Collective Dipole Oscillation Of Spinorbit Coupled Bosons Trapped In A One Dimensional Optical Lattice

As a highly coherent pure system,the cold atom system provides an important sample for the study of quantum system.Benefit from the experiment achievement of Bose-Einstein condensation and the higher tunability of optical lattice,people can study many condensed matter and solid physics in the optical-atom system.With the development of related experiments and theories,the spin-orbit coupling effect in solid materials has also been introduced into the optical lattice system.By using laser,one can couple the momentum of the cold atoms in the optical lattice with the internal spin state,and then make the lattice system present a variety of quantum phases and topological properties,which can prove some theories and conjectures in condensed matter physics.In recent years,with the extensive development of cold atom experiment in optical lattice,people have begun to pay attention to the non-equilibrium dynamics and other thermodynamic statistical properties in optical lattice system.In this work we study the model of flux lattice,specifically a two-leg BoseHubbard ladder lattice subject to effective magnetic flux,which can be implemented using spin-orbit coupled cold atoms trapped in an optical lattice.We consider that collective dipole oscillations are activated in this model via quenching an external harmonic trapping potential and show that this system can exhibit unique dynamical behaviors.A dynamical slowing down in collective dipole oscillations will take place near the transition point between the Meissner superfuild and vortex superfluid phases,which agrees quantitatively with a variational analysis.We show that such a quantum phase transition can also be probed via the damping of the collective dipole oscillation.The specific dynamical phenomena are explained with eigenspectra and level populations after the quenching.In the presence of interactions,the time-dependent density-matrix renormalization group(t DMRG)method is hired to study the collective dynamics.The case with weak interactions is similar to that without interactions,except that interactions tend to enhance damping.In addition to that,Bragg reflection can be observed when the quenching displacement exceeds a critical value.The case with strong interactions is also studied,in which case the phase transition points will be dramatically changed and the system can even move into the Mott insulator phase,which will greatly affect the corresponding collective dynamics.The phenomena predicted in this work can be readily observed in currently available experiments on atom flux lattices.