Shifts and widths of collective excitations in trapped Bose gases determined by the dielectric formalism

We utilize a two-gas model to simulate collective oscillations of a Bose-Einstein condensate at finite temperatures. The condensate is described using a generalized GrossPitaevskii equation, which is coupled to a thermal cloud modelled by a Monte Carlo algorithm. This allows us to include the collective dynamics of both the condensed and non-condensed components self-consistently. We simulate quadrupolar excitations, and measure the damping rate and frequency as a function of temperature. We also observe revivals in condensate oscillations at high temperatures, and in the thermal cloud at low temperature. Extensions of the model to include non-equilibrium effects and describe more complex phenomena are discussed.PACS numbers: 03.75. Fi, 05.30.Jp, 67.40.Db The first experimental observation of Bose-Einstein condensation (BEC) in magnetically trapped alkali atoms in 1995 [1-3] was a precursor to an explosion of interest in the properties of weakly-interacting Bose gases. Much of the subsequent theory [4] has focused on the dynamics of the condensate, including phenomena such as collective excitations and vortex motion. In the limit of zero temperature, one can represent the condensate by a macroscopic wavefunction analogous to a classical field. In this case the behavior can be described in terms of the GrossPitaevskii (GP) equation, which has the form of a nonlinear Shrödinger equation. Extension of the description to finite temperatures, where one must include fluctuations upon the condensate wavefunction, is a considerable challenge. However, the motivation is clear, as such a description would allow direct comparison with experiments where a non-condensed thermal cloud is present, as well as revealing new phenomena such as damping of collective modes [5][6][7][8][9][10] and the decay of metastable vortices [11,12].Amongst the most compelling evidence for the validity of the GP equation at low temperatures is its quantitative agreement with experiment for low-energy collective modes. However, consistent theoretical descriptions at higher temperatures have proved far more elusive, where experiments have demonstrated marked frequency shifts and damping of the condensate modes in the presence of a significant non-condensed component [9,10]. Theoretical studies have tended to concentrate on one of two regimes, depending upon the density and temperature of the system. At high densities, where collisions are sufficiently rapid to force the system into local equilibrium, the dynamics of the condensate and thermal cloud can be described by a set of coupled hydrodynamical equations [13][14][15]. Damping mechanisms in this case are of a dissipative type (i.e. viscosity and thermal relaxation). For very dilute systems or at low temperatures the mean free path of the elementary excitations become comparable to the size of the system and collisions play only a minor role. Damping in this collisionless regime is not related to thermalization processes but to coupling between excitations, and can be described within the fr...

supporting

confidence: 80%

“…2. The figure shows a small downward shift in frequency for T < 0.6T 0 c [9,10,17,33]. An increase in frequency above 0.6T 0 c is also observed; however, this is not as large as that seen in the JILA experiment [9], where the frequency approaches 2ω x in this region.…”

mentioning

confidence: 77%

Damping and revivals of collective oscillations in a finite-temperature model of trapped Bose-Einstein condensation

Jackson

Adams

2001

“…The purpose of the present paper is to examine the validity of the Kohn theorem in a specific finite temperature approximation within the dielectric formalism. It was introduced and studied in a previous paper [9]. It was shown there that its results agree with those results which can also be calculated in the Minguzzi and Tosi approach [8], but that it gives additional results, in particular for the 1-particle Green's functions.…”

Section: Introductionsupporting

confidence: 68%

Kohn mode for trapped Bose gases within the dielectric formalism

Reidl¹,

Bene

Graham³

et al. 2001

Self Cite

The presence of undamped harmonic center of mass oscillations of a weakly interacting Bose gas in a harmonic trap is demonstrated within the dielectric formalism for a previously introduced finite temperature approximation including exchange. The consistency of the approximation with the Kohn theorem is thereby demonstrated. The Kohn modes are found explicitly, generalizing an earlier zero-temperature result found in the literature. It is shown how the Kohn mode disappears from the single-particle spectrum, while remaining in the density oscillation spectrum, when the temperature increases from below to above the condensation temperature. 03.75.Fi,05.30.Jp,67.40.Db

“…Particularly motivated by the desire to explain the properties of Bose-condensed gases at finite temperature, a number of extensions have been proposed. These include generalizations [58,59,60,61,62,63,64] of linear response theory [65,66], stochastic interpretations of the Gross-Pitaevskii equation [67,68,69,70,71], Hartree-Fock-Bogoliubov approaches [72,73,74,75,76,77,78], a variety of kinetic theories [79,80,81,82,83,84,85,86,87,88,89,90], and a cumulant-based formalism [21,91,92,93].…”

Section: Introductionmentioning

confidence: 99%

Number-conserving approach to a minimal self-consistent treatment of condensate and noncondensate dynamics in a degenerate Bose gas

Gardiner

Morgan

2007

. (2007) 'A number-conserving approach to a minimal self-consistent treatment of condensate and non-condensate dynamics in a degenerate Bose gas.', Physical review A., 75 . p. 43621.Further information on publisher's website: Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. 3008 (1998)]. We consider what is effectively an expansion in powers of the ratio of non-condensate to condensate particle numbers, rather than inverse powers of the total number of particles. This requires the number of condensate particles to be a majority, but not necessarily almost equal to the total number of particles in the system. We argue that a second-order treatment of the relevant dynamical equations of motion is the minimum order necessary to provide consistent coupled condensate and non-condensate number dynamics for a finite total number of particles, and show that such a second-order treatment is provided by a suitably generalized Gross-Pitaevskii equation, coupled to the Castin-Dum numberconserving formulation of the Bogoliubov-de Gennes equations. The necessary equations of motion can be generated from an approximate third-order Hamiltonian, which effectively reduces to second order in the steady state. Such a treatment as described here is suitable for dynamics at occurring at finite temperature, where there is a significant non-condensate fraction from the outset, or dynamics leading to dynamical instabilities, where depletion of the condensate can also lead to a significant non-condensate fraction, even if the non-condensate fraction is initially negligible.