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arXiv:0805.1358 · Physical Review A

Phonon background versus analog Hawking radiation in Bose-Einstein condensates

Sebastian Wüster

Published Aug 12, 2008• 19 citations
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Abstract

We determine the feasibility of detecting analog Hawking radiation in a Bose-Einstein condensate in the presence of atom-loss-induced heating. We find that phonons created by three-body losses overshadow those due to analog Hawking radiation. To overcome this problem, three-body losses may have to be suppressed, for example, as proposed by Search et al. [Phys. Rev. Lett. 92, 140401 (2004)]. The reduction of losses to a few percent of their normal rate is typically sufficient to suppress the creation of loss phonons on the time scale of fast analog Hawking phonon detection.

DOI
10.1103/physreva.78.021601

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We determine the feasibility of detecting analog Hawking radiation in a Bose-Einstein condensate in the presence of atom-loss-induced heating. We find that phonons created by three-body losses overshadow those due to analog Hawking radiation. To overcome this problem, three-body losses may have to be suppressed, for example, as proposed by Search et al. [Phys. Rev. Lett. 92, 140401 (2004)]. The reduction of losses to a few percent of their normal rate is typically sufficient to suppress the creation of loss phonons on the time scale of fast analog Hawking phonon detection.
The sonic analog of Hawking radiation can now be experimentally recreated in Bose-Einstein condensates that contain an acoustic black hole. In these experiments the signal strength and approximate analog Hawking temperature increase for denser condensates, which however also suffer increased atom losses from inelastic collisions. To determine how these affect analog Hawking radiation, we numerically simulate creation of the latter in a Bose-Einstein condensate in the presence of atomic losses, including nonunitary quantum field dynamics using the truncated Wigner approximation. In particular we explore modifications of density-density correlations through which the radiation has been analyzed so far. We find no evidence that losses directly alter the basic picture of the analog Hawking effect; instead all consequences that we find are indirect: Losses increase the contrast of the correlation signal, which we attribute to condensate heating by the losses, in turn leading to a component of stimulated radiation in addition to the spontaneous one. Other indirect consequences are the modification of the white-hole instability pattern and a change of slope of the Hawking tongue.
Observing quantum particle creation by black holes (Hawking radiation) in the astrophysical context is, in ordinary situations, hopeless. Nevertheless the Hawking effect, which depends only on kinematical properties of wave propagation in the presence of horizons, is present also in nongravitational contexts, for instance in stationary fluids undergoing supersonic flow. We present results on how to observe the analog Hawking radiation in Bose-Einstein condensates by a direct measurement of the density correlations due to the phonon pairs (Hawking quanta-partner) created by the acoustic horizon.
Quasi-one-dimensional outflow from a dilute gas Bose-Einstein condensate reservoir is a promising system for the creation of analog Hawking radiation. We use numerical modeling to show that stable sonic horizons exist in such a system under realistic conditions, taking into account the transverse dimensions and three-body loss. We find that loss limits the analog Hawking temperatures achievable in the hydrodynamic regime, with sodium condensates allowing the highest temperatures. A condensate of 3000030\phantom{\rule{0.2em}{0ex}}00030000 atoms, with transverse confinement frequency ${\ensuremath{\omega}}_{\ensuremath{\perp}}=6800\ifmmode\times\else\texttimes\fi{}2\ensuremath{\pi}\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$, yields horizon temperatures of about 20nK20\phantom{\rule{0.3em}{0ex}}\mathrm{nK}20nK over a period of 50ms50\phantom{\rule{0.3em}{0ex}}\mathrm{ms}50ms. This is at least four times higher than for other atoms commonly used for Bose-Einstein condensates.
Based on doubly detuned Raman transitions between (meta)stable atomic or molecular states and recently developed atom counting techniques, a detection scheme for sound waves in dilute Bose-Einstein condensates is proposed whose accuracy might reach down to the level of a few or even single phonons. This scheme could open up a new range of applications including the experimental observation of quantum radiation phenomena such as the Hawking effect in sonic black-hole analogues or the acoustic analogue of cosmological particle creation.
Based on doubly detuned Raman transitions between (meta) stable atomic or molecular states and recently developed atom counting techniques, a detection scheme for sound waves in dilute Bose-Einstein condensates is proposed whose accuracy might reach down to the level of a few or even single phonons. This scheme could open up a new range of applications including the experimental observation of quantum radiation phenomena such as the Hawking effect in sonic black-hole analogues or the acoustic analogue of cosmological particle creation. PACS: 03.75.Kk, 04.70.Dy, 42.65.Dr.
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.