111 research outputs found
Damping in 2D and 3D dilute Bose gases
Damping in 2D and 3D dilute gases is investigated using both the
hydrodynamical approach and the Hartree-Fock-Bogoliubov (HFB) approximation .
We found that the both methods are good for the Beliaev damping at zero
temperature and Landau damping at very low temperature, however, at high
temperature, the hydrodynamical approach overestimates the Landau damping and
the HFB gives a better approximation. This result shows that the comparison of
the theoretical calculation using the hydrodynamical approach and the
experimental data for high temperature done by Vincent Liu (PRL {\bf21} 4056
(1997)) is not proper. For two-dimensional systems, we show that the Beliaev
damping rate is proportional to and the Landau damping rate is
proportional to for low temperature and to for high temperature. We
also show that in two dimensions the hydrodynamical approach gives the same
result for zero temperature and for low temperature as HFB, but overestimates
the Landau damping for high temperature.Comment: 11 pages, 4 figure
BCS-BEC crossover in a system of microcavity polaritons
We investigate the thermodynamics and signatures of a polariton condensate
over a range of densities, using a model of microcavity polaritons with
internal structure. We determine a phase diagram for this system including
fluctuation corrections to the mean-field theory. At low densities the
condensation temperature, T_c, behaves like that for point bosons. At higher
densities, when T_c approaches the Rabi splitting, T_c deviates from the form
for point bosons, and instead approaches the result of a BCS-like mean-field
theory. This crossover occurs at densities much less than the Mott density. We
show that current experiments are in a density range where the phase boundary
is described by the BCS-like mean-field boundary. We investigate the influence
of inhomogeneous broadening and detuning of excitons on the phase diagram.Comment: 20 pages, 6 figure
Production of three-body Efimov molecules in an optical lattice
We study the possibility of associating meta-stable Efimov trimers from three
free Bose atoms in a tight trap realised, for instance, via an optical lattice
site or a microchip. The suggested scheme for the production of these molecules
is based on magnetically tunable Feshbach resonances and takes advantage of the
Efimov effect in three-body energy spectra. Our predictions on the energy
levels and wave functions of three pairwise interacting 85Rb atoms rely upon
exact solutions of the Faddeev equations and include the tightly confining
potential of an isotropic harmonic atom trap. The magnetic field dependence of
these energy levels indicates that it is the lowest energetic Efimov trimer
state that can be associated in an adiabatic sweep of the field strength. We
show that the binding energies and spatial extents of the trimer molecules
produced are comparable, in their magnitudes, to those of the associated
diatomic Feshbach molecule. The three-body molecular state follows Efimov's
scenario when the pairwise attraction of the atoms is strengthened by tuning
the magnetic field strength.Comment: 21 pages, 8 figures (final version
Theory of Bose-Einstein condensation for trapped atoms
We outline the general features of the conventional mean-field theory for the
description of Bose-Einstein condensates at near zero temperatures. This
approach, based on a phenomenological model, appears to give excellent
agreement with experimental data. We argue, however, that such an approach is
not rigorous and cannot contain the full effect of collisional dynamics due to
the presence of the mean-field. We thus discuss an alternative microscopic
approach and explain, within our new formalism, the physical origin of these
effects. Furthermore, we discuss the potential formulation of a consistent
finite-temperature mean-field theory, which we claim necessiates an analysis
beyond the conventional treatment.Comment: 12 pages. To appear in Phil. Trans. R. Soc. Lond. A 355 (1997
Quantum Kinetic Theory of BEC Lattice Gas:Boltzmann Equations from 2PI-CTP Effective Action
We continue our earlier work [Ana Maria Rey, B. L. Hu, Esteban Calzetta,
Albert Roura and Charles W. Clark, Phys. Rev. A 69, 033610 (2004)] on the
nonequilibrium dynamics of a Bose Einstein condensate (BEC) selectively loaded
into every third site of a one-dimensional optical lattice. From the
two-particle irreducible (2PI) closed-time-path (CTP) effective action for the
Bose- Hubbard Hamiltonian, we show how to obtain the Kadanoff-Baym equations of
quantum kinetic theory. Using the quasiparticle approximation, we show that the
local equilibrium solutions of these equations reproduce the second- order
corrections to the self-energy originally derived by Beliaev. This work paves
the way for the use of effective action methods in the derivation of quantum
kinetic theory of many atom systems.Comment: 21 pages, 0 figures, minor editorial changes were mad
Non-perturbative renormalization-group approach to zero-temperature Bose systems
We use a non-perturbative renormalization-group technique to study
interacting bosons at zero temperature. Our approach reveals the instability of
the Bogoliubov fixed point when and yields the exact infrared
behavior in all dimensions within a rather simple theoretical framework.
