Oscillation Properties Of Matter-wave Solitons In Harmonic Potentials

Bose-Einstein condensate(BEC)has become a good platform to investigate the motion of solitons,due to the high controllability of atom-atom interactions and external potentials.The motion of solitons in external potentials can well reflect their particle properties.Numerous experimental and theoretical studies have shown that the profile and velocity of solitons remain unchanged after collisions.Due to that harmonic potential is one of the widely used bound potentials in BEC experiments,soliton oscillation properties are widely discussed in this potential.It is worth noting that the collision process of soliton not only reflects its particle characteristics,but also generally has a phase and position shift of soliton.The position shift is manifested as a sudden position deviation relative to the original trajectory after soliton collision.This position shift is related to the amplitude and collision velocity of two solitons.When the soliton amplitudes are determined,the smaller the collision velocity,the more obvious the position shift.However,in the past studies on motion of multiple solitons in harmonic potentials,the influence of position shift on its oscillation properties has not been addressed clearly.Based on soliton collision properties,we expect that the position shift caused by collision will significantly change the oscillation period of solitons in harmonic potential.In this thesis,we systematically investigate the modification of oscillation properties of two kinds of matter wave solitons caused by position shift in harmonic potentials.And the oscillation properties of dark-bright solitons are further discussed under different confine of harmonic potentials.The concrete content are as follows:(1)In the attractive interaction BEC,we review the oscillation properties of single-bright soliton,and investigate the modification of the oscillation period of two-bright solitons caused by position shift in harmonic potentials.The modification of oscillation periods is discussed for three different collisions,including coherent collisions within components,incoherent collisions between components,and the co-existence of the two collisions.The modified oscillation periods are described by defining a characterized speed,with the aid of asymptotic analysis on related exact analytic soliton solutions in integrable cases.Our theoretical and numerical results show that the change of the period induced by collision can be used to distinguish coherent and incoherent collisions between solitons.(2)In the repulsive interaction BEC,we extend previous study of scalar dark soliton to the dark-bright soliton cases.We systematically discuss its oscillation properties under different confine of harmonic potentials.When external potential field is applied to bright soliton component,we discussed the conditions of oscillation and the unique oscillation period of soliton.We further investigate the collision of two solitons,and theoretically give the modification of oscillation periods caused by the position shift.When external potential field is applied to dark soliton component,our results show that the oscillation period of dark-bright soliton is significantly different from that of scalar dark soliton and bright soliton,and the effect of the number of bright soliton particles on oscillation period is discussed.When external potential fields are applied to both components,we discuss the effect of ratio of applied potential on the oscillation period of dark-bright soliton.As the potential of the bright soliton component changes from anti-harmonic to harmonic potential and continues to increase,the oscillation period of the dark-bright soliton gradually increases until it can no longer oscillate.We give a theoretical explanation under the quasi-particle image for the relevant numerical simulation results.Our results reveal that the position shift caused by soliton collision can significantly change the oscillation period of solitons in harmonic potentials,and further enriches the understanding of oscillation properties of dark solitons.