19 research outputs found
Calculation of the microcanonical temperature for the classical Bose field
The ergodic hypothesis asserts that a classical mechanical system will in
time visit every available configuration in phase space. Thus, for an ergodic
system, an ensemble average of a thermodynamic quantity can equally well be
calculated by a time average over a sufficiently long period of dynamical
evolution. In this paper we describe in detail how to calculate the temperature
and chemical potential from the dynamics of a microcanonical classical field,
using the particular example of the classical modes of a Bose-condensed gas.
The accurate determination of these thermodynamics quantities is essential in
measuring the shift of the critical temperature of a Bose gas due to
non-perturbative many-body effects.Comment: revtex4, 10 pages, 1 figure. v2: updated to published version. Fuller
discussion of numerical results, correction of some minor error
Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
We review phase space techniques based on the Wigner representation that
provide an approximate description of dilute ultra-cold Bose gases. In this
approach the quantum field evolution can be represented using equations of
motion of a similar form to the Gross-Pitaevskii equation but with stochastic
modifications that include quantum effects in a controlled degree of
approximation. These techniques provide a practical quantitative description of
both equilibrium and dynamical properties of Bose gas systems. We develop
versions of the formalism appropriate at zero temperature, where quantum
fluctuations can be important, and at finite temperature where thermal
fluctuations dominate. The numerical techniques necessary for implementing the
formalism are discussed in detail, together with methods for extracting
observables of interest. Numerous applications to a wide range of phenomena are
presented.Comment: 110 pages, 32 figures. Updated to address referee comments. To appear
in Advances in Physic
Calorimetry of Bose-Einstein condensates
We outline a practical scheme for measuring the thermodynamic properties of a
Bose-Einstein condensate as a function of internal energy. We propose using
Bragg scattering and controlled trap manipulations to impart a precise amount
of energy to a near zero temperature condensate. After thermalisation the
temperature can be measured using standard techniques to determine the state
equation . Our analysis accounts for interaction effects and the
excitation of constants of motion which restrict the energy available for
thermalisation.Comment: 6 pages, 1 figure. Updated to published versio
Quantum depletion of collapsing Bose-Einstein condensates
We perform the first numerical three-dimensional studies of quantum field
effects in the Bosenova experiment on collapsing condensates by E. Donley et
al. [Nature 415, 39 (2002)] using the exact experimental geometry. In a
stochastic truncated Wigner simulation of the collapse, the collapse times are
larger than the experimentally measured values. We find that a finite
temperature initial state leads to an increased creation rate of uncondensed
atoms, but not to a reduction of the collapse time. A comparison of the
time-dependent Hartree-Fock-Bogoliubov and Wigner methods for the more
tractable spherical trap shows excellent agreement between the uncondensed
populations. We conclude that the discrepancy between the experimental and
theoretical values of the collapse time cannot be explained by Gaussian quantum
fluctuations or finite temperature effects.Comment: 9 pages, 4 figures, replaced with published versio
Classical Region of a Trapped Bose Gas
The classical region of a Bose gas consists of all single-particle modes that
have a high average occupation and are well-described by a classical field.
Highly-occupied modes only occur in massive Bose gases at ultra-cold
temperatures, in contrast to the photon case where there are highly-occupied
modes at all temperatures. For the Bose gas the number of these modes is
dependent on the temperature, the total number of particles and their
interaction strength. In this paper we characterize the classical region of a
harmonically trapped Bose gas over a wide parameter regime. We use a
Hartree-Fock approach to account for the effects of interactions, which we
observe to significantly change the classical region as compared to the
idealized case. We compare our results to full classical field calculations and
show that the Hartree-Fock approach provides a qualitatively accurate
description of classical region for the interacting gas.Comment: 6 pages, 5 figures; updated to include new results with interaction
Numerical method for evolving the dipolar projected Gross-Pitaevskii equation
We describe a method for evolving the projected Gross-Pitaevskii equation
(PGPE) for an interacting Bose gas in a harmonic oscillator potential, with the
inclusion of a long-range dipolar interaction. The central difficulty in
solving this equation is the requirement that the field is restricted to a
small set of prescribed modes that constitute the low energy c-field 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 dipolar PGPE. We introduce a set of
auxiliary oscillator states to perform a Fourier transform necessary to
evaluate the dipolar interaction in reciprocal space. We extensively
characterize the accuracy of our approach, and derive Ehrenfest equations for
the evolution of the angular momentum.Comment: 16 pages, 6 figures. Updated to published versio
Yang-Yang thermometry and momentum distribution of a trapped one-dimensional Bose gas
We describe the use of the exact Yang-Yang solutions for the one-dimensional
Bose gas to enable accurate kinetic-energy thermometry based on the
root-mean-square width of an experimentally measured momentum distribution.
Furthermore, we use the stochastic projected Gross-Pitaevskii theory to provide
the first quantitative description of the full momentum distribution
measurements of Van Amerongen et al., Phys. Rev. Lett. 100, 090402 (2008). We
find the fitted temperatures from the stochastic projected Gross-Pitaevskii
approach are in excellent agreement with those determined by Yang-Yang
kinetic-energy thermometry.Comment: 5 pages, 3 figures. v2: Updated to published versio
Superfluidity of an interacting trapped quasi-2D Bose gas
We investigate the harmonically trapped interacting Bose gas in a quasi-2D
geometry using the classical field method. The system exhibits quasi-long-range
order and non-classical rotational inertia at temperatures below the
Berezinskii-Kosterlitz-Thouless cross-over to the superfluid state. In
particular, we compute the scissors-mode oscillation frequencies and find that
the irrotational mode changes its frequency as the temperature is sweeped
across the cross-over thus providing microscopic evidence for the emergence of
superfluidity.Comment: 9 pages, 7 figure