24 research outputs found
The Projected Gross-Pitaevskii Equation for harmonically confined Bose gases
We extend the Projected Gross Pitaevskii equation formalism of Davis et al.
[Phys. Rev. Lett. \bf{87}, 160402 (2001)] to the experimentally relevant case
of harmonic potentials. We outline a robust and accurate numerical scheme that
can efficiently simulate this system. We apply this method to investigate the
equilibrium properties of a harmonically trapped three-dimensional Bose gas at
finite temperature, and consider the dependence of condensate fraction,
position and momentum distributions, and density fluctuations on temperature.
We apply the scheme to simulate an evaporative cooling process in which the
preferential removal of high energy particles leads to the growth of a
Bose-Einstein condensate. We show that a condensate fraction can be inferred
during the dynamics even in this non-equilibrium situation.Comment: 11 pages, 7 figure
Critical temperature of a trapped Bose gas: comparison of theory and experiment
We apply the Projected Gross-Pitaevskii equation (PGPE) formalism to the
experimental problem of the shift in critical temperature of a
harmonically confined Bose gas as reported in Gerbier \emph{et al.} [Phys. Rev.
Lett. \textbf{92}, 030405 (2004)]. The PGPE method includes critical
fluctuations and we find the results differ from various mean-field theories,
and are in best agreement with experimental data. To unequivocally observe
beyond mean-field effects, however, the experimental precision must either
improve by an order of magnitude, or consider more strongly interacting
systems. This is the first application of a classical field method to make
quantitative comparison with experiment.Comment: revtex4, four pages, three figures. v2: updated to published version.
Several additions to figures, and better explanations in text in response to
referee comment
Finite temperature phase diagram of a spin-1 Bose gas
We formulate a self-consistent Hartree-Fock theory for a spin-1 Bose gas at
finite temperature and apply it to characterizing the phase diagram. We find
that spin coherence between thermal atoms in different magnetic sub-levels
develops via coherent collisions with the condensed atoms, and is a crucial
factor in determining the phase diagram. We develop analytical expressions to
characterize the interaction and temperature dependent shifts of the phase
boundaries.Comment: 11 pages, 5 figure
Numerical method for evolving the Projected Gross-Pitaevskii equation
In this paper we describe a method for evolving the projected
Gross-Pitaevskii equation (PGPE) for a Bose gas in a harmonic oscillator
potential. The central difficulty in solving this equation is the requirement
that the classical field is restricted to a small set of prescribed modes that
constitute the low energy classical region of the system. We present a scheme,
using a Hermite-polynomial based spectral representation, that precisely
implements this mode restriction and allows an efficient and accurate solution
of the PGPE. We show equilibrium and non-equilibrium results from the
application of the PGPE to an anisotropic trapped three-dimensional Bose gas.Comment: 12 pages, 5 figures. To appear in Phys. Rev. E. Convergence results
added, a few minor changes made and typos fixe
Bragg Spectroscopy of ultracold atoms loaded in an optical lattice
We study Bragg spectroscopy of ultra-cold atoms in one-dimensional optical
lattices as a method for probing the excitation spectrum in the Mott insulator
phase, in particular the one particle-hole excitation band. Within the
framework of perturbation theory we obtain an analytical expression for the
dynamic structure factor and use it to calculate the imparted
energy which has shown to be a relevant observable in recent experiments. We
test the accuracy of our approximations by comparing them with numerically
exact solutions of the Bose-Hubbard model in restricted cases and establish the
limits of validity of our linear response analysis. Finally we show that when
the system is deep in the Mott insulator regime, its response to the Bragg
perturbation is temperature dependent. We suggest that this dependence might be
used as a tool to probe temperatures of order of the Mott gap.Comment: 4 pages, 3 figure