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Fluctuations quantiques et effets non-linéaires dans les condensats de Bose-Einstein : des ondes de choc dispersives au rayonnement de Hawking acoustique

Abstract : This thesis is devoted to the study of the analogue of Hawking radiation in Bose-Einstein condensates. The first chapter presents new configurations of experimental interest making it possible to realize the acoustic equivalent of a gravitational black hole in the flow of a one-dimensional atomic condensate. In each case we give an analytical description of the flow pattern, the associated quantum fluctuations, and the spectrum of Hawking radiation. Analysis of the two-body density correlations in position and momentum space emphasizes the occurrence of signals revealing the Hawking effect in our systems. By demonstrating a sum rule verified by the connected two-body density matrix we show that the long-range density correlations have to be associated to the diagonal modifications of the two-body density matrix when the flow of the condensate presents an acoustic horizon. Motivated by recent experimental studies of wave patterns generated in semiconductor microcavity polariton condensates we analyze in a second chapter superfluid and dissipative characteristics of the flow of a nonresonantly pumped one-dimensional polariton condensate past a localized obstacle. We examine the response of the condensate in the weak-perturbation limit and by means of Whitham theory in the nonlinear regime. We identify a time-dependent regime separating two types of stationary and dissipative flow: a mostly viscous one at low velocity and another one characterized by Cherenkov radiation of density waves at large velocity. Finally we present polarization effects obtained by including the spin of polaritons in the description of the condensate and show in the third chapter that similar effects in the presence of an acoustic horizon could be used to experimentally demonstrate Hawking radiation in polariton condensates.
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https://tel.archives-ouvertes.fr/tel-00875349
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Submitted on : Monday, October 21, 2013 - 6:02:12 PM
Last modification on : Monday, January 11, 2021 - 10:10:03 AM
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Pierre-Élie Larré. Fluctuations quantiques et effets non-linéaires dans les condensats de Bose-Einstein : des ondes de choc dispersives au rayonnement de Hawking acoustique. Autre [cond-mat.other]. Université Paris Sud - Paris XI, 2013. Français. ⟨NNT : 2013PA112158⟩. ⟨tel-00875349⟩

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