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arXiv:2408.17292 · Comptes Rendus Physique

Analog Hawking radiation from a spin-sonic horizon in a two-component Bose–Einstein condensate

Anna Berti, Lennart Fernandes, Salvatore Butera, Alessio Recati, Michiel Wouters, Iacopo Carusotto

Published Jan 20, 2025• 4 citations
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Abstract

We theoretically study stimulated and spontaneous Hawking emission from an analog horizon for spin modes in a two-component Bose–Einstein condensate, both with and without a coherent coupling between the two components. We highlight the conceptual and practical advantages that these systems offer to the experimental observation of the phenomenon, namely the possibility of working with massive elementary excitations and the experimental accessibility of the different quadratures of the spin excitations. In particular, we go beyond the relativistic regimes previously addressed in the literature, and identify various observables that show a signature of the Hawking process, as well as additional features associated with the massive nature of the modes, such as undulations . Semi-analytical calculations of the scattering properties of the horizon and of two-point correlation functions of the emitted radiation in an ideal stationary setup are supported by time-dependent numerical simulations based on Gross–Pitaevskii and Bogoliubov theory.

DOI
10.5802/crphys.226

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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 properties of a 2+12+12+1-dimensional sonic black hole (SBH) that can be realized in a quasi-two-dimensional two-component spin-orbit-coupled Bose-Einstein condensate (BEC). The corresponding equation for phase fluctuations in the total density mode that describes phonon field in the hydrodynamic approximation is described by a scalar field equation in 2+12+12+1 dimension whose space-time metric is significantly different from that of the SBH realized from a single component BEC that was studied experimentally and, theoretically, meticulously in literature. Given the breakdown of the irrotationality constraint of the velocity field in such spin-orbit-coupled BEC, we study in detail how the time evolution of such a condensate impacts the various properties of the resulting SBH. By time evolving the condensate in a suitably created laser-induced potential, we show that such a sonic black hole is formed in an annular region bounded by an inner and outer event horizon as well as elliptical ergosurfaces. We observe amplifying density modulation due to the formation of such sonic horizons and show how they change the nature of analog Hawking radiation emitted from such a sonic black hole by evaluating the density-density correlation at different times, using the truncated Wigner approximation (TWA) for different values of spin-orbit coupling parameters. We finally investigate the thermal nature of such analog Hawking radiation.
We model a sonic black-hole analog in a quasi-one-dimensional Bose-Einstein condensate, using a Gross-Pitaevskii equation matching the configuration of a recent experiment by Steinhauer [Nat. Phys. 10, 864 (2014)]. The model agrees well with important features of the experimental observations, demonstrating their hydrodynamic nature. We find that a zero-frequency bow wave is generated at the inner (white-hole) horizon, which grows in proportion to the square of the background condensate density. The relative motion of the black- and white-hole horizons produces a Doppler shift of the bow wave at the black hole, where it stimulates the emission of monochromatic Hawking radiation. The mechanism is confirmed using temporal and spatial windowed Fourier spectra of the condensate. Mean field behavior similar to that in the experiment can thus be fully explained without the presence of self-amplifying Hawking radiation.
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 properties of a 2+12+12+1 dimensional Sonic black hole (SBH) that can be realised, in a quasi-two-dimensional two-component spin-orbit coupled Bose-Einstein condensate (BEC). The corresponding equation for phase fluctuations in the total density mode that describes phonon field in the hydrodynamic approximation is described by a scalar field equation in 2+12+12+1 dimension whose space-time metric is significantly different from that of the SBH realised from a single component BEC that was studied experimentally, and, theoretically meticulously in literature. Given the breakdown of the irrotationality constraint of the velocity field in such spin-orbit coupled BEC, we study in detail how the time evolution of such condensate impacts the various properties of the resulting SBH. By time evolving the condensate in a suitably created laser-induced potential, we show that such a sonic black hole is formed, in an annular region bounded by inner and outer event horizon as well as elliptical ergo-surfaces. We observe amplifying density modulation due to the formation of such sonic horizons and show how they change the nature of analogue Hawking radiation emitted from such sonic black hole by evaluating the density-density correlation at different times, using the truncated Wigner approximation (TWA) for different values of spin-orbit coupling parameters. We finally investigate the thermal nature of such analogue Hawking radiation.
We consider a simple realization of an event horizon in the flow of a one-dimensional two-component Bose-Einstein condensate. Such a condensate has two types of quasiparticles; In the system we study, one corresponds to density fluctuations and the other to polarization fluctuations. We treat the case where a horizon occurs only for one type of quasiparticles (the polarization ones). We study the one- and two-body signal associated to the analog of spontaneous Hawking radiation and demonstrate by explicit computation that it consists only in the emission of polarization waves. We discuss the experimental consequences of the present results in the domain of atomic Bose-Einstein condensates and also for the physics of exciton-polaritons in semiconductor microcavities.