104 research outputs found
Solitary-wave description of condensate micro-motion in a time-averaged orbiting potential trap
We present a detailed theoretical analysis of micro-motion in a time-averaged
orbiting potential trap. Our treatment is based on the Gross-Pitaevskii
equation, with the full time dependent behaviour of the trap systematically
approximated to reduce the trapping potential to its dominant terms. We show
that within some well specified approximations, the dynamic trap has
solitary-wave solutions, and we identify a moving frame of reference which
provides the most natural description of the system. In that frame eigenstates
of the time-averaged orbiting potential trap can be found, all of which must be
solitary-wave solutions with identical, circular centre of mass motion in the
lab frame. The validity regime for our treatment is carefully defined, and is
shown to be satisfied by existing experimental systems.Comment: 12 pages, 2 figure
Quantum turbulence and correlations in Bose-Einstein condensate collisions
We investigate numerically simulated collisions between experimentally
realistic Bose-Einstein condensate wavepackets, within a regime where highly
populated scattering haloes are formed. The theoretical basis for this work is
the truncated Wigner method, for which we present a detailed derivation, paying
particular attention to its validity regime for colliding condensates. This
paper is an extension of our previous Letter [A. A. Norrie, R. J. Ballagh, and
C. W. Gardiner, Phys. Rev. Lett. 94, 040401 (2005)] and we investigate both
single-trajectory solutions, which reveal the presence of quantum turbulence in
the scattering halo, and ensembles of trajectories, which we use to calculate
quantum-mechanical correlation functions of the field
Three-body recombination of ultracold Bose gases using the truncated Wigner method
We apply the truncated Wigner method to the process of three-body
recombination in ultracold Bose gases. We find that within the validity regime
of the Wigner truncation for two-body scattering, three-body recombination can
be treated using a set of coupled stochastic differential equations that
include diffusion terms, and can be simulated using known numerical methods. As
an example we investigate the behaviour of a simple homogeneous Bose gas.Comment: Replaced paper same as original; correction to author list on
cond-mat mad
Temporal coherence, anomalous moments, and pairing correlations in the classical-field description of a degenerate Bose gas
The coherence properties of degenerate Bose gases have usually been expressed
in terms of spatial correlation functions, neglecting the rich information
encoded in their temporal behavior. In this paper we show, using a Hamiltonian
classical-field formalism, that temporal correlations can be used to
characterize familiar properties of a finite-temperature degenerate Bose gas.
The temporal coherence of a Bose-Einstein condensate is limited only by the
slow diffusion of its phase, and thus the presence of a condensate is indicated
by a sharp feature in the temporal power spectrum of the field. We show that
the condensate mode can be obtained by averaging the field for a short time in
an appropriate phase-rotating frame, and that for a wide range of temperatures,
the condensate obtained in this approach agrees well with that defined by the
Penrose-Onsager criterion based on one-body (spatial) correlations. For time
periods long compared to the phase diffusion time, the field will average to
zero, as we would expect from the overall U(1) symmetry of the Hamiltonian. We
identify the emergence of the first moment on short time scales with the
concept of U(1) symmetry breaking that is central to traditional mean-field
theories of Bose condensation. We demonstrate that the short-time averaging
procedure constitutes a general analog of the 'anomalous' averaging operation
of symmetry-broken theories by calculating the anomalous thermal density of the
field, which we find to have form and temperature dependence consistent with
the results of mean-field theories.Comment: 11 pages, 6 figures. v3: Final version. Typos fixed, and other minor
change
Kinetics of Bose-Einstein Condensation in a Trap
The formation process of a Bose-Einstein condensate in a trap is described
using a master equation based on quantum kinetic theory, which can be well
approximated by a description using only the condensate mode in interaction
with a thermalized bath of noncondensate atoms. A rate equation of the form n =
2W(n)[(1-exp((mu_n - mu)/kT))n + 1] is derived, in which the difference between
the condensate chemical potential mu_n and the bath chemical potential mu gives
the essential behavior. Solutions of this equation, in conjunction with the
theoretical description of the process of evaporative cooling, give a
characteristic latency period for condensate formation and appear to be
