Roles of energy eigenstates and eigenvalues in equilibration of isolated quantum systems

We show that eigen-energies and energy eigenstates play different roles in the equilibration process of an isolated quantum system. Their roles are revealed numerically by exchanging the eigen-energies between an integrable model and a non-integrable model. We ?find that the structure of eigenenergies of a non-integrable model characterized by non-degeneracy ensures that quantum revival occurs rarely whereas the energy eigenstates of a non-integrable model suppress the fluctuations for the equilibrated quantum state. Our study is aided with a quantum entropy that describes how randomly a wave function is distributed in quantum phase space. We also demonstrate with this quantum entropy the validity of Berry's conjecture for energy eigenstates. This implies that the energy eigenstates of a non-integrable model appear indeed "random"

Interaction Effects on Wannier Functions for Bosons in Optical Lattice

We have numerically calculated the single band Wannier functions for interacting Bose gases in optical lattices with a self-consistent approach. We find that the Wannier function is broadened by repulsive atom interaction. The tunneling parameter J and on-site interaction U computed with the broadened Wannier functions are found to change significantly for different atomic number per site. Our theory can explain the nonuniform atomic clock shift observed in [Campbell et al., Science 313, 649 (2006)]

Superfluidity of Bose-Einstein condensates in ultracold atomic gases

Liquid helium 4 had been the only bosonic superfluid available in experiments for a long time. This situation was changed in 1995, when a new superfluid was born with the realization of the Bose-Einstein condensation in ultracold atomic gases. The liquid helium 4 is strongly interacting and has no spin; there is almost no way to change its parameters, such as interaction strength and density. The new superfluid, Bose-Einstein condensate (BEC), offers various aspects of advantages over liquid helium. On the one hand, BEC is weakly interacting and has spin degrees of freedom. On the other hand, it is convenient to tune almost all the parameters of a BEC, for example, the kinetic energy by spin-orbit coupling, the density by the external potential, and the interaction by Feshbach resonance. Great efforts have been devoted to studying these new aspects of superfluidity, and the results have greatly enriched our understanding of superfluidity. Here we review these developments by focusing on the stability and critical velocity of various superfluids. The BEC systems considered include a uniform superfluid in free space, a superfluid with its density periodically modulated, a superfluid with artificially engineered spin-orbit coupling, and a superfluid of pure spin current. Due to the weak interaction, these BEC systems can be well described by the mean field Gross-Pitaevskii theory and their superfluidity, in particular critical velocities, can be examined with Landau's theory of superfluid. Experimental proposals to observe these new aspects of superfluidity are discussed.Comment: review article for Chinese Physics B, 15 papes, 9 figure

Bose-Einstein Condensate in a Honeycomb Optical Lattice: Fingerprint of Superfluidity at the Dirac Point

Mean-field Bloch bands of a Bose-Einstein condensate in a honeycomb optical lattice are computed. We find that the topological structure of the Bloch bands at the Dirac point is changed completely by the atomic interaction of arbitrary small strength: the Dirac point is extended into a closed curve and an intersecting tube structure arises around the original Dirac point. These tubed Bloch bands are caused by the superfluidity of the system. Furthermore, they imply the inadequacy of the tight-binding model to describe an interacting Boson system around the Dirac point and the breakdown of adiabaticity by interaction of arbitrary small strength