Quasi-steady radiation of sound from turbulent sonic ergoregions

Abstract

Sonic Hawking radiation has recently been observed in dilute Bose-Einstein condensates (BECs), but it remains an open question whether this landmark achievement of atomic physics can lead to new insights into the effects on Hawking radiation of nonlinear back-reaction and new short-distance physics, as was originally hoped by Unruh when he introduced the sonic analogy. Furthermore, studies of sonic analog black holes have until now concentrated on (1+1)-dimensional scenarios, but Unruh's sonic analogy for curved spacetime is only valid in more than one spatial dimension. We therefore model the evolution of a (2+1)-dimensional sonic black hole in a dilute BEC, over a long enough time to let the initial Corley-Jacobson instabilities saturate in vortex production and give way to a long-lived quasi-stationary state. In this quasi-equilibrium state we find the initial laminar ergoregion replaced by a turbulent zone that steadily radiates sound, but with a non-thermal power spectrum.Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.1 By this term we mean all effects resulting from the full nonlinear theory that act back on the black hole and that are neglected in Hawking's derivation. In the context of analog gravity in BEC mean-field theory the full theory is the nonlinear Gross-Pitaevskii theory; neglecting the nonlinear back-reaction corresponds to the linear Bogoliubov approximation. 2 From [3] above: 'This system forms an excellent theoretical laboratory where many of the unknown effects that quantum gravity could exert on black hole evaporation can be modeled. ... At distances of 10 −8 cm, the assumptions ... of a smooth background flow are no longer valid just as in gravity one expects the concept of a smooth space-time on which the various relativistic fields propagate to break down at scales of 10 −33 cm. Furthermore, the phonons emitted are quantum fluctuations of the fluid flow and thus affect their own propagation in exactly the same way that graviton emission affects the space-time on which the various relativistic fields propagate.' In the last sentence Unruh cannot really have meant that quantum gravity must be exactly like hydrodynamics, but rather just that nonlinear back-reaction of some kind will surely occur in both quantum gravity and hydrodynamics-and that this is a reason for pursuing analog experiments.

Turbulent Steady States in Two-Dimensional Sonic Black Holes: Superfluid Vortices and Emission of Sound

“…We emphasize that these are not pathological features of white holes, but are generic for finite ergoregions; they are also present when atom sinks allow purely black holes of finite size [12]. In sonic black holes of D > 1 spatial dimensions, moreover, the number of dynamically unstable modes tends to be large [13].…”

“…In contrast to previous work on one-dimensional black hole analogs, our system is in (2+1) dimensions. The extra dimension is significant because (1+1)-dimensional black holes lack Bekenstein-Hawking entropy (which is proportional to the horizon measure), and because Unruh's exact mapping between hydrodynamic sound propagation and massless field evolution in curved spacetime is only globally valid in (D + 1) dimensions with D > 1 [13].…”

“…The thus linearized GPE couples δΨ and δΨ * in a system known as the Bogoliubov-de Gennes equations (BdG). The long wavelength limit of the BdG describes sound waves in a hydrodynamic background and can thus be mapped onto the field equation of a massless field in curved spacetime [2,13]. At short wavelengths, however, BdG allows propagation faster than the speed of long-wavelength sound.…”

“…These perturbations are random with a probability distribution given by the ground state Wigner function of the BdG excitations in a Ψ 0 = √ ρ 0 exp(iθ 0 ) = α exp(ivx) background with completely uniform g and V equal to the values outside the ergoregion. (See [13] for a discussion why it is advantageous to switch to the hydrodynamic variables ρ and θ.) This represents an experiment in which a uniform condensate is prepared at zero temperature, and then g and V within 0 < x < L are suddenly altered to create the ergoregion.…”

Acoustic analog of Hawking radiation in quantized circular superflows of Bose-Einstein condensates

“…In this work we address quasi-1D atomic BEC confined in a toroidal trap. This setting, which is available in experiments [25][26][27][28][29], was used for studies of diverse matter-wave patterns maintained by circular flows, i.e., effects induced by the angular momentum [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44].…”