Energy-space random walk in a driven disordered Bose gas

Yansheng Zhang; Gevorg Martirosyan; Christopher Junhong Ho; Jiří Etrych; Christoph Eigen; Zoran Hadzibabic

doi:10.5802/crphys.168

Energy-space random walk in a driven disordered Bose gas
[Marche aléatoire dans l’espace des énergies d’un gaz de bosons forcé en présence de désordre]

Yansheng Zhang ¹ ; Gevorg Martirosyan ¹ ; Christopher Junhong Ho ¹ ; Jiří Etrych ¹ ; Christoph Eigen ¹ ; Zoran Hadzibabic ¹

¹ Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, UK

Comptes Rendus. Physique, Online first (2023), pp. 1-19.

Résumé
Abstract

Motivés par l’observation expérimentale [1] que le forçage d’un gaz de bosons sans interaction dans une boîte 3D en présence d’un faible désordre conduit à une croissance de l’énergie en loi de puissance, $E \propto t^{η}$ avec $η = 0, 46 (2)$ , et à des distributions en impulsion exponentielles comprimées révélant une loi d’échelle dynamique sous-jacente, nous effectuons des études numériques et analytiques systématiques de ce système. Des simulations de l’équation de Schrödinger montrent un passage de $η \approx 0, 5$ à $η \approx 0, 4$ lorsqu’on augmente la force du désordre, ce qui laisse supposer l’existence de deux régimes dynamiques différents. Nous présentons un modèle semi-classique qui rend compte des résultats des simulations et permet de comprendre la dynamique en termes de marche aléatoire dans l’espace des énergies, grâce à quoi un passage de la loi d’échelle $E \propto t^{1 / 2}$ à la loi $E \propto t^{2 / 5}$ est obtenu analytiquement. Les deux lois limites correspondent au fait que la marche aléatoire est limitée par le taux de la diffusion élastique induite par le désordre ou au contraire par le taux avec lequel le forçage peut modifier l’énergie du système. Nos résultats fournissent une base théorique aux futures études expérimentales.

Motivated by the experimental observation [1] that driving a non-interacting Bose gas in a 3D box with weak disorder leads to power-law energy growth, $E \propto t^{η}$ with $η = 0.46 (2)$ , and compressed-exponential momentum distributions that show dynamic scaling, we perform systematic numerical and analytical studies of this system. Schrödinger-equation simulations reveal a crossover from $η \approx 0.5$ to $η \approx 0.4$ with increasing disorder strength, hinting at the existence of two different dynamical regimes. We present a semi-classical model that captures the simulation results and allows an understanding of the dynamics in terms of an energy-space random walk, from which a crossover from $E \propto t^{1 / 2}$ to $E \propto t^{2 / 5}$ scaling is analytically obtained. The two limits correspond to the random walk being limited by the rate of the elastic disorder-induced scattering or the rate at which the drive can change the system’s energy. Our results provide the theoretical foundation for further experiments.

Reçu le : 2023-07-07
Révisé le : 2023-09-29
Accepté le : 2023-11-14
Première publication : 2024-02-02

DOI : 10.5802/crphys.168

Keywords: Ultracold atoms, Disordered system, Dynamic scaling, Continuous-time random walk, Chaos
Mot clés : Atomes froids, Système désordonné, Loi d’échelle dynamique, Marche aléatoire en temps continu, Chaos

Affiliations des auteurs :

Yansheng Zhang ¹ ; Gevorg Martirosyan ¹ ; Christopher Junhong Ho ¹ ; Jiří Etrych ¹ ; Christoph Eigen ¹ ; Zoran Hadzibabic ¹

¹ Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, UK

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Yansheng Zhang and Gevorg Martirosyan and Christopher Junhong Ho and Ji\v{r}{\'\i} Etrych and Christoph Eigen and Zoran Hadzibabic},
     title = {Energy-space random walk in a driven disordered {Bose} gas},
     journal = {Comptes Rendus. Physique},
     publisher = {Acad\'emie des sciences, Paris},
     year = {2023},
     doi = {10.5802/crphys.168},
     language = {en},
     note = {Online first},
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Yansheng Zhang; Gevorg Martirosyan; Christopher Junhong Ho; Jiří Etrych; Christoph Eigen; Zoran Hadzibabic. Energy-space random walk in a driven disordered Bose gas. Comptes Rendus. Physique, Online first (2023), pp. 1-19. doi : 10.5802/crphys.168.

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