Transport Of Spin-orbit Coupled Bose-einstein Condensates In Lattice With Defects

In recent years,the investigations concerning the transport properties of cold atoms in a deep annular lattice have become a hot topic in modern physics.The successful realization of ultracold atoms in an optical lattices has made it be an ideal playground to explore a variety of fascinating quantum phenomena.Especially,the spin-orbit coupled Bose-Einstein condensates in optical lattice has been realized in the experiment,which makes the system with transport property become a hot issue.In addition,many research are mainly focus on pure lattice,but in the reality system,optical lattice always exist impurities or defects.Hence,the transportation property of the disordered nonlinear discrete system has become a challenging issue.Particularly,the competition between defect and atomic interaction plays a crucial role in transportation property of the system and induces rich phenomena,such as,the inhibiting of transportation and superfluid regime.We mainly investigate the conditions for crossing from a superfluid regime to a normal regime.In this paper,the specific contents and conclusions are as follows:Firstly,the physical background and the related physical knowledge are briefly introduced,including Bose-Einstein condensate,spin-orbit coupling and the effect of defect in the system.Secondly,we theoretically investigate the propagation properties of spinorbit(SO)coupled Bose-Einstein condensate in an optical lattices with defects.By using the tight-binding and two-mode ansatz approximation,we find that the coupled effects of SO-coupling,Raman coupling,Zeeman field and atomic interactions can control the superfluidity of the system.Particularly,there exists a critical scattering length for crossing from a normal regime to a superfluid regime.The critical scattering length for supporting the superfluidity strongly depends on the defect type,SO-coupling,Raman coupling,Zeeman field and quasimomentum of the plane waves.The SO-coupling and quasimomentum induce the system more easily entering into the superfluid regime,while the pure Raman coupling and pure Zeeman field inhibit the system entering into the superfluid regime.Interestingly,the coupled effect between Raman coupling and Zeeman field can both enhance and suppress the system entering into the superfluid regime.In addition,the superfluidity of the system also depends on the defect type.Thirdly,we theoretically investigate the periodic modulation effect on propagation properties of Bose-Einstein condensate(BEC)in a deep annular lattice with defects both analytically and numerically.By using the two-mode ansatz and the tight-binding approximation,we find that the coupled effects of periodic modulated atomic interactions and quasi-momentum can control the superfluidity of the system.Particularly,we find that the system enters the superfluid regime is only related to the defects,when there is no periodic modulation in the system.However,when the periodic modulation is considered,we find that the critical condition for the system entering the superfluid regime is not only in relation to the defects but also to the momentum of the plane waves,the periodic modulated amplitude and the periodic modulated frequency.Specially,the increases of modulated amplitude and quasi-momentum or the decrease of modulated frequency can make it easier for the system enter the superfluid regime.This engineering provides a possible means for studying the periodic modulation effect on propagation properties and the corresponding dynamics of BECs in disordered optical lattice.Finally,we summarize the main results and give an outlook of the future in ultracold atoms field.