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Non-locality and back-reaction in acoustic black holes and non-linearity in quantum fluid dynamics

Giorgio Ciliberto

Published Jun 26, 2025• 0 citations
Publisher

Abstract

This thesis is mainly about quan- tum correlations and non-linear fluctuations in quantum fluids. It focuses especially on collec- tive quantum fluctuations, i.e. sound waves, in the stationary flow of a 1D Bose-Einstein quasi- condensate which exhibits an acoustic horizon, i.e. a transition from subsonic to supersonic flow. Quantum phenomena generated by the presence of the horizon are investigated. The thesis also presents a brief excursus on two- dimensional turbulence in a quantum fluid. We study quantum non-separability, non- locality and back-reaction of the acoustic Hawking radiation emitted by an analog black hole. The entanglement and non-local correlations within the tripartite system of quasi-particles emitted from the acoustic horizon are first in- vestigated. Back-reaction equations govern- ing the effect of such acoustic radiation on the inhomogeneous background are derived and stationary solutions are considered. Finally, a phenomenological theory based on topological constraints for vortex creation and annihilation is effectively applied to experimental data, thus accounting for the growth and decay of turbulence.

DOI
10.6094/unifr/268289

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This thesis is mainly about quan- tum correlations and non-linear fluctuations in quantum fluids. It focuses especially on collec- tive quantum fluctuations, i.e. sound waves, in the stationary flow of a 1D Bose-Einstein quasi- condensate which exhibits an acoustic horizon, i.e. a transition from subsonic to supersonic flow. Quantum phenomena generated by the presence of the horizon are investigated. The thesis also presents a brief excursus on two- dimensional turbulence in a quantum fluid. We study quantum non-separability, non- locality and back-reaction of the acoustic Hawking radiation emitted by an analog black hole. The entanglement and non-local correlations within the tripartite system of quasi-particles emitted from the acoustic horizon are first in- vestigated. Back-reaction equations govern- ing the effect of such acoustic radiation on the inhomogeneous background are derived and stationary solutions are considered. Finally, a phenomenological theory based on topological constraints for vortex creation and annihilation is effectively applied to experimental data, thus accounting for the growth and decay of turbulence.
Non-localité et rétro-action dans les trous noirs acoustiques et non-linéarité dans les fluides quantiques Cette thèse porte essentiellement sur les corrélations quantiques et les fluctuations non-lineaires dans les fluides quantiques. Elle se concentre spéficiquement sur les fluctuations quantiques collectives, à savoir les ondes sonores, dans le flux stationnaire d'un quasi- condensat 1D de Bose-Einstein qui présente un horizon acoustique, c'est-à-dire une transition du flux d'un régime subsonique à un régime supersonique. Les phénomènes quantiques générés par la présence de l'horizon sont étudiés. La thèse présente également un bref excursus sur les turbulences dans un fluide quantique bidimensionnel.Nous étudions la non-séparabilité quantique, la non-localité et la rétro-action du rayonnement acoustique de Hawking émis par un trou noir analogue. L'intrication et les corrélations non locales au sein du système tri- partite de quasi-particules émises par l'horizon acoustique sont d'abord étudiées. Les équations de rétro-action qui régissent l'effet de ce rayonnement acoustique sur le fond inhomogène sont dérivées et des solutions stationnaires sont considérées. Enfin, une théorie phénoménologique basée sur des contraintes topologiques pour la création et l'annihilation de vortex est appliquée efficacement aux don- nées expérimentales, permettant ainsi de rendre compte des phases de croissance et de décroissance des turbulences.
We extend the Gross-Pitaevskii equation to incorporate the effect of quantum fluctuations onto the flow of a weakly interacting Bose-Einstein condensate. Applying this framework to an analog black hole in a quasi-one-dimensional, transonic flow, we investigate how acoustic Hawking radiation back-reacts on the background condensate. Our results point to the emergence of stationary density and velocity undulations in the supersonic region (analogous to the black hole interior) and enable to evaluate the change in upstream and downstream Mach numbers caused by Hawking radiation. These findings provide new insight into the interplay between quantum fluctuations and analog gravity in Bose-Einstein condensates.
In a previous article, we studied stationary solutions to the dynamics of a Bose-Einstein condensate corresponding to acoustic (or Unruh) black or white holes, namely, configurations where the flow becomes supersonic, creating a horizon for phonons. In this paper, we consider again the Gross-Pitaevskii equation, but looking for stationary numerical solutions in the case where the couplings are position dependent in a prescribed manner. Initially, we consider a two-dimensional quantum gas in a funnel-like spatial metric. We then reinterpret this solution as a solution in a flat metric but with spatially dependent coupling and external potential. In these solutions, the local speed of sound and the magnitude of flow velocity cross, indicating the existence of a supersonic region and therefore of sonic analogs of black and white holes and wormholes. We discuss the numerical techniques used. We also study phase (and density) fluctuations in these solutions and derive approximate acoustic metric tensors. For certain external potentials, we find uniform-density acoustic-black-hole configurations and obtain their Hawking temperature.
Observing quantum particle creation by black holes (Hawking radiation) in the astrophysical context is, in ordinary situations, hopeless. Nevertheless the Hawking effect, which depends only on kinematical properties of wave propagation in the presence of horizons, is present also in nongravitational contexts, for instance in stationary fluids undergoing supersonic flow. We present results on how to observe the analog Hawking radiation in Bose-Einstein condensates by a direct measurement of the density correlations due to the phonon pairs (Hawking quanta-partner) created by the acoustic horizon.
We study acoustic white holes in a steadily flowing atomic Bose–Einstein condensate. A white hole configuration is obtained when the flow velocity goes from a super-sonic value in the upstream region to a sub-sonic one in the downstream region. The scattering of phonon wavepackets on a white hole horizon is numerically studied in terms of the Gross–Pitaevskii equation of mean-field theory: dynamical stability of the acoustic white hole is found, as well as a signature of a nonlinear back-action of the incident phonon wavepacket onto the horizon. The correlation pattern of density fluctuations is numerically studied by means of the truncated-Wigner method, which includes quantum fluctuations. Signatures of the white hole radiation of correlated phonon pairs by the horizon are characterized; analogies and differences with Hawking radiation from acoustic black holes are discussed. In particular, a short wavelength feature is identified in the density correlation function, whose amplitude steadily grows in time since the formation of the horizon. The numerical observations are quantitatively interpreted by means of an analytical Bogoliubov theory of quantum fluctuations for a white hole configuration within the step-like horizon approximation.
Simulation of a sonic black-hole/white-hole pair in a (2+1)-dimensional Bose-Einstein condensate shows formation of superfluid vortices through dynamical instabilities seeded by initial quantum noise. The instabilities saturate in a quasi-steady state of superfluid turbulence within the supersonic region, from which sound waves are emitted in qualitative resemblance to Hawking radiance. The power spectrum of the radiation from the slowly decaying two-dimensional sonic black hole is strongly non-thermal, however.