Theoretical Study Of Soliton And Interference In Bose-einstein Condensate

Since the realization of Bose-Einstein condensates (BECs) in dilute alkali-metalgases, lots of theoretical and experimental studies of BECs have been reported such assolitons, vortices, josephson oscillation, chaos and symmetry breaking. In anotherregard, the Bose-Einstein condensates have long coherence time and highcontrollability, they as ideal coherent sources have been widely used to study matterwave interference. In the mean-field approximation, the condensates may bedescribed by a macroscopic wavefunction. This theory paves a way toward studyingthe properties of condensates theoretically. In this thesis, we theoretically investigatethe soliton and interference in Bose-Einstein condensates. Our detailed research workcan be divided into three sections.In the first section, spinor Bose–Einstein condensates has internal degree offreedom, this freedom is due to the hyperfine spin of atom. When spinor condensatesare trapped in a magnetic potential, the spin degree of freedom is frozen. While whenspinor condensates are trapped in an optical potential, the spin degree of freedomcomes into play. Here we consider spin-1Bose–Einstein condensates which aretrapped in a harmonic potential with different nonlinearity coefficients. We illustratethe dynamics of soliton breathers in one-component, two-component andthree-component states by numerically solving one-dimensional time-dependentcoupled Gross–Pitaecskii (GP) equations. The condensate in one-component stateform soliton breather when scattering length are changed with time. In thetwo-component state, two condensates with repulsive interspecies interactions and attractive interaction make elastic collision and novel soliton breathers are created; thetwo condensates without interspecies interaction form stable bright soliton; the twocondensates with repulsive interspecies interaction and repulsive intraspeciesinteraction make inelastic collision and no soliton created in two condensates. Inthree-component state soliton breathers are generated in three codensates, spinorexchange collision is found. Besides, possible reasons for creating those solitonbreathers are discussed in thesis.In the second section, we demonstrate the the dynamical evolution oftwo-component Bose–Einstein condensates which are trapped in a cylindrical well bysolving the coupled GP equations numerically. We present that, due to intercomponentinteraction and different initial component populations, different numbers of ring darksolitons are generated in two components at the same time. These solitons all havedensity zeros (minima) accompanied with phase jumps, the phase jumps can causelarge superfluid velocities. At phase jump points those ring dark solitons have zerosuperfluid currents, while those ring gray solitons have large superfluid currents. Allsolitons are unstable and will evolve into other soliton states after a brief time.In the end, we study the interference between two condensates with repulsiveinteraction, which is investigated by numerical solution of the one-dimensionaltime-dependent GP equation. The two condensates are initially prepared in adouble-well potential. This potential consists two truncated harmonic wells centeredat different positions. The two condensates can form periodic interference pattern,while dark solitons are generated when two condensates overlap. The evolution oftwo condensates is described by the ground state and excited states ofone-dimensional harmonic oscillator wavefunctions. Due to the existence ofatom-atom interactions, many atoms are transferred among ground state and excitedstates, atom transfer coincides with the variation of the energy of system.