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.
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.
Keywords: Bose gases, Bose–Einstein condensate, Temporal coherence, Trapped gases, Ultracold atoms
@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/
[1] Bell correlations in a Bose–Einstein condensate, Science, Volume 352 (2016), p. 441
[2] Scalable spin squeezing for quantum-enhanced magnetometry with Bose–Einstein condensates, Phys. Rev. Lett., Volume 113 (2014)
[3] Integrated Mach-Zehnder interferometer for Bose–Einstein condensates, Nat. Commun., Volume 4 (2013), p. 2077
[4] Observation of Bose–Einstein condensation in a dilute atomic vapor, Science, Volume 269 (1995), p. 198
[5] Bose–Einstein condensation in a gas of sodium atoms, Phys. Rev. Lett., Volume 75 (1995), p. 3969
[6] Theory of Bose–Einstein condensation in trapped gases, Rev. Mod. Phys., Volume 71 (1999), p. 463
[7] Condensation of semiconductor microcavity exciton polaritons, Science, Volume 298 (2002), p. 199
[8] Bose–Einstein condensation of exciton polaritons, Nature, Volume 443 (2006), p. 409
[9] Superfluidity of polaritons in semiconductor microcavities, Nat. Phys., Volume 5 (2009), p. 805
[10] Evidence for a Bose–Einstein condensate of excitons, Europhys. Lett., Volume 107 (2014)
[11] Quantum kinetic theory. IV. Intensity and amplitude fluctuations of a Bose–Einstein condensate at finite temperature including trap loss, Phys. Rev. A, Volume 58 (1998), p. 1450
[12] Decoherence of Bose–Einstein condensates in traps at finite temperature, Phys. Rev. Lett., Volume 81 (1998), p. 5262
[13] Orthogonality catastrophe and decoherence of a confined Bose–Einstein condensate at finite temperature, Phys. Rev. A, Volume 63 (2000)
[14] Nondiffusive phase spreading of a Bose–Einstein condensate at finite temperature, Phys. Rev. A, Volume 75 (2007)
[15] Genuine phase diffusion of a Bose–Einstein condensate in the microcanonical ensemble: a classical field study, Phys. Rev. A, Volume 78 (2008)
[16] Coherence time of a Bose–Einstein condensate, Phys. Rev. A, Volume 80 (2009)
[17] Spatial and temporal coherence of a Bose-condensed gas (M. Modugno; A. Bramati, eds.), Physics of Quantum Fluids: New Trends and Hot Topics in Atomic and Polariton Condensates, Springer Ser. Solid-State Sci., vol. 177, Springer, Berlin, 2013
[18] Brouillage thermique d'un gaz cohérent de fermions, C. R. Phys., Volume 17 (2016), p. 789 | DOI
[19] Bose–Einstein condensation of atoms in a uniform potential, Phys. Rev. Lett., Volume 110 (2013)
[20] Damping of low-energy excitations of a trapped Bose–Einstein condensate at finite temperatures, Phys. Rev. Lett., Volume 80 (1998), p. 2269
[21] Limit of spin squeezing in trapped Bose–Einstein condensates, Europhys. Lett., Volume 102 (2013)
[22] Classical quasiparticle dynamics in trapped Bose condensates, Phys. Rev. A, Volume 56 (1997), p. 4879
[23] Classical quasiparticle dynamics and chaos in trapped Bose condensates, Physica D, Volume 131 (1999), p. 141
[24] Low temperature Bose–Einstein condensates in time dependent traps: beyond the -symmetry breaking approach, Phys. Rev. A, Volume 57 (1998), p. 3008
[25] Quantum statistical mechanics in a closed system, Phys. Rev. A, Volume 43 (1991), p. 2046
[26] Chaos and quantum thermalization, Phys. Rev. E, Volume 50 (1994), p. 888
[27] Thermalization and its mechanism for generic isolated quantum systems, Nature, Volume 452 (2008), p. 854
[28] Many-body problem in quantum mechanics and quantum statistical mechanics, Phys. Rev., Volume 105 (1957), p. 1119
[29] Achieving a BCS transition in an atomic Fermi gas, Phys. Rev. Lett., Volume 92 (2004)
[30] Collapses and revivals of Bose–Einstein condensates formed in small atomic samples, Phys. Rev. Lett., Volume 77 (1996), p. 2158
[31] Relative phase of two Bose–Einstein condensates, Phys. Rev. A, Volume 55 (1997), p. 4330
[32] Damping in dilute Bose gases: a mean-field approach, Phys. Rev. A, Volume 57 (1998), p. 2949
[33] Creating long-lived neutral atom traps in a cryogenic environment, Phys. Rev. A, Volume 51 (1995), p. 1403
[34] Confinement of anti-hydrogen for 1000 seconds, Nat. Phys., Volume 7 (2011), p. 558
[35] Phase dynamics of Bose–Einstein condensates: losses versus revivals, Eur. Phys. J. D, Volume 4 (1998), p. 247
[36] Three-body recombination at vanishing scattering lengths in an ultracold Bose gas, Phys. Rev. Lett., Volume 113 (2014)
[37] Measurement of s-wave scattering lengths in a two-component Bose–Einstein condensate, Phys. Rev. A, Volume 87 (2013)
[38] Numerical Recipes, Cambridge University Press, Cambridge, UK, 1988
[39] Finite-temperature perturbation theory for a spatially inhomogeneous Bose-condensed gas, Phys. Rev. A, Volume 58 (1998), p. 3146
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