14 research outputs found
Momentum distribution and coherence of a weakly interacting Bose gas after a quench
We consider a weakly interacting uniform atomic Bose gas with a
time-dependent nonlinear coupling constant. By developing a suitable Bogoliubov
treatment we investigate the time evolution of several observables, including
the momentum distribution, the degree of coherence in the system, and their
dependence on dimensionality and temperature. We rigorously prove that the
low-momentum Bogoliubov modes remain frozen during the whole evolution, while
the high-momentum ones adiabatically follow the change in time of the
interaction strength. At intermediate momenta we point out the occurrence of
oscillations, which are analogous to Sakharov oscillations. We identify two
wide classes of time-dependent behaviors of the coupling for which an exact
solution of the problem can be found, allowing for an analytic computation of
all the relevant observables. A special emphasis is put on the study of the
coherence property of the system in one spatial dimension. We show that the
system exhibits a smooth "light-cone effect," with typically no
prethermalization.Comment: 24 pages, 12 figure
Two-dimensional superflow past an obstacle of arbitrary penetrability: Exact results for the critical velocity
We report analytical and numerical results for the critical velocity for
dissipationless motion of a two-dimensional scalar superfluid past a localized
and static repulsive obstacle. In contrast to most of the state of the art, our
study is not restricted to an impenetrable obstacle, nor to a quartic
interaction. This makes it possible to get closer to recent experiments with
atomic Bose-Einstein condensates and paraxial superfluids of light.Comment: 9 pages, 2 figure
Stationary transport above the critical velocity in a one-dimensional superflow past an obstacle
We consider in this work the different possible stationary flows of a one
dimensional quantum fluid in the mean-field regime. We focus on the supersonic
regime where a transition from a time dependent flow to a stationary
diffractive flow occurs at a given critical velocity. We give nonperturbative
results for this critical velocity in the presence of a localised obstacle of
arbitrary size and strength. In addition, we discuss the existence of
superfluid-like solution in the supersonic regime due to resonant transport and
provide a complete map of the different regimes of stationary transport of a
quantum fluid.Comment: 7 pages and 5 pages of supplementary materia
Weakly interacting disordered Bose gases out of equilibrium: from multiple scattering to superfluidity
We explore the quench dynamics of a two-dimensional, weakly interacting
disordered Bose gas for various relative strengths of interactions and
disorder. This allows us to identify two well distinct out-of-equilibrium
regimes. When interactions are smaller than the disorder, the gas experiences
multiple scattering and exhibits a short-range spatial coherence. At short time
this coherence is only smoothly affected by interactions, via a diffusion
process of the particles' energies. When interactions are larger than the
disorder, scattering ceases and the gas behaves more and more like a fluid,
ultimately like a superfluid at low energy. In the superfluid regime, the gas
exhibits a long-range algebraic coherence, characteristic of a pre-thermal
regime in disorder.Comment: 6 pages, 4 figure
Experimental observation of turbulent coherent structures in a superfluid of light
We experimentally explore the rich variety of nonlinear coherent structures
arising in a turbulent flow of superfluid light past an obstacle in an
all-optical configuration. The different hydrodynamic regimes observed are
organised in a unique phase diagram involving the velocity of the flow and the
diameter of the obstacle. Then, we focus on the vortices nucleated in the wake
of the obstacle by investigating their intensity profile and the dependence of
the radius of their core on the healing length. Our results pave the way for
further investigations on turbulence in photon superfluids and provide
versatile experimental tools for simulating quantum transport with nonlinear
light
Quantum fluctuations and nonlinear effects in Bose-Einstein condensates : From dispersive shock waves to acoustic Hawking radiation
