerful method to generate artificial fluxes for cold atom.Applying the present results,we suggest a scheme for designing a spin-dependent switchlike couplers and quantum motor.In the last chapter,we conclude the thesis and look forward to the future in this research field.