Frequency beating and damping of breathing oscillations of a harmonically trapped one-dimensional quasicondensate

Francis A. Bayocboc, Jr.; Karen V. Kheruntsyan

doi:10.5802/crphys.131

Frequency beating and damping of breathing oscillations of a harmonically trapped one-dimensional quasicondensate
[Battement en fréquence et amortissement des oscillations de respiration d’un quasi-condensat unidimensionnel harmoniquement piégé]

Francis A. Bayocboc, Jr.¹ ; Karen V. Kheruntsyan ¹

¹ School of Mathematics and Physics, The University of Queensland, Brisbane, Queensland 4072, Australia

Comptes Rendus. Physique, Volume 24 (2023) no. S3, pp. 15-38.

Résumé
Abstract

Nous étudions les oscillations de respiration (monopolaires) et leur amortissement dans un gaz de bosons unidimensionnel (1D) harmoniquement piégé dans le régime de quasi-condensat en utilisant une méthode de champ classique à température non nulle. En caractérisant les oscillations par le comportement de la largeur quadratique moyenne du profil de densité sur des temps longs, nous constatons que celle-ci présente un battement de deux fréquences distinctes. Ceci signifie que le gaz de bosons 1D n’oscille pas à la fréquence d’un seul mode de respiration, comme l’ont trouvé les études précédentes, mais sous l’effet de deux modes de respiration superposés, l’un oscillant à une pulsation proche de $\sim \sqrt{3} ω$ et l’autre à $\sim 2 ω$ , où $ω$ est la pulsation de piégeage. Le mode de respiration à $\sim \sqrt{3} ω$ domine le battement à basse température, dans le régime fortement quasi-condensé, et est attribué aux oscillations de la partie centrale de la distribution de densité, composée de particules occupant les niveaux de basse énergie fortement peuplés. Le mode de respiration à $\sim 2 ω$ , en revanche, domine le battement à des températures plus élevées, proches du régime du gaz de bosons presque parfait, et est attribué aux oscillations des ailes de la distribution de densité, composées de particules thermiques dans des niveaux de plus haute énergie. Les deux modes de respiration ont des taux d’amortissement distincts, celui de la composante centrale étant environ quatre fois plus grand que celui des ailes.

We study the breathing (monopole) oscillations and their damping in a harmonically trapped one-dimensional (1D) Bose gas in the quasicondensate regime using a finite-temperature classical field approach. By characterising the oscillations via the dynamics of the density profile’s rms width over long time, we find that the rms width displays beating of two distinct frequencies. This means that the 1D Bose gas oscillates not at a single breathing mode frequency, as found in previous studies, but as a superposition of two distinct breathing modes, one oscillating at frequency close to $≃ \sqrt{3} ω$ and the other at $≃ 2 ω$ , where $ω$ is the trapping frequency. The breathing mode at $\sim \sqrt{3} ω$ dominates the beating at lower temperatures, deep in the quasicondensate regime, and can be attributed to the oscillations of the bulk of the density distribution comprised of particles populating low-energy, highly-occupied states. The breathing mode at $≃ 2 ω$ , on the other hand, dominates the beating at higher temperatures, close to the nearly ideal, degenerate Bose gas regime, and is attributed to the oscillations of the tails of the density distribution comprised of thermal particles in higher energy states. The two breathing modes have distinct damping rates, with the damping rate of the bulk component being approximately four times larger than that of the tails component.

Reçu le : 2022-07-01
Révisé le : 2022-11-22
Accepté le : 2022-11-23
Première publication : 2023-03-16
Publié le : 2024-05-31

DOI : 10.5802/crphys.131

Keywords: Ultracold Atoms, Dynamics of 1D Bose Gases, Classical Field Simulations, Breathing Mode Oscillations, Damping of Collective Oscillations
Mot clés : Atomes ultrafroids, Dynamique des gaz de Bose 1D, Simulations de champs classiques, Oscillations du mode respiratoire, Amortissement des oscillations collectives

Affiliations des auteurs :

Francis A. Bayocboc, Jr. ¹ ; Karen V. Kheruntsyan ¹

¹ School of Mathematics and Physics, The University of Queensland, Brisbane, Queensland 4072, Australia

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Frequency beating and damping of breathing oscillations of a harmonically trapped one-dimensional quasicondensate},
     journal = {Comptes Rendus. Physique},
     pages = {15--38},
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Francis A. Bayocboc, Jr.; Karen V. Kheruntsyan. Frequency beating and damping of breathing oscillations of a harmonically trapped one-dimensional quasicondensate. Comptes Rendus. Physique, Volume 24 (2023) no. S3, pp. 15-38. doi : 10.5802/crphys.131. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.131/

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