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Quantum depletion signature of emerging sonic horizons in a quasi-one-dimensional Bose-Einstein condensate

Caio C. Holanda Ribeiro, Sang-Shin Baak, Uwe R. Fischer

Published Mar 8, 2021• 0 citations
OpenAlex

Abstract

We consider the quasi-one-dimensional (quasi-1D) model of a sonic black hole in a dilute Bose-Einstein condensate. It is shown that an accurate treatment of the dimensional reduction to quasi-1D leads to a finite condensate quantum depletion even for axially infinite systems, and an intrinsic nonthermality of the black hole radiation spectrum. By calculating the depletion, we derive a {\em first-order} many-body signature of the sonic horizon, represented by a distinct peak in the depletion power spectrum. This peak constitutes a readily experimentally accessible tool to detect quantum sonic horizons even when a negligible Hawking radiation flux is created by the black hole.

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We consider the quasi-one-dimensional (quasi-1D) model of a sonic black hole in a dilute Bose-Einstein condensate. It is shown that an accurate treatment of the dimensional reduction to quasi-1D leads to a finite condensate quantum depletion even for axially infinite systems, and an intrinsic nonthermality of the black hole radiation spectrum. By calculating the depletion, we derive a {\em first-order} many-body signature of the sonic horizon, represented by a distinct peak in the depletion power spectrum. This peak constitutes a readily experimentally accessible tool to detect quantum sonic horizons even when a negligible Hawking radiation flux is created by the black hole.
We theoretically propose a finite-size quasi-one-dimensional Bose-Einstein condensate with coherent source and drain placed at its two ends, which can in principle sustain a stationary sonic black hole with a single event horizon. Our analysis is focused on the condensate persistence against quantum fluctuations. We show that similar to black hole-white hole pairs, dynamical instabilities occur. Investigating in detail the instabilities' dependence on the system parameters, we also identify windows of formally infinite black hole lifetimes. By using quantum depletion of the condensate as a diagnostic tool, we validate the usage of Bogoliubov theory to describe the analog Hawking process, and establish novel signatures of Hawking radiation in the depleted cloud, both inside and outside the event horizon.
We consider a sonic analog of a black hole realized in the one-dimensional flow of a Bose-Einstein condensate. Our theoretical analysis demonstrates that one- and two-body momentum distributions accessible by present-day experimental techniques provide clear direct evidence (i) of the occurrence of a sonic horizon, (ii) of the associated acoustic Hawking radiation, and (iii) of the quantum nature of the Hawking process. The signature of the quantum behavior persists even at temperatures larger than the chemical potential.
We study the dynamics of sonic black hole horizon formation of quasi-one-dimensional (1D) Bose-Einstein condensate incorporating higher-order quintic nonlinear interaction. Based on the one dimensional Gross-Pitaevskii equation with nonlinearity up to the quintic order, we derived a novel analytical formula for the key dynamical variables of sonic horizon formation using the modified variational method and exact F-expansion method. We obtained good agreement between the key dynamical variables from the two different methods. The stabilization effects of higher-order nonlinear interaction along with the more precise location of the sonic horizon boundary were illustrated. The theoretical results obtained in this work can be used to guide relevant experimental observations of sonic black hole-related dynamics incorporating the effects of higher-order nonlinear interaction.
We report numerical evidence of Hawking emission of Bogoliubov phonons from a sonic horizon in a flowing one-dimensional atomic Bose–Einstein condensate. The presence of Hawking radiation is revealed from peculiar long-range patterns in the density–density correlation function of the gas. Quantitative agreement between our fully microscopic calculations and the prediction of analog models is obtained in the hydrodynamic limit. New features are predicted and the robustness of the Hawking signal against a finite temperature discussed.
We study the two-body momentum correlation signal in a quasi one dimensional Bose-Einstein condensate in the presence of a sonic horizon. We identify the relevant correlation lines in momentum space and compute the intensity of the corresponding signal. We consider a set of different experimental procedures and identify the specific issues of each measuring process. We show that some inter-channel correlations, in particular the Hawking quantum-partner one, are particularly well adapted for witnessing quantum non-separability, being resilient to the effects of temperature and/or quantum quenches.