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arXiv:1810.04860 · Physical Review A

(2+1) -dimensional sonic black hole from a spin-orbit-coupled Bose-Einstein condensate and its analog Hawking radiation

Inderpreet Kaur, Sankalpa Ghosh

Published Aug 17, 2020• 8 citations
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Abstract

We study the properties of a $2+1$-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 $2+1$ 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.

DOI
10.1103/physreva.102.023314

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[Formula : see text]-dimensional sonic black hole from a spin-orbit-coupled Bose-Einstein condensate and its analog Hawking radiation

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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 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.
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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 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.