Properties Of Solitons In Fractional-order Bose-einstein Condensates

Fractional diffraction model is a novel fractional quantum physics model,which is of great significance for the study of space beam propagation dynamics.This paper based on the nonlinear fractional Schr（?）dinger equation,investigates the formation and propagation be-havior of nonlinear optical solitons in fractional quantum couplers and matter wave solitons in fractional spin-orbit-coupled Bose-Einstein condensates.The specific research contents are as follows:First,Newton iterative method is used to solve the nonlinear fractional Schr（?）dinger equation with intermodal coupling,and soliton steady-state solutions are obtained.Bloch spectra with the linear periodic structure are obtained by the plane wave expansion method.The difference between fractional diffraction and conventional diffraction band structures is compared.The results show that the band gap moves down and the bandwidth Narrows with the decrease of Lévy index.The effects of the normalized linear coupling constantand the normalized Kerr nonlinear strength2)on the shape of solitons with different parameters are studied.The results show that,with the decrease of,the two components show an opposite trend when other parameters are fixed.The influence of2)on the shape of the soliton is affected by the interference of the fractional diffraction term,showing different trends.The effects of Lévy indexand chemical potentialon soliton stability were studied by linear stability analysis,and the stability of soliton was verified twice by Crank-Nicolson real-time evolution method.The results show that there are stable solitons in the fractional coupler,with the increase ofand,the solitons become more stable.Second,the steady-state solutions of matter-wave solitons in fractional-order spin-orbit-coupled Bose-Einstein condensates were found using Crank-Nicolson imaginary-time evo-lution and variational energy functional methods.Based on the characteristics of static bright solitons,two kinds of wave equations are proposed,which satisfy the symmetries ofandrespectively.In both cases,the basic properties of bright solitons are studied.The re-sults show that the spin-orbit coupling strength=1.0 may be a transition point,and around this point,the two cases of soliton state and the pseudo-spin polarizations in non-zero detun-ing show opposite changes.Then,based on the stable solution,an initial velocity is given to the wave function,and the influence of the motion velocity on the dynamic characteristics of the solitons is obtained.It is found that the moving solitons need a longer time to reach the equilibrium in non-zero detuning than in zero detuning.Last,the interference behavior of moving bright solitons in spin-orbit-coupled Bose-Einstein condensates with space fraction diffraction is discussed,which is affected by Lévy index,spin-orbit coupling strength,detuningand phase.The results show that with the decrease of,the collision area of solitons changes,the number of central bright stripes is also affected,and even several groups of interference fringes appear.With the increase of,the collision time of solitons is advanced and the overall collision time is extended due to the occurrence of multiple interference fringes.Differentwill affect the number of central bright stripes,and the image of population transfer can be observed.In addition,the change of the pseudo-spin polarizationwithis also studied,and observe the phenomenon of polarization reversal,the atomic number of the two components exchange at this point.