Dynamical Properties Of Solitons In Single-and Two-species Bose-Einstein Condensates

The experimental realization of Bose-Einstein condensation (BEC) provides aunique platform to explore the nonlinear matter wave. Especially, due to thesuccessfully observation of bright, dark and vector matter wave solitons, nonlinearproperties in BEC has been one of hot topic in the fields of both nonlinear science andultracold atomic physics. Theoretically, the properties of the BEC are usuallydescribed by the Gross-Pitaevskii (GP) equation based on the mean-fieldapproximation. In the GP equation, the controlling macroscopical parameters are thethe external potential and s-wave scattering length(SL) representing the strength ofatomic interaction. Expermetally, the external potential can be tuned by the externalmagnetic field or laser, and the atomic interaction can be controlled by means ofFeshbach resonance. To date, it was shown that the nonlinearly properties of BECdepend strongly on the external potentials and atomic interaction. In this thesis,considering the time-dependent SL, we study the propagating and collision propertiesof BECs trapped in the harmonic potentials and/or optical lattice potential. The mainworks of this thesis are organized as follows:Firstly, considering time-dependence of both SL and external potential, we studythe collisional behaviors of two bright solitons in a single-species BEC by developingDarboux transformation. It is found that the amplitude and width of each soliton, andthe distance between two solitons can be controlled by tuning SL. For linearlyincreased SL but nonlinearly decreased external potential, especially, the atom transferbetween two solitons is observed. This opens possibilities for future application inatoms transport. Furthermore, the collision types, either head-on,“chase”, or periodiccollision between two solitons can be controlled by tuning both SL and externalpotential.Secondly, considering a periodically oscillating harmonic potential, we explorethe propagating properties of bright solitons in a single-species BEC. It is found thatunder a slow oscillating potential, soliton movement exhibits a nonperiodic oscillation,different from the periodic oscillation under a time-independent harmonic potential.Furthermore, the head-on and/or “chase” collisions of two solitons have been obtained,which can be controlled by the oscillation frequency of potential.For two-species BECs, thirdly, we study the propagating properties of bright-bright solitons under the external harmonic potentials. For the separatedbright-bright solitons, it is shown that the interactions between bright-bright solitonsvary from repulsive to attractive interactions with the increasing their separatingdistances, and the bright-bright solitons are localized at equilibrium position. Thesestable bright solitons may open possibilities for future applications in coherent atomicoptics. For the overlapped bright-bright solitons, interestingly, a transition behaviorfrom oscillation to localization is observed with the increased interspecies SL andfixed intraspecies SL. Meanwhile, this transition behavior can be controlled by tuningthe transverse trapping frequency of harmonic potential. Then, we study the collisionproperties of bright-bright solitons in two-species BECs with the harmonic externalpotentials. When the intraspecies SL are fixed but the interspecies SL increasedexponentially, the bright-bright solitons show a transmission and trapping collision.And the two separate solitons can merge into a single bound complex which possessesa very high peak and a very narrow width due to the stronger attractive interspeciesinteractions. When the interspecies interaction is exponentially decreased, areflection-transmission collision transition is observed for the repulsive interspeciesinteraction.Furthermore, we study numerically the dynamics of bright-bright gap solitons intwo-species BECs trapped in an optical lattice. It is shown that the directions ofmotion and oscillations of the bright-bright solitons in the first gap can be effectivelycontrolled by adjusting the lattice constant and depth, respectively. Especially, twoseparated solitons in the first gap can be localized in the optical lattice, and the fissionof each localized soliton is newly observed due to the increasing of the lattice depeth.In addition, we find that the collisional type of bright-bright solitons, eithertransmission-or reflection-collision, also depends on the lattice depeth.