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arXiv:2304.10667 · Physical Review A

Observation of self-oscillating supersonic flow across an acoustic horizon in two dimensions

Hikaru Tamura, Sergei Khlebnikov, Cheng-An Chen, Chen-Lung Hung

Published Aug 11, 2025• 5 citations
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Abstract

The authors create a spatially bounded supersonic region in a two-dimensional atomic superfluid, forming an acoustic analogue of a black-hole horizon. The observed superflow appears to be modulated by quasi-periodic bursts of superluminal signals. By measuring their frequencies, the authors find agreement with numerical simulations of soliton oscillation frequencies within the black-hole horizon, where solitons are emitted due to the Landau instability.

DOI
10.1103/t2sn-kx99

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The authors create a spatially bounded supersonic region in a two-dimensional atomic superfluid, forming an acoustic analogue of a black-hole horizon. The observed superflow appears to be modulated by quasi-periodic bursts of superluminal signals. By measuring their frequencies, the authors find agreement with numerical simulations of soliton oscillation frequencies within the black-hole horizon, where solitons are emitted due to the Landau instability.
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Acoustic analogues of black holes (dumb holes) are generated when a supersonic fluid flow entrains sound waves and forms a trapped region from which sound cannot escape. The surface of no return, the acoustic horizon, is qualitatively very similar to the event horizon of a general relativity black hole. In particular Hawking radiation (a thermal bath of phonons with temperature proportional to the "surface gravity") is expected to occur. In this note we consider quasi-one-dimensional supersonic flow of a Bose–Einstein condensate (BEC) in a Laval nozzle (converging-diverging nozzle), with a view to finding which experimental settings could magnify this effect and provide an observable signal. We discuss constraints and problems for our model and identify the issues that should be addressed in the near future in order to set up an experiment. In particular we identify an experimentally plausible configuration with a Hawking temperature of order 70 n K; to be contrasted with a condensation temperature of the order of 90 n K.
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.
We consider elongated condensates that cross twice the speed of sound. In the absence of periodic boundary conditions, the phonon spectrum possesses a discrete and finite set of complex frequency modes that induce a laser effect. This effect constitutes a dynamical instability and is due to the fact that the supersonic region acts as a resonant cavity. We numerically compute the complex frequencies and density–density correlation function. We obtain patterns with very specific signatures. In terms of the gravitational analogy, the flows we consider correspond to a pair of black hole and white hole horizons, and the laser effect can be conceived as self-amplified Hawking radiation. This is verified by comparing the outgoing flux at early time with the standard black hole radiation.
We study dynamical processes in coherently coupled atomic Bose-Einstein condensates. Josephson effects in ring-shaped and dumbbell geometries are theoretically investigated. Conditions for observation of the Josephson effect are revealed. We found that multicharged persistent current in toroidal condensate can be robust even for supersonic atomic flow. In numerical simulations the acoustic analogues of event horizon in quantized superflow were observed. These theoretical finding open perspectives for investigation of Bose Josephson junctions and quantum aspects of acoustic analogue of Hawking radiation in existing experimental setups.