[Coherence time of a Bose–Einstein condensate in an isolated harmonically trapped gas]
We study the condensate phase dynamics in a low-temperature equilibrium gas of weakly interacting bosons, harmonically trapped and isolated from the environment. We find that at long times, much longer than the collision time between Bogoliubov quasi-particles, the variance of the phase accumulated by the condensate grows with a ballistic term quadratic in time and a diffusive term affine in time. We give the corresponding analytical expressions in the limit of a large system, in the collisionless regime and in the ergodic approximation for the quasi-particle motion. When properly rescaled, they are described by universal functions of the temperature divided by the Thomas–Fermi chemical potential. The same conclusion holds for the mode damping rates. Such universality class differs from the previously studied one of the homogeneous gas.
Nous étudions la dynamique de phase à l'équilibre d'un condensat dans un gaz de bosons en interaction faible harmoniquement piégé et isolé de l'environnement. Nous trouvons qu'au bout d'un temps long devant le temps de collision typique entre les quasi-particules de Bogolioubov, la variance du déphasage du condensat comporte en général un terme balistique quadratique en temps et un terme diffusif affine en temps. Nous donnons des expressions analytiques des coefficients correspondants, à la limite d'un grand système, dans le régime faiblement collisionnel et dans l'approximation ergodique pour le mouvement des quasi-particules. Correctement adimensionnés, ils sont décrits, tout comme les taux d'amortissement des modes, par des fonctions universelles de la température ramenée au potentiel chimique de Thomas–Fermi du condensat. Cette classe d'universalité diffère de celle précédemment étudiée du gaz spatialement homogène.
Keywords: Bose gases, Bose–Einstein condensate, Temporal coherence, Trapped gases, Ultracold atoms
Yvan Castin 1; Alice Sinatra 1
@article{CRPHYS_2018__19_5_316_0,
author = {Yvan Castin and Alice Sinatra},
title = {Temps de coh\'erence d'un condensat de {Bose{\textendash}Einstein} dans un gaz isol\'e harmoniquement pi\'eg\'e},
journal = {Comptes Rendus. Physique},
pages = {316--336},
publisher = {Elsevier},
volume = {19},
number = {5},
year = {2018},
doi = {10.1016/j.crhy.2018.04.001},
language = {fr},
}
TY - JOUR AU - Yvan Castin AU - Alice Sinatra TI - Temps de cohérence d'un condensat de Bose–Einstein dans un gaz isolé harmoniquement piégé JO - Comptes Rendus. Physique PY - 2018 SP - 316 EP - 336 VL - 19 IS - 5 PB - Elsevier DO - 10.1016/j.crhy.2018.04.001 LA - fr ID - CRPHYS_2018__19_5_316_0 ER -
Yvan Castin; Alice Sinatra. Temps de cohérence d'un condensat de Bose–Einstein dans un gaz isolé harmoniquement piégé. Comptes Rendus. Physique, Volume 19 (2018) no. 5, pp. 316-336. doi : 10.1016/j.crhy.2018.04.001. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2018.04.001/
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