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arXiv:1211.1761 · Physical Review A

Violation of Cauchy-Schwarz inequalities by spontaneous Hawking radiation in resonant boson structures

Juan Ramón Muñoz de Nova, Fernando Sols, Ivar Zapata

Published Apr 7, 2014• 41 citations
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Abstract

The violation of a classical Cauchy-Schwarz (CS) inequality is identified as an unequivocal signature of spontaneous Hawking radiation in sonic black holes. This violation can be particularly large near the peaks in the radiation spectrum emitted from a resonant boson structure forming a sonic horizon. As a function of the frequency-dependent Hawking radiation intensity, we analyze the degree of CS violation and the maximum violation temperature for a double barrier structure separating two regions of subsonic and supersonic condensate flow. We also consider the case where the resonant sonic horizon is produced by a space-dependent contact interaction. In some cases, CS violation can be observed by direct atom counting in a time-of-flight experiment. We show that near the conventional zero-frequency peak, the decisive CS violation cannot occur.

DOI
10.1103/physreva.89.043808

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The violation of a classical Cauchy-Schwarz (CS) inequality is identified as an unequivocal signature of spontaneous Hawking radiation in sonic black holes. This violation can be particularly large near the peaks in the radiation spectrum emitted from a resonant boson structure forming a sonic horizon. As a function of the frequency-dependent Hawking radiation intensity, we analyze the degree of CS violation and the maximum violation temperature for a double barrier structure separating two regions of subsonic and supersonic condensate flow. We also consider the case where the resonant sonic horizon is produced by a space-dependent contact interaction. In some cases, CS violation can be observed by direct atom counting in a time-of-flight experiment. We show that near the conventional zero-frequency peak, the decisive CS violation cannot occur.
The violation of a classical Cauchy-Schwarz (CS) inequality is identified as an unequivocal signature of spontaneous Hawking radiation in sonic black holes. This violation can be particularly large near the peaks in the radiation spectrum emitted from a resonant boson structure forming a sonic horizon. As a function of the frequency-dependent Hawking radiation intensity, we analyze the degree of CS violation and the maximum violation temperature for a double barrier structure separating two regions of subsonic and supersonic condensate flow. We also consider the case where the resonant sonic horizon is produced by a space-dependent contact interaction. In some cases, CS violation can be observed by direct atom counting in a time-of-flight experiment. We show that near the conventional zero-frequency peak, the decisive CS violation cannot occur.
We study double-barrier interfaces separating regions of asymptotically subsonic and supersonic flow of Bose-condensed atoms. These setups contain at least one black hole sonic horizon from which the analogue of Hawking radiation should be generated and emitted against the flow in the subsonic region. Multiple coherent scattering by the double-barrier structure strongly modulates the transmission probability of phonons, rendering it very sensitive to their frequency. As a result, resonant tunneling occurs with high probability within a few narrow frequency intervals. This gives rise to highly non-thermal spectra with sharp peaks. We find that these peaks are mostly associated with decaying resonances and only occasionally with dynamical instabilities. Even at achievable non-zero temperatures, the radiation peaks can be dominated by spontaneous emission, i.e. enhanced zero-point fluctuations, and not, as is often the case in analogue models, by stimulated emission.
We consider a sonic black-hole scenario where an atom condensate flows through a subsonic-supersonic interface. We discuss several criteria that reveal the existence of nonclassical correlations resulting from the quantum character of the spontaneous Hawking radiation. We unify previous general work as applied to Hawking radiation analogs. We investigate the measurability of the various indicators and conclude that, within a class of detection schemes, only the violation of quadratic Cauchy-Schwarz inequalities can be discerned. We show numerical results that further support the viability of measuring deep quantum correlations in concrete scenarios.
I present a microscopic description of Hawking radiation in sonic black holes. A one-dimensional Fermi-degenerate liquid squeezed by a smooth barrier forms a transonic flow, a sonic analog of a black hole. The quantum treatment of the noninteracting case establishes a close relationship between sonic Hawking radiation and quantum tunneling through the barrier. Quasiparticle excitations appear at the barrier and are then radiated with a thermal distribution in exact agreement with Hawking's formula. The signature of the radiation can be found in the dynamic structure factor, which can be measured in a scattering experiment. The possibility for experimental verification of this new transport phenomenon for ultracold atoms is discussed.
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 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.