Cette thèse est dédiée à l'étude de l'analogue du rayonnement de Hawking dans les condensats de Bose-Einstein. Le premier chapitre présente de nouvelles configurations d'intérêt expérimental permettant de réaliser l'équivalent acoustique d'un trou noir gravitationnel dans l'écoulement d'un condensat atomique unidimensionnel. Nous donnons dans chaque cas une description analytique du profil de l'écoulement, des fluctuations quantiques associées et du spectre du rayonnement de Hawking. L'analyse des corrélations à deux corps de la densité dans l'espace des positions et des impulsions met en évidence l'émergence de signaux révélant l'effet Hawking dans nos systèmes. En démontrant une règle de somme vérifiée par la matrice densité à deux corps connexe, on montre que les corrélations à longue portée de la densité doivent être associées aux modifications diagonales de la matrice densité à deux corps lorsque l'écoulement du condensat présente un horizon acoustique. Motivés par des études expérimentales récentes de profils d'onde générés dans des condensats de polaritons en microcavité semi-conductrice, nous analysons dans un second chapitre les caractéristiques superfluides et dissipatives de l'écoulement autour d'un obstacle localisé d'un condensat de polaritons unidimensionnel obtenu par pompage incohérent. Nous examinons la réponse du condensat dans la limite des faibles perturbations et au moyen de la théorie de Whitham dans le régime non-linéaire. On identifie un régime dépendant du temps séparant deux types d'écoulement stationnaire et dissipatif : un principalement visqueux à faible vitesse et un autre caractérisé par un rayonnement de Cherenkov d'ondes de densité à grande vitesse. Nous présentons enfin des effets de polarisation obtenus en incluant le spin des polaritons dans la description du condensat et montrons dans le troisième chapitre que des effets similaires en présence d'un horizon acoustique pourraient être utilisés pour démontrer expérimentalement le rayonnement de Hawking dans les condensats de polaritons.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
Fluctuations quantiques et effets non-linéaires dans les condensats de Bose-Einstein : des ondes de choc dispersives au rayonnement de Hawking acoustique
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.Cette thèse est dédiée à l'étude de l'analogue du rayonnement de Hawking dans les condensats de Bose-Einstein. Le premier chapitre présente de nouvelles configurations d'intérêt expérimental permettant de réaliser l'équivalent acoustique d'un trou noir gravitationnel dans l'écoulement d'un condensat atomique unidimensionnel. Nous donnons dans chaque cas une description analytique du profil de l'écoulement, des fluctuations quantiques associées et du spectre du rayonnement de Hawking. L'analyse des corrélations à deux corps de la densité dans l'espace des positions et des impulsions met en évidence l'émergence de signaux révélant l'effet Hawking dans nos systèmes. En démontrant une règle de somme vérifiée par la matrice densité à deux corps connexe, on montre que les corrélations à longue portée de la densité doivent être associées aux modifications diagonales de la matrice densité à deux corps lorsque l'écoulement du condensat présente un horizon acoustique. Motivés par des études expérimentales récentes de profils d'onde générés dans des condensats de polaritons en microcavité semi-conductrice, nous analysons dans un second chapitre les caractéristiques superfluides et dissipatives de l'écoulement autour d'un obstacle localisé d'un condensat de polaritons unidimensionnel obtenu par pompage incohérent. Nous examinons la réponse du condensat dans la limite des faibles perturbations et au moyen de la théorie de Whitham dans le régime non-linéaire. On identifie un régime dépendant du temps séparant deux types d'écoulement stationnaire et dissipatif : un principalement visqueux à faible vitesse et un autre caractérisé par un rayonnement de Cherenkov d'ondes de densité à grande vitesse. Nous présentons enfin des effets de polarisation obtenus en incluant le spin des polaritons dans la description du condensat et montrons dans le troisième chapitre que des effets similaires en présence d'un horizon acoustique pourraient être utilisés pour démontrer expérimentalement le rayonnement de Hawking dans les condensats de polaritons
Low-energy prethermal phase and crossover to thermalization in nonlinear kicked rotors
International audienceIn the presence of interactions, periodically driven quantum systems generically thermalize to an infinite-temperature state. Recently, however, it was shown that in random kicked rotors with local interactions, this long-time equilibrium could be strongly delayed by operating in a regime of weakly fluctuating random phases, leading to the emergence of a metastable thermal ensemble. Here we show that when the random kinetic energy is smaller than the interaction energy, this system in fact exhibits a much richer dynamical phase diagram, which includes a low-energy prethermal phase characterized by a light-cone spreading of correlations in momentum space. We develop a hydrodynamic theory of this phase and find a very good agreement with exact numerical simulations. We finally explore the full dynamical phase diagram of the system and find that the transition toward full thermalization is characterized by relatively sharp crossovers