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Physical Review Letters

Detection Scheme for Acoustic Quantum Radiation in Bose-Einstein Condensates

Ralf Schützhold

Published Nov 10, 2006• 46 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.97.190405

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•Jan 1, 2006•0 citations
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.
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.
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 acoustic white holes in a steadily flowing atomic Bose–Einstein condensate. A white hole configuration is obtained when the flow velocity goes from a super-sonic value in the upstream region to a sub-sonic one in the downstream region. The scattering of phonon wavepackets on a white hole horizon is numerically studied in terms of the Gross–Pitaevskii equation of mean-field theory: dynamical stability of the acoustic white hole is found, as well as a signature of a nonlinear back-action of the incident phonon wavepacket onto the horizon. The correlation pattern of density fluctuations is numerically studied by means of the truncated-Wigner method, which includes quantum fluctuations. Signatures of the white hole radiation of correlated phonon pairs by the horizon are characterized; analogies and differences with Hawking radiation from acoustic black holes are discussed. In particular, a short wavelength feature is identified in the density correlation function, whose amplitude steadily grows in time since the formation of the horizon. The numerical observations are quantitatively interpreted by means of an analytical Bogoliubov theory of quantum fluctuations for a white hole configuration within the step-like horizon approximation.
The analogy between the propagation of a massless scalar field in curved spacetime and the propagation of sound waves in a Bose-Einstein Condensate (BEC) gives rise to the possibility of observing the analogues of black hole radiance effects, such as Hawking Radiation and superradiance, in the laboratory. In order to provide a solid foundation for realising such analogue gravity models in an experimental setting, we have conducted a numerical investigation of phonon scattering from a BEC vortex by solving the time-dependent Gross-Pitaevskii (GP) equation, describing the dynamics of dilute gas BECs. The consideration of phonon superradiance in BECs in advance of Hawking Radiation is motivated by the fact superradiance may be easier to detect. ¶ We first present the results of one-dimensional simulations of sound waves propagating in a BEC and reflecting from a vortex-like density profile. Using these results as a guide, two-dimensional simulations of sound propagation in a BEC, and reflection from a BEC vortex, are performed. The technique of propagating the wavefunction in imaginary time was employed to find the vortex ground state. The accuracy of the simulations and the convergence of the solution to the vortex ground state was verified using a range of numerical diagnostics. Finally, preliminary simulations were performed within the superradiant frequency regime for the purposes of determining whether the amplification of incoming waves occurs given an appropriate choice of parameters. Overall, the two-dimensional modelling of reflection of cylindrical waves from a BEC vortex provides a basis for a systematic study of phonon superradiance in BECs.