Quantum Tunneling And Phase Diagram Of Spinor Dipolar Condensate In Two Representations

The magnetic dipole-dipole interaction(MDDI) has significant effects on spinor Bose gas for its long-range and anisotropic properties. So the magnetic structure and dynamic properties of the spinor dipolar condensate have been studied extensively under the mean field approximation. In this thesis, we discussed its quantum ground state phase diagram and quantum tunneling under single-mode approximation with the exact diagonalization method in the Fock state representation and pseudo-angular momentum representation.Firstly, taking the toy model of two-particle system for instance, we have analyzed the essential distinction and connection between the two representations. The transition matrix for two-particle case is easily generalized to many particles in the numerical exact diagonalization. Then we discussed the ground state of spinor condensate in both representations. The quantum phase diagram is found to match the mean field results perfectly. We then discussed the influence of the initial states on spin mixing dynamics as well as the competition between the second-order Zeeman effect and spin exchange interaction.Secondly, we have obtained a biaxial spin model from the anisotropically trapped dipolar condensate in the single-mode approximation. The quantum phase diagrams by means of the exact diagonalization method reveal that in the ferromagnetic phase region the system is equivalent to the biaxial molecular magnets model. The exact diagonalization results both in Fock representation and pseudo-angular momentum representation show that the energy level splitting between the ground state and the first excited state oscillates with the external field applied along the hard axis, suggesting the famous macroscopic quantum tunneling effect in dipolar spinor condensate. The influence from the linear term on the energe splitting is negligible.