Modulation Instability And Matter-wave Solitons In Bose-einstein Condensates Coupled With Helicoidal Spin-orbit Coupling

In recent years,with the realization of Bose-Einstein condensate(BEC)in the experiment,many nonlinear dynamical behaviors such as the soliton generation and superfluid-insulator transition et al were found continually in BEC.Modulation instability(MI)plays a key role in the development of these nonlinear dynamics and has an important influence on plasma physics,magnetomechanics,nonlinear optics,hydrodynamics,BEC dynamics and other physical fields.Recently,with the successful realization of spin-orbit coupling in BEC system,the enthusiasm for the study of cold atom systems has been stimulated again.Spinorbit coupling not only brings many adjustable parameters,but also brings more and more interesting phenomena due to its nonlinear characteristics.For example,there will be more diverse soliton structures(bright soliton,dark soliton and stripe soliton)in the spin-orbit coupling BEC system.In this paper,we mainly investigate the modulation instability and matter-wave solitons in Bose-Einstein condensates with helicoidal spin-orbit coupling.Firstly,the research background and methods of this paper including the basic theory of BEC,the experimental realization of spin-orbit coupling in BEC,and the current research status of the modulation instability and matter-wave soliton in spin-orbit coupling BEC are briefly introduced.Secondly,we theoretically study the MI of the two-component helicoidal spin-orbit coupled BECs.The effects of the helicoidal gauge potential,spin-orbit coupling,and atomic interactions on MI are investigated.The results indicate that the presence of the helicoidal gauge potential breaks the symmetric properties of MI,strongly modifies the distribution of the MI region and the MI gain in parameters space,and the MI can be excited even when the miscibility condition for the atomic interactions is satisfied.Furthermore,the effect of the helicoidal gauge potential on MI is strongly coupled with the intra and intercomponent atomic interactions.Particularly,with the increase of the helical gauge potential,the MI gain increases for the repulsive atomic interaction case,however,theMI gain decreases for the attractive atomic interaction case.The direct numerical simulations are performed to support the analytical predictions,and a good agreement is found.Thirdly,we study the various types of matter-wave soliton solutions in BEC with helicoidal spin-orbit coupling.By using the Multi-scale perturbation method,the two-component coupled Gross-Pitaevskill equations describing the BEC system with helicoidal spin-orbit coupling are simplified into an effective nonlinear Schr¨odinger equation.According to this equation we not only obtain the soliton solutions of the system,but also analyze the energy band structure of the system and find that the helicoidal gauge potential,spin-orbit coupling,Zeeman splitting effect and atomic interactions have a great influence on the type of soliton.It is found that the presence of helicoidal gauge potential breaks the symmetric structure of the energy band in the momentum space,and the energy band of the system will change from a single-well structure to a double-well structure with the increase of the helicoidal gauge potential.Another finding is that the group speed of the matter wave soliton is not related to the strength of spin-orbit coupling and Zeeman splitting effect but is only related to the helicoidal gauge potential when the momentum is zero,and it is numerically equal to the value of the helicoidal gauge potential.In addition,the research reveals that there only exists positive mass dark solitons or negative mass bright solitons when the atom interaction is repulsive.On the contrary,the system only exists positive mass bright solitons or negative mass dark solitons when the atom interaction is attractive.Finally,we summarize the main results of this paper and give an outlook of the research work in the future.