Theoretical Problems In Spinor Bose-Einstein Condensation

The essential properties of degenerate quantum gases depend on the range, strength and symmetry of atomic interactions. In spinor Bose-Einstein condensates (BEC), one can not only tune the short-range contact interaction using Feshbach resonances but also investigate effects of the long-range and anisotropic interaction. In this thesis we mainly study the properties of spinor Bose-Einstein condensates, including superfluidity, tunneling dynamics and quantum entanglement. The work relates mainly to Bose-Hubbard model, quantum tunneling model, quantum phase transition in spinor Bose-Einstein condensates.In Chapter 2, we start from spin-1 Bose-Hubbard model and derive the energy spectra in terms of Bogoliubov transformation for cold bosons in optical lattices, which indicate the dependence of superfluidity on the spin-exchange interaction. Our observation is that the critical velocities of the superfluid flow are spin-component dependent and can be controlled by adjusting the laser lights that form the optical lattice. Possible experiments to detect the superfluid phase and component separation of spinor BEC are also discussed.In Chapter 3, we describe a semiclassical treatment of the dynamics of dipolar spinor condensates. As a result of the conservation of atom numbers and total hyperfine spin of the condensates, the classical equations of motion are derived. The interplay of spin-exchange and magnetic dipole-dipole interaction leads to the phenomena of spontaneous magnetization and the novel "macroscopic quantum self-trapping".Quantum entanglement is one of the most essential and fascinating features of quantum mechanics. We study the entanglement characteristics ofmulti-component Bose-Einstein condensates ------ multipartite andmultimodal systems. Chapter 4 is devoted to proposing generation and manipulation of entangled atom states in an antiferromagnetic spin-1 BEC under magnetic field with gradient and also investigating the dynamics of the entropy of entanglement. Chapter 5 pays attention to the simplest quantumtunneling model------two tunnel-coupled BEC. We study the eigen problemand entanglement characteristics with perturbation method for both weak and strong tunnel couplings, from which some new features are explored.The research in this thesis attributes to the crossover of theoretical physics, condensed matter physics and atom physics.