Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2411.06678 · Journal of Physics A Mathematical and Theoretical

Stationary acoustic black hole solutions in Bose–Einstein condensates and their Borel analysis

Sachin Vaidya, Martı́n Kruczenski

Published Apr 22, 2025• 2 citations
arXivHTMLPDF

Abstract

Abstract In this article, we study the dynamics of a Bose–Einstein condensate (BEC) with the idea of finding solutions that could possibly correspond to the so-called acoustic (or Unruh) black/white holes. These are flows with horizons where the speed of the flow changes from sub-sonic to super-sonic. This is because sound cannot return from the supersonic to the subsonic regions. The speed of sound plays the role of the speed of light in a gravitational black hole, with an important difference being that there are excitations that can go faster than the speed of sound and therefore can escape the sonic black hole. Here, the motion of the BEC is described by the Gross–Pitaevskii equation (GPE). More specifically, we discuss singular Stationary solutions of GPE in 2D (with circular symmetry) and 3D (with spherical symmetry). We use these solutions to study the local speed of sound and magnitude of flow velocity of the condensate to determine whether they cross, indicating the potential existence of a sonic analog of a black/white hole. We discuss the numerical techniques used and also study the semi-analytical Laplace–Borel resummation of asymptotic series solutions to see how well they agree with numerical solutions. We also study how the resurgent transseries plays a role in these solutions.

DOI
10.1088/1751-8121/adcf61

Related papers

Acoustic black holes, white holes, and wormholes in Bose-Einstein condensates in two dimensions

Sachin Vaidya, Martı́n Kruczenski

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.

arXiv:2412.02727•Physical Review A•Apr 14, 2025•0 citations

The Study of Formation of Sonic Black Hole in One-Dimensional Bose-Einstein Condensate

Haoquan Xu, Qingru Wang, Ying Wang +3 more

Based on the one-dimensional Gross-Pitaevskii equation (GPE) model, this work studies the formation of acoustic black holes in one-dimensional Bose Einstein condensate (BEC) in harmonic oscillator external potential, and extending the applicable scenarios of the GPE model for its specific application of simulating the formation conditions of acoustic black holes in one-dimensional systems. At the same time, We deepen the understanding of the analytical formula for determining the production conditions of acoustic black holes and the evolution formula of the radius of acoustic black holes.

Journal of applied physical science international•Oct 10, 2023•0 citations

Realization of a Sonic Black Hole Analog in a Bose-Einstein Condensate

Oren Lahav, Amir Itah, Alex Blumkin +4 more

We have created an analog of a black hole in a Bose-Einstein condensate. In this sonic black hole, sound waves, rather than light waves, cannot escape the event horizon. A steplike potential accelerates the flow of the condensate to velocities which cross and exceed the speed of sound by an order of magnitude. The Landau critical velocity is therefore surpassed. The point where the flow velocity equals the speed of sound is the sonic event horizon. The effective gravity is determined from the profiles of the velocity and speed of sound. A simulation finds negative energy excitations, by means of Bragg spectroscopy.

arXiv:0906.1337•Physical Review Letters•Dec 7, 2010•336 citations

Acoustic white holes in flowing atomic Bose–Einstein condensates

Carlos Mayoral, Alessio Recati, Alessandro Fabbri +3 more

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.

arXiv:1009.6196•New Journal of Physics•Feb 4, 2011•71 citations

Sonic black holes with thick horizons in BECs

Daniel Peñalver, Marco De Vito, Roberto Balbinot +1 more

We consider simple one dimensional models of acoustic black holes formed by Bose-Einstein condensates where the flow is stepwise homogeneous. We shall concentrate on the case in which an extended sonic region is present, i.e. a region where the flow velocity equals exactly the speed of sound. These models can be thought of as acoustic black holes with a thick horizon. Particular attention will be devoted to the number of created particles and to the density-density correlation functions, these latter being at present time the experimental tool to identify Hawking like radiation in acoustic black holes.

