Optomechanical Backreaction of Quantum Field Processes in Dynamical Casimir Effect

Yu-Cun Xie; Salvatore Butera; Bei-Lok Hu

doi:10.5802/crphys.186

Article de recherche

Optomechanical Backreaction of Quantum Field Processes in Dynamical Casimir Effect
[Rétroaction optomécanique des processus de champs quantiques dans l’effet Casimir dynamique]

Yu-Cun Xie ¹ ; Salvatore Butera ² ; Bei-Lok Hu ³

¹ Department of Physics, University of Maryland, College Park, MD 20742, USA
² School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK
³ Maryland Center for Fundamental Physics and Joint Quantum Institute, University of Maryland, College Park, MD 20742, USA

Comptes Rendus. Physique, Online first (2024), pp. 1-22.

Résumé
Abstract

Au cours des deux dernières décennies, les chercheurs en gravitation analogique ont conçu de nombreuses expériences en laboratoire pour tester certains effets importants de la gravité semi-classique ; le rayonnement de Hawking–Unruh dans les fluides et des BEC étant des exemples frappants. L’analogue de la création de particules cosmologiques est l’effet Casimir dynamique, car les deux phénomènes partagent le même mécanisme physique sous-jacent, à savoir l’amplification paramétrique des fluctuations du vide dans le champ quantique par un univers en expansion ou par une frontière se déplaçant rapidement. Il a été démontré que la rétroaction de la création de particules cosmologiques au temps de Planck joue un rôle important dans l’isotropisation et l’homogénéisation de l’univers primitif. Le problème correspondant de la compréhension des effets de rétroaction des processus de champ quantique dans l’effet Casimir dynamique est l’objectif de ce travail. Nous présentons des analyses des processus de champ quantique dans deux systèmes modèles : en 1+1D : un anneau (composé de deux miroirs ponctuels identifiés aux deux extrémités) dont le rayon dépend du temps, et en 3+1D : une boîte conductrice rectangulaire symétrique dont la longueur d’un côté peut changer avec le temps. Dans les deux cas, la dépendance temporelle du rayon ou de la longueur n’est pas prescrite – aucun agent externe n’est présent – mais déterminée uniquement par la rétroaction de la création de particules et les effets connexes. Nous constatons que pour 1+1D, le seul effet de champ quantique dû à l’anomalie de trace tend à accélérer la contraction de l’anneau au-delà de celle déjà présente due à la force d’attraction plus faible de l’effet Casimir statique. Pour la boîte rectangulaire, le taux d’expansion ou de contraction de la boîte est ralenti par rapport à celui dû à l’effet Casimir statique. Nos conclusions concordent avec les résultats obtenus dans les problèmes de rétroaction cosmologique, qui peuvent être résumés dans ce que l’on appelle la loi de Lenz quantique, selon laquelle la rétroaction agit dans le sens de l’opposition à de nouveaux changements, ce qui signifie la suppression de la création de particules et un ralentissement de la dynamique du système. En conclusion, nous mentionnons également deux classes de problèmes connexes, et d’importance théorique pour des recherches ultérieures.

Dynamical Casimir effect (DCE) and cosmological particle creation (CPC) share the same underlying physical mechanism, that of parametric amplification of vacuum fluctuations in the quantum field by an expanding universe or by a fast moving boundary. Backreaction of cosmological particle creation at the Planck time has been shown to play a significant role in the isotropization and homogenization of the early universe. Understanding the backreaction effects of quantum field processes in DCE is the goal of this work. We present analyses of quantum field processes in two model systems: in 1+1D, a ring with time-dependent radius, and in 3+1D, a symmetric rectangular conducting box with one moving side. In both cases the time-dependence of the radius or the length is determined solely by the backreaction of particle creation and related effects, there is no external agent. We find that for 1+1D, the only quantum field effect due to the trace anomaly tends to accelerate the contraction of the ring over and above that due to the attractive force in the static Casimir effect. For the rectangular box the expansion or contraction is slowed down compared to that due to the static Casimir effect. Our findings comply with what is known as the quantum Lenz law, found in cosmological backreaction problems: the backreaction works in the direction of opposing further changes, which means the suppression of particle creation and a slow down of the system dynamics. In conclusion we suggest two related classes of problems of theoretical significance for further investigations.

Reçu le : 2023-08-22
Révisé le : 2024-01-03
Accepté le : 2024-04-04
Première publication : 2024-06-13

DOI : 10.5802/crphys.186

Keywords: backreaction, dynamical Casimir effect, nonequilibrium quantum field, vacuum fluctuations, quantum fields in curved spacetime, adiabatic regularization
Mot clés : rétroaction, effet Casimir dynamique, champ quantique hors équilibre, fluctuations du vide, champs quantiques dans un espace-temps courbe, régularisation adiabatique

Affiliations des auteurs :

Yu-Cun Xie ¹ ; Salvatore Butera ² ; Bei-Lok Hu ³

¹ Department of Physics, University of Maryland, College Park, MD 20742, USA
² School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK
³ Maryland Center for Fundamental Physics and Joint Quantum Institute, University of Maryland, College Park, MD 20742, USA

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Yu-Cun Xie and Salvatore Butera and Bei-Lok Hu},
     title = {Optomechanical {Backreaction} of {Quantum} {Field} {Processes} in {Dynamical} {Casimir} {Effect}},
     journal = {Comptes Rendus. Physique},
     publisher = {Acad\'emie des sciences, Paris},
     year = {2024},
     doi = {10.5802/crphys.186},
     language = {en},
     note = {Online first},
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Yu-Cun Xie; Salvatore Butera; Bei-Lok Hu. Optomechanical Backreaction of Quantum Field Processes in Dynamical Casimir Effect. Comptes Rendus. Physique, Online first (2024), pp. 1-22. doi : 10.5802/crphys.186.

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