2,108 research outputs found
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
Extended Bose-Hubbard model with pair tunneling: spontaneous symmetry breaking, effective ground state and fragmentation
The extended Bose-Hubbard model for a double-well potential with pair
tunneling is studied through both exact diagonalization and mean field theory
(MFT). When pair tunneling is strong enough, the ground state wavefunction
predicted by the MFT is complex and doubly degenerate while the quantum ground
state wavefunction is always real and unique. The time reversal symmetry is
spontaneously broken when the system transfers from the quantum ground state
into one of the mean field ground states upon a small perturbation. As the gap
between the lowest two levels decreases exponentially with particle number, the
required perturbation inducing the spontaneous symmetry breaking (SSB) is
infinitesimal for particle number of typical cold atom systems. The quantum
ground state is further analyzed with the Penrose-Onsager criterion, and is
found to be a fragmented condensate. The state also develops the pair
correlation and has non-vanishing pair order parameter instead of the
conventional single particle order parameter. When this model is generalized to
optical lattice, a pair superfluid can be generated. The mean field ground
state can be regarded as effective ground state in this simple model. The
detailed computation for this model enables us to offer an in-depth discussion
of the relation between SSB and effective ground state, giving a glimpse on how
nonlinearity arises in the SSB of a quantum system.Comment: 6 pages, 6 figure
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