The Symmetry Breaking And Tunneling Dynamics Of Bose-Einstein Condensation

After the experimental realization of quantum degeneracy in Bosonic and Fermionic gases of alkali mental atoms, there are many investigations on mixtures system, such as the degenerate Bose-Bose mixtures85Rb-87Rb and87Rb-41K, the degenerate Bose-Fermi mixtures6Li-7Li,40K-41K and87Rb-40K, and the degenerate Fermi-Fermi mixtures40K-40K and6Li-6Li in different hyperfine states. Obviously, many exciting results have been predicted and observed. Meanwhile, there have been many studies on its property under different trapping conditions:harmonic, double-well, periodic optical-lattice, which is easy to control in the experiments. With the development of magnetic and optical Feshbach resonance, it makes the technology of tuning the scattering length to be easier and easier. These technology developments give us a unique opportunity to investigate the macroscopic quantum dynamics of Bose-Einstein Condensate in a double-well potential.In this paper, we investigate the symmetry breaking and tunneling dynamics of BEC. By solving the Gross-Pitaevskii equations, we investigate the tunneling dynamics of Fermi-Fermi mixture, the symmetry breaking of Bose-Fermi mixture, the symmetry breaking and tunneling dynamics of F=1spinor BEC:(1) We investigate the macroscopic quantum tunneling dynamics of Fermi-Fermi mixtures in a double-well potential. Using an effective one-dimensional form of Gross-Pitaevskii equation (GPE), which is derived from the density functional of Fermi superfluid in the unitarity limit, we show the two distinct types of macroscopic quantum self-trapping and their transition between each other with the altering parameter ΛAB/|Λ|in zero-mode and;π-mode for|ΛA|=|ΛB|or|ΛA|≠|ΛB|. The "swapping phase", which is predicted by Satija et al [Phys. Rev. A79,033616(2009)], can be seen in both zero mode and π mode for an appropriate value of ΛAB/|Λ|. We also show some results about the tunneling dynamics with different initial population imbalance S(0) and the particle numbers N.(2) We investigate the properties of the one-dimensional Bose-Fermi mixture in triple-well potentials with two equally populated spin components at zero temperature. Based on the coupled equation for a Bose-Fermi mixture system, we investigate the effect of different strengths of the interspecies and intraspecies interaction that induced by changing the particle numbers of boson and fermion. The several novel density profiles of ground state in distinct regions in the phase diagram of the (NF, NB) plane are demonstrated. In addition, the densities variation picture as function of NB at fixed NF, which clearly shows the transition among some of these density profiles, is illustrated.(3) We investigate theoretically symmetry breaking and tunneling dynamics in the mixture of three Zeeman states of F=1spinor Bose-Einstein condensate in a triple-well potential. We demonstrate several novel density profiles of symmetric and asymmetric ground states of the three Zeeman states in the phase diagram of the (λn,λs) plane, where λn and λs are the coefficients of the spin-independent and spin-dependent interactions. The variation of density as a function λs at fixed λn, which clearly shows the transition among distinct types of symmetric and asymmetric ground states, is also illustrated. In addition, the tunneling dynamics of F=1spinor Bose-Einstein condensate in a triple-well potential is also demonstrated.