Dynamics And Ground State Properties Of A Two-component Bose-Einstein Condensate

In the past twenty years, the realization of Bose-Einstein condensation (BEC) in alkali atomic gas is one of the most important achievements in the low temperature Physics. It can provide the unique opportunities for exploring quantum coherent phenomena and many-body Physics. So it has attracted many theoretical and experimental studies.Bose-Einstein condensation in cold atomic gas is a kind of macroscopic quantum phenomena, which can be characterized by an order parameter. The dynamics and ground state of Bose-Einstein condensation can often be studied from the Gross-Pitaevskii equation, which is based on mean field theory. Mean field theory is well applied to Bose-Einstein condensation at zero temperature. In this thesis, we have studied the nonlinear waves in Bose-Einstein condensation by the method of fluid dynamics, which includes the nonlinear periodic wave and solitary wave. The ground state of a spherically trapped Bose-Einstein condensation has been numerically studied. From the calculations, we can see that the interaction between atoms can make much influence on the condensate. Josephson effect is one of macroscopic coherent phenomena, which plays important role in superconducting Physics. The similar tunneling c an be realized in a two-component Bose-Einstein condensate. A two-component Bose-Einstein condensate can be formed in a double trapping potential. Another case is the atoms in different hyperfine states. In this thesis, we studied the tunneling effects of a two-component BEC in different hyperfine states. Plasmon oscillation is one kind of the tunneling effects. And another is the macroscopic self-trapping phenomena, which results from the nonlinearity.In the last chapter, we have studied the microscopic properties of a two-component Bose-Einstein condensate in different hyperfine states. We have applied Green’s function method to a two-component BEC and obtained the excitation spectrum. The spectrum is found to have two branches. One is in the phonon form, and another is of single-particle form. There is energy gap in the single-particle excitation. Quantum depletion and ground state energy have been calculated in this thesis. With the obtained excitations, we can calculate the Landau critical velocity of a two-component BEC. The structure factor has been obtained in this thesis. It is found that the static structure factor comprises only the phonon excitation, and the single-particle one does no contributions to the structure factor. It is because the phonon excitation comes from the microscopic structure and single-particle one results from the spin effect. The disintegration of the single-particle excitation is prohibited for the energy gap. So only the phonon excitations do contributions to the Beliave damping effect, and we have calculated the damping coefficient.