The Soliton Dynamics Of Two-Component Bose-Einstein Condensates

Since the observation of two-component Bose-Einstein condensates (BECs) in the experiments, there are plenty of researches concentrating on the nonlinear phenomena of multi-component BEC. Experimentally, the controllable two macroscopical parameters are the external trapping potential and the strength of interatomic interactions. And the interatomic interactions could be modulated by means of Feshbach Resonance. In multi-component BECs, the interatomic interactions include both the intraspecies interactions and the interspecies interactions. Theoretically, the ultra-cold two-component BECs system in the mean field approximation can be well described by coupled time-dependent Gross-Pitaevskii (GP) equations. In this thesis, beginning with GP equations and applying multiple-scale method, we analytically study the dynamical properties of the two-component Bose-Einstein condensates trapped in a harmonic plus quartic anharmonic potential, and the dynamical properties and collision properties of the solitons in two-component BECs with time-dependent interspecies interactions. The thesis is organized as follows:In chapter one, we introduce the elementary knowledge, the basic concept and theory of BEC. Then, we state the related experimental implementation and current theoretical research of two-component BECs. Based on the mean-field theory, we briefly deduce the GP equations, which govern the dynamics of the condensates. Finally, we present the multiple-scale method, which will be used in the following chapters for theoretical analysis, and give a summary of our work in this thesis at the end of this chapter.In chapter two, by using the multiple-scale method, we analytically study dynamical properties of two-component BECs trapped in a harmonic plus quartic anharmonic potential. It is shown that the anharmonic potential has an important effect on the dark solitons of the condensates. Especially, when the strength of the anharmonic external potential increases, the fusion of the two solitons becomes faster. This implies that the fusion of the two solitons can be controlled by an anharmonic potential.In chapter three, we analytically study the soliton dynamical properties of two-component BECs with time-dependent interspecies scattering length by using the multiple-scale method. It is shown that the interspecies scattering length has an important effect on the solitons collision property of the condensates. The position, the time, and the frequency of the collision between two solitons are relative to the time-dependent interspecies scattering length of the condensates. That is to say, the collision property of the two solitons in two-component Bose-Einstein condensates can be controlled by the time-dependent interspecies scattering length. Additionally, the amplitude of the solitons is also close related to the time-dependent interspecies scattering length.In Final chapter, we make a summary of our work and give some prospects in future works.