arXiv:2607.11396•Physical review. D/Physical review. D.•Sep 3, 2026•0 citations

Sonic black holes in dilute Bose-Einstein condensates

Luis J. Garay, J. R. Anglin, J. I. Cirac +1 more

The sonic analog of a gravitational black hole in dilute-gas Bose-Einstein condensates is investigated. It is shown that there exist both dynamically stable and unstable configurations which, in the hydrodynamic limit, exhibit behaviors completely analogous to that of gravitational black holes. The dynamical instabilities involve the creation of quasiparticle pairs in positive and negative energy states. We illustrate these features in two qualitatively different one-dimensional models, namely, a long, thin condensate with an outcoupler laser beam providing an ``atom sink,'' and a tight ring-shaped condensate. We also simulate the creation of a stable sonic black hole by solving the Gross-Pitaevskii equation numerically for a condensate subject to a trapping potential which is adiabatically deformed. A sonic black hole could, in this way, be created experimentally with state-of-the-art or planned technology.

arXiv:gr-qc/0005131•Physical Review A•Jan 17, 2001•297 citations
Abstract In this article, we study the dynamics of a Bose–Einstein condensate (BEC) with the idea of finding solutions that could possibly correspond to the so-called acoustic (or Unruh) black/white holes. These are flows with horizons where the speed of the flow changes from sub-sonic to super-sonic. This is because sound cannot return from the supersonic to the subsonic regions. The speed of sound plays the role of the speed of light in a gravitational black hole, with an important difference being that there are excitations that can go faster than the speed of sound and therefore can escape the sonic black hole. Here, the motion of the BEC is described by the Gross–Pitaevskii equation (GPE). More specifically, we discuss singular Stationary solutions of GPE in 2D (with circular symmetry) and 3D (with spherical symmetry). We use these solutions to study the local speed of sound and magnitude of flow velocity of the condensate to determine whether they cross, indicating the potential existence of a sonic analog of a black/white hole. We discuss the numerical techniques used and also study the semi-analytical Laplace–Borel resummation of asymptotic series solutions to see how well they agree with numerical solutions. We also study how the resurgent transseries plays a role in these solutions.
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.
Based on the one-dimensional Gross-Pitaevskii equation (GPE) model, this work studies the formation of acoustic black holes in one-dimensional Bose Einstein condensate (BEC) in harmonic oscillator external potential, and extending the applicable scenarios of the GPE model for its specific application of simulating the formation conditions of acoustic black holes in one-dimensional systems. At the same time, We deepen the understanding of the analytical formula for determining the production conditions of acoustic black holes and the evolution formula of the radius of acoustic black holes.
We have created an analog of a black hole in a Bose-Einstein condensate. In this sonic black hole, sound waves, rather than light waves, cannot escape the event horizon. A steplike potential accelerates the flow of the condensate to velocities which cross and exceed the speed of sound by an order of magnitude. The Landau critical velocity is therefore surpassed. The point where the flow velocity equals the speed of sound is the sonic event horizon. The effective gravity is determined from the profiles of the velocity and speed of sound. A simulation finds negative energy excitations, by means of Bragg spectroscopy.
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.
We consider simple one dimensional models of acoustic black holes formed by Bose-Einstein condensates where the flow is stepwise homogeneous. We shall concentrate on the case in which an extended sonic region is present, i.e. a region where the flow velocity equals exactly the speed of sound. These models can be thought of as acoustic black holes with a thick horizon. Particular attention will be devoted to the number of created particles and to the density-density correlation functions, these latter being at present time the experimental tool to identify Hawking like radiation in acoustic black holes.
The sonic analog of a gravitational black hole in dilute-gas Bose-Einstein condensates is investigated. It is shown that there exist both dynamically stable and unstable configurations which, in the hydrodynamic limit, exhibit behaviors completely analogous to that of gravitational black holes. The dynamical instabilities involve the creation of quasiparticle pairs in positive and negative energy states. We illustrate these features in two qualitatively different one-dimensional models, namely, a long, thin condensate with an outcoupler laser beam providing an ``atom sink,'' and a tight ring-shaped condensate. We also simulate the creation of a stable sonic black hole by solving the Gross-Pitaevskii equation numerically for a condensate subject to a trapping potential which is adiabatically deformed. A sonic black hole could, in this way, be created experimentally with state-of-the-art or planned technology.