Finite-temperature excitations of Bose gases in anisotropic traps

Reidl, Jürgen; Csordás, András; Graham, R.; Szépfalusy, P.

doi:10.1103/physreva.59.3816

Cited by 43 publications

(65 citation statements)

References 28 publications

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“…This is the lowest non-trivial order at which such a consistent description is possible for a finite number of particles [101]. One might have expected higher-order fluctuation operator terms to be necessary in the non-condensate evolution for a treatment consistent with the generalized Gross-Pitaevskii equation [75]. This is not so; consistent number dynamics in fact require that there be no extension to the modified Bogoliubov-De Gennes equations [Eq.…”

Section: Number Evolutionmentioning

confidence: 99%

“…(75) A similar generalized Gross-Pitaevskii equation can be derived within a symmetry-breaking context [78], but without the integral term on the second line of Eq. (75). Before discussing the role of this term, we note that the projectors Q(r, r ′ ) in the modified Bogoliubov-de Gennes equations [Eq.…”

Section: Deduction Of the Generalized Gross-pitaevskii Equationmentioning

confidence: 99%

“…(75)] to the fluctuation operator normal and anomalous densities. This is unlike the case in Section IV C, where the result of the simple time-dependent Gross-Pitaevskii equation [Eq.…”

Section: Deduction Of the Generalized Gross-pitaevskii Equationmentioning

confidence: 99%

“…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%

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

Gardiner

Morgan

2007

Phys. Rev. A

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. (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.

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Section: Number Evolutionmentioning

confidence: 99%

Section: Deduction Of the Generalized Gross-pitaevskii Equationmentioning

confidence: 99%

“…(75)] to the fluctuation operator normal and anomalous densities. This is unlike the case in Section IV C, where the result of the simple time-dependent Gross-Pitaevskii equation [Eq.…”

Section: Deduction Of the Generalized Gross-pitaevskii Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Gardiner

Morgan

2007

Phys. Rev. A

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“…Naturally, the number of basis states used in the discrete, quantum mechanical calculation is limited by an upper energy cutoff, ǫ cut , which must be introduced consistently in all angular momentum subspaces. To account for the contributions above the energy cutoff, we use the semi-classical approximation [25,26], so that…”

Section: B Numerical Methodsmentioning

confidence: 99%

Coherence properties of the two-dimensional Bose-Einstein condensate

Gies

Hutchinson

2004

Phys. Rev. A

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We present a detailed finite-temperature Hartree-Fock-Bogoliubov (HFB) treatment of the twodimensional trapped Bose gas. We highlight the numerical methods required to obtain solutions to the HFB equations within the Popov approximation, the derivation of which we outline. This method has previously been applied successfully to the three-dimensional case and we focus on the unique features of the system which are due to its reduced dimensionality. These can be found in the spectrum of low-lying excitations and in the coherence properties. We calculate the Bragg response and the coherence length within the condensate in analogy with experiments performed in the quasione-dimensional regime [Richard et al., Phys. Rev. Lett. 91, 010405 (2003)] and compare to results calculated for the one-dimensional case. We then make predictions for the experimental observation of the quasicondensate phase via Bragg spectroscopy in the quasi-two-dimensional regime.

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Density Oscillations in Trapped Bose Condensates at Finite Temperature

Fliesser¹,

Graham²

Directions in Quantum Optics

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Finite-temperature excitations of Bose gases in anisotropic traps

Cited by 43 publications

References 28 publications

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

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

Coherence properties of the two-dimensional Bose-Einstein condensate

Density Oscillations in Trapped Bose Condensates at Finite Temperature

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