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arXiv:quant-ph/0602180

On the detectability of quantum radiation in Bose-Einstein condensates

Ralf Schützhold

Published Feb 22, 2006• 8 citations
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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. PACS: 03.75.Kk, 04.70.Dy, 42.65.Dr.

DOI
10.48550/arxiv.quant-ph/0602180

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arXiv:0805.1358•Physical Review A•Aug 12, 2008•19 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. PACS: 03.75.Kk, 04.70.Dy, 42.65.Dr.
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.
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.
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.
There are a number of interesting phenomena that are predicted to be a result of the behaviour of general relativity close to a black hole. The most well known of these is Hawking radiation. Although well established, the theory of Hawking radiation is unsupported by experiment, since black holes cannot be investigated in the lab. However, there is a strong similarity between the equations governing the behaviour of a sound wave in inviscid irrotational fluid systems and a massless scalar field in a gravitational system. This similarity provides hope that effects like Hawking radiation can be investigated in analogous fluid systems. The requirement that potential fluid analogues be barotropic, inviscid and irrotational indicates that superfluids would be the logical object of experiments designed to analyse such systems. The most easily controlled superfluid to which experimentalists have access is a Bose Einstein Condensate in an appropriately designed trap, and there is interest in designing an experiment to look for Hawking radiation in a BEC. A BEC is also ideal for that purpose because of the extremely low temperatures at which the condensation occurs, given the very low temperature of Hawking radiation. However, Hawking radiation itself is a very subtle effect, and it would be very hard to detect. This means that a related but more conspicuous effect is interesting as a stepping stone