261 research outputs found
Finite size effects for the gap in the excitation spectrum of the one-dimensional Hubbard model
We study finite size effects for the gap of the quasiparticle excitation
spectrum in the weakly interacting regime one-dimensional Hubbard model with
on-site attraction. Two type of corrections to the result of the thermodynamic
limit are obtained. Aside from a power law (conformal) correction due to
gapless excitations which behaves as , where is the number of
lattice sites, we obtain corrections related to the existence of gapped
excitations. First of all, there is an exponential correction which in the
weakly interacting regime () behaves as in the extreme limit of ,
where is the hopping amplitude, is the on-site energy, and
is the gap in the thermodynamic limit. Second, in a finite
size system a spin-flip producing unpaired fermions leads to the appearance of
solitons with non-zero momenta, which provides an extra (non-exponential)
contribution . For moderate but still large values of
, these corrections significantly increase and may
become comparable with the conformal correction. Moreover, in the case
of weak interactions where , the exponential correction
exceeds higher order power law corrections in a wide range of parameters,
namely for , and so does
even in a wider range of . For sufficiently small number of particles,
which can be of the order of thousands in the weakly interacting regime, the
gap is fully dominated by finite size effects.Comment: 17 pages, 5 figure
Dynamics of dark solitons in elongated Bose-Einstein condensates
We find two types of moving dark soliton textures in elongated Bose-Einstein
condensates: non-stationary kinks and proper dark solitons. The former have a
curved notch region and rapidly decay by emitting phonons and/or proper dark
solitons. The proper moving solitons are characterized by a flat notch region
and we obtain the diagram of their dynamical stability. At finite temperatures
the dynamically stable solitons decay due to the thermodynamic instability. We
develop a theory of their dissipative dynamics and explain experimental data.Comment: ~ 5 pages, 1 figur
Vortex structures in rotating Bose-Einstein condensates
We present an analytical solution for the vortex lattice in a rapidly
rotating trapped Bose-Einstein condensate (BEC) in the lowest Landau level and
discuss deviations from the Thomas-Fermi density profile. This solution is
exact in the limit of a large number of vortices and is obtained for the cases
of circularly symmetric and narrow channel geometries. The latter is realized
when the trapping frequencies in the plane perpendicular to the rotation axis
are different from each other and the rotation frequency is equal to the
smallest of them. This leads to the cancelation of the trapping potential in
the direction of the weaker confinement and makes the system infinitely
elongated in this direction. For this case we calculate the phase diagram as a
function of the interaction strength and rotation frequency and identify the
order of quantum phase transitions between the states with a different number
of vortex rows.Comment: 17 pages, 12 figures, with addition
Measurement of interaction energy near a Feshbach resonance in a 6Li Fermi gas
We investigate the strongly interacting regime in an optically trapped Li
Fermi mixture near a Feshbach resonance. The resonance is found at G
in good agreement with theory. Anisotropic expansion of the gas is interpreted
by collisional hydrodynamics. We observe an unexpected and large shift (G)
between the resonance peak and both the maximum of atom loss and the change of
sign of the interaction energy.Comment: 4 pages, 4 figure
Production of Long-Lived Ultracold Li2 Molecules from a Fermi gas
We create weakly-bound Li2 molecules from a degenerate two component Fermi
gas by sweeping a magnetic field across a Feshbach resonance. The atom-molecule
transfer efficiency can reach 85% and is studied as a function of magnetic
field and initial temperature. The bosonic molecules remain trapped for 0.5 s
and their temperature is within a factor of 2 from the Bose-Einstein
condensation temperature. A thermodynamical model reproduces qualitatively the
experimental findings
Spin waves in a one-dimensional spinor Bose gas
We study a one-dimensional (iso)spin 1/2 Bose gas with repulsive
delta-function interaction by the Bethe Ansatz method and discuss the
excitations above the polarized ground state. In addition to phonons the system
features spin waves with a quadratic dispersion. We compute analytically and
numerically the effective mass of the spin wave and show that the spin
transport is greatly suppressed in the strong coupling regime, where the
isospin-density (or ``spin-charge'') separation is maximal. Using a
hydrodynamic approach, we study spin excitations in a harmonically trapped
system and discuss prospects for future studies of two-component ultracold
atomic gases.Comment: 4 pages, 1 figur
Mott-insulator phase of coupled 1D atomic gases in a 2D optical lattice
We discuss the 2D Mott insulator (MI) state of a 2D array of coupled finite
size 1D Bose gases. It is shown that the momentum distribution in the lattice
plane is very sensitive to the interaction regime in the 1D tubes. In
particular, we find that the disappearance of the interference pattern in time
of flight experiments will not be a signature of the MI phase, but a clear
consequence of the strongly interacting Tonks-Girardeau regime along the tubes.Comment: 4 pages, 3 figure
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