The Ground State And Dynamics Properties Of F=1 Spinor Bose-Einstein Condensates

Since the MIT group succeeded in trapping a 23Na condensate in an optical potential, spinor Bose-Einstein Condensates (BEC) as a new subject gives rise to a rich variety of phenomena:such as spin domains, textures, spin vortex, phase separation, fragmentation and spin mixing dynamics. In this paper, we maily study two subjects:the ground state properties of spinor BEC mixture and the spin mixing dynamics of the Zeeman component and the system magnetization induced by a magnetic field gradient.Firstly, we study the ground-state properties of a mixture of two spin-1 condensates in the absence of an external magnetic field. As the collisional symmetry between interspecies bosonic atoms is broken, the interspecies coupling interaction and interspecies singlet-pairing interaction arise. The ground state can be calculated using the angular momentum theory analytically under the Degenrate Internal-states Approximation (DIA). We categorize all possible ground states and compute their characteristic atom number fluctuations, focusing especially on the the AA phase, where the ground state becomes fragmented and atomic-number fluctuations exhibit drastically different features from a single standalone spin-1 polar condensate. Our results are further supported by numerical simulations of the full quantum many-body system. The full quantum approach of exact diagonalization is adopted numerically to consider the more general case with interspecies singlet-pairing interaction. We illustrate the competition between the interspecies coupling and paring interactions and find that as singlet-pairing interaction dominates (or the total spin vanishes), there are still different types of singlet formations which are well determined by coupling interaction.Secondly, we study the spin-mixing dynamics of spin-1 atoms in a weak nonuniform magnetic field with field gradient, which can flip the spin from +1 to-1 so that the magnetization is not a constant any more. The dynamics of atoms population on mF=0 Zeeman component, as well as the system magnetization, are illustrated for both ferromagnetic and polar interaction cases in the mean-field theory. We find that the dynamics of system magnetization can be tuned between the Josephson-like oscillation similar to the case of double well and the interesting self-trapping, i.e., the spin-mixing dynamics sustains a spontaneous magnetization. Meanwhile, the dynamics of mF=0 Zeeman component population may be sufficiently suppressed for initially imbalanced number distribution in the case of polar interaction. A "beat-frequency" oscillation of the magnetization emerges in the case of balanced initial distribution for polar interaction, which vanishes for ferromagnetic interaction.