It also enables to compute the low-energy properties in terms of the parameters
of a microscopic model. In one-dimension and for not too strong interactions,
it yields a good picture of the Luttinger-liquid behavior of the superfluid
phase.Comment: v1) 6 pages, 8 figures; v2) added references; v3) corrected typo
Nonequilibrium Dynamics of Optical Lattice-Loaded BEC Atoms: Beyond HFB Approximation
In this work a two-particle irreducible (2PI) closed-time-path (CTP)
effective action is used to describe the nonequilibrium dynamics of a Bose
Einstein condensate (BEC) selectively loaded into every third site of a
one-dimensional optical lattice. The motivation of this work is the recent
experimental realization of this system at National Institute of Standards and
Technology (NIST) where the placement of atoms in an optical lattice is
controlled by using an intermediate superlattice. Under the 2PI CTP scheme with
this initial configuration, three different approximations are considered: a)
the Hartree-Fock-Bogoliubov (HFB) approximation, b) the next-to-leading order
1/ expansion of the 2PI effective action up to second order in the
interaction strength and c) a second order perturbative expansion in the
interaction strength. We present detailed comparisons between these
approximations and determine their range of validity by contrasting them with
the exact many body solution for a moderate number of atoms and wells. As a
general feature we observe that because the second order 2PI approximations
include multi-particle scattering in a systematic way, they are able to capture
damping effects exhibited in the exact solution that a mean field collisionless
approach fails to produce. While the second order approximations show a clear
improvement over the HFB approximation our numerical result shows that they do
not work so well at late times, when interaction effects are significant.Comment: 34 pages, 7 figure
Dynamical Structure Factor and Spin-Density Separation for a Weakly-Interacting Two-Component Bose Gas
We show that spin-density separation in a Bose gas is not restricted to 1D
but also occurs in higher dimension. The ratio () of the intra-species
atom-atom interaction strength to the inter-species interaction strength,
strongly influences the dynamics of spin-density separation and the elementary
excitations. The density wave is phonon-like for all values of . For
, spin wave is also phonon-like. The spin waves have a quadratic
dispersion in the coupling regime, while in the phase separated
regime () the spin waves are found to be damped. The dynamical
structure factor (DSF) reveals two distinct peaks corresponding to the density
and spin waves for . For there is only one DSF peak
corresponding to the density wave.Comment: 4 pages, 2 figure
Infrared behavior of interacting bosons at zero temperature
We review the infrared behavior of interacting bosons at zero temperature.
After a brief discussion of the Bogoliubov approximation and the breakdown of
perturbation theory due to infrared divergences, we present two approaches that
are free of infrared divergences -- Popov's hydrodynamic theory and the
non-perturbative renormalization group -- and allow us to obtain the exact
infrared behavior of the correlation functions. We also point out the
connection between the infrared behavior in the superfluid phase and the
critical behavior at the superfluid--Mott-insulator transition in the
Bose-Hubbard model.Comment: 8 pages, 4 figures. Proceedings of the 19th International Laser
Physics Workshop, LPHYS'10 (Foz do Iguacu, Brazil, July 5-9, 2010
Weakly Interacting, Dilute Bose Gases in 2D
This article surveys a number of theoretical problems and open questions in
the field of two-dimensional dilute Bose gases with weak repulsive
interactions. In contrast to three dimensions, in two dimensions the formation
of long-range order is prohibited by the Bogoliubov-Hohenberg theorem, and
Bose-Einstein condensation is not expected to be realized. Nevertheless, first
experimental indications supporting the formation of the condensate in low
dimensional systems have been recently obtained. This unexpected behaviour
appears to be due to the non-uniformity, introduced into a system by the
external trapping potential. Theoretical predictions, made for homogeneous
systems, require therefore careful reexamination.
We survey a number of popular theoretical treatments of the dilute weakly
interacting Bose gas and discuss their regions of applicability. The
possibility of Bose-Einstein condensation in a two-dimensional gas, the
validity of perturbative t-matrix approximation and diluteness condition are
issues that we discuss in detail.Comment: Survey, 25 pages RMP style, revised version, refs added, some changes
made, accepted for publication in Rev. Mod. Phy
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