consistent with the observed behavior of both rubidium and sodium condensate
formation.Comment: 9 pages, Revte
Generation of directional, coherent matter beams through dynamical instabilities in Bose-Einstein condensates
We present a theoretical analysis of a coupled, two-state Bose-Einstein
condensate with non-equal scattering lengths, and show that dynamical
instabilities can be excited. We demonstrate that these instabilities are
exponentially amplified resulting in highly-directional,
oppositely-propagating, coherent matter beams at specific momenta. To
accomplish this we prove that the mean field of our system is periodic, and
extend the standard Bogoliubov approach to consider a time-dependent, but
cyclic, background. This allows us to use Floquet's theorem to gain analytic
insight into such systems, rather than employing the usual Bogoliubov-de Gennes
approach, which is usually limited to numerical solutions. We apply our theory
to the metastable Helium atom laser experiment of Dall et al. [Phys. Rev. A 79,
011601(R) (2009)] and show it explains the anomalous beam profiles they
observed. Finally we demonstrate the paired particle beams will be
EPR-entangled on formation.Comment: Corrected reference
Quantum Kinetic Theory of Condensate Growth---Comparison of Experiment and Theory
In a major extension of our previous model (C.W. Gardiner, P. Zoller,
R.J. Ballagh and M.J. Davis, Phys. Rev. Lett. 79, 1793 (1997)) of condensate
growth, we take account of the evolution of the occupations of lower trap
levels, and of the full Bose-Einstein formula for the occupations of higher
trap levels. We find good agreement with experiment, especially at higher
temperatures. We also confirm the picture of the ``kinetic'' region of
evolution, introduced by Kagan et al, for the time up to the initiation of the
condensate. The behavior after initiation essentially follows our original
growth equation, but with a substantially increased rate coefficient W^{+}.Comment: RevTeX, 4 pages and 4 eps figure
Output of a pulsed atom laser
We study the output properties of a pulsed atom laser consisting of an
interacting Bose-Einstein condensate (BEC) in a magnetic trap and an additional
rf field transferring atoms to an untrapped Zeeman sublevel. For weak output
coupling we calculate the dynamics of the decaying condensate population, of
its chemical potential and the velocity of the output atoms analytically.Comment: 4 pages, RevTeX. Full ps file available on
http://mpqibmr1.mpq.mpg.de:5000/~man
Finite-temperature dynamics of a single vortex in a Bose-Einstein condensate: Equilibrium precession and rotational symmetry breaking
We consider a finite-temperature Bose-Einstein condensate in a
quasi-two-dimensional trap containing a single precessing vortex. We find that
such a configuration arises naturally as an ergodic equilibrium of the
projected Gross-Pitaevskii equation, when constrained to a finite conserved
angular momentum. In an isotropic trapping potential the condensation of the
classical field into an off-axis vortex state breaks the rotational symmetry of
the system. We present a methodology to identify the condensate and the
Goldstone mode associated with the broken rotational symmetry in the
classical-field model. We also examine the variation in vortex trajectories and
thermodynamic parameters of the field as the energy of the microcanonical field
simulation is varied.Comment: 21 pages, 10 figures. v2: Minor changes and corrections to figures
and text. To appear in PR
Dynamical thermalization and vortex formation in stirred 2D Bose-Einstein condensates
We present a quantum mechanical treatment of the mechanical stirring of
Bose-Einstein condensates using classical field techniques. In our approach the
condensate and excited modes are described using a Hamiltonian classical field
method in which the atom number and (rotating frame) energy are strictly
conserved. We simulate a T = 0 quasi-2D condensate perturbed by a rotating
anisotropic trapping potential. Vacuum fluctuations in the initial state
provide an irreducible mechanism for breaking the initial symmetries of the
condensate and seeding the subsequent dynamical instability. Highly turbulent
motion develops and we quantify the emergence of a rotating thermal component
that provides the dissipation necessary for the nucleation and motional-damping
of vortices in the condensate. Vortex lattice formation is not observed, rather
the vortices assemble into a spatially disordered vortex liquid state. We
discuss methods we have developed to identify the condensate in the presence of
an irregular distribution of vortices, determine the thermodynamic parameters
of the thermal component, and extract damping rates from the classical field
trajectories.Comment: 22 pages, 15 figures. v2: Minor refinements made at suggestion of
referee. Discussion of other treatments revised. To appear in Phys. Rev.
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