Vector Solitons And Their Wave Properties In Bose-Einstein Condensate

Bose-Einstein condensate(BEC)provides a good platform for the investigation of solitons,due to the atom-atom interactions and high controllability.Solitons possess both particle properties and wave properties.The particle properties,characterized by their ability to both move and undergo mutual collisions without deformation,have been widely investigated.Recently,the wave properties of solitons,mainly including nonlinear interference,nonlinear tunneling and internal state transition,have became a focus issue.The interference between solitons is typically nonlinear and can resist strong disturbance.It may facilitate future applications in interferometry for precision measurement.The atom-atom interactions of multicomponent BEC include not only intraspecies collisions between atoms but also interspecies collisions between atoms,which leads to much richer dynamics compared to the single-component BEC.Therefore,multicomponent BEC provides an excellent platform for the investigation of vector solitons.In this thesis,we study the wave properties of vector solitons: i)we provide the Darboux transformation(DT)method for solving the exact solutions of non-degenerate bright solitons.The interference and tunneling periods of non-degenerate bright solitons have been quantitatively obtained by defining the effective energy of solitons;ii)we present the first quantitative investigation of the interference and tunneling properties of vector dark solitons;iii)we propose the DT method of deriving multivalley dark soliton solution,and firstly demonstrate that the width-dependent parameters of solitons significantly affect the velocity and phase jump regions of multivalley dark solitons;iv)we propose a method with using the perturbation eigenvector to judge the different types of localized wave perturbation to choose the modulation instability branch;v)we present a scheme for measuring the phase jump of the Akhmediev breather based on the particle transition between components.These results enrich the types of vector solitons and deepen the understanding of soliton wave properties.It could be meaningful for high-precision measurement and quantum information fields.The concrete content are as follows:(1)The studies of interference properties are extended from scalar bright solitons to degenerate bright solitons.The results demonstrate that their interference and tunneling properties are similar to scalar bright solitons.Particularly,through developing the DT method,we obtain the exact nondegenerate bright soliton solutions in multicomponent BEC with attractive interactions.It is revealed that non-degenerate solitons are formed by the incoherent superposition of solitons in different components.We find that the interference of non-degenerate bright solitons presents multiperiodicity.The interference periods are obtained quantitatively by defining the effective energy of the soliton.Moreover,our analysis demonstrate that the collision of nondegenerate bright solitons is indeed inelastic,since it contains the coherent collision between solitons in the same component and the incoherent collision between solitons in the different components.(2)We study the interference properties of bright-dark solitons(dark-bright solitons)in a two component BEC with attractive(repulsive)interactions.We derive the bright-dark soliton solutions and dark-bright solitons solutions which can be applied to characterize the physical meaning of the parameters and analyzing the interference properties.The results demonstrate that the wave properties of bright solitons in one component can give rise to the interference and tunneling behavior of dark solitons in another component.Particularly,for the attractive BEC,we exhibit that interference effects between the two dark solitons can induce some shorttime density humps;for the repulsive BEC,the temporal-spatial interference periods of darkbright solitons have lower limits.On the contrary,wave properties are absent for scalar dark solitons and vector dark-dark solitons.These results have deepened our understanding of wave properties of dark solitons.(3)Based on the studies for non-degenerate bright soliton in BEC with attractive interactions,we further develop the DT method to obtain the multivalley dark soliton in multicomponent BEC with repulsive interactions.We demonstrate that the width-dependent parameters of solitons significantly affect the velocity and phase jump regions of multivalley dark solitons.Strikingly,a multivalley dark soliton is transformed into a breather after colliding with the single-valley dark soliton.This phenomenon occurs because the effective energies of solitons in the three components mix during the collision process.Furthermore,we explore the interference and tunneling properties of the multivalley dark soliton,which show multiple interference periods.Meanwhile,the width parameter affects the upper limit of the speed,thus each interference period admits an alterable lower limit.These properties are significantly different from the interference properties of single-valley dark solitons and non-degenerate bright solitons.(4)Considering that particle transition channels can emerge in the multicomponent BEC(such as single-particle transition,pair-particle transition),we further investigated the internal state transition in the two-component BEC with the pair-particle transition effects.On the one hand,we study the internal state transition induced by interference effects,and four types localized waves are obtained.The modulational instability analyses show that there are two modulational instability branches on the plane wave background.A possible way is suggested to clarify which modulational instability branch is chosen for a weak perturbation,when it admits more than one modulational instability branch.By this way we can understand the excitation mechanism of these localized waves more clearly.On the other hand,we study the internal state transition dynamics induced by the modulational instability.We propose a theoretical scheme for controlled particle transition efficiency by weak periodic perturbations.The particle transition efficiency can be changed by varying the perturbation period.The particle transition efficiency can be used to measure the phase jump of Akhmediev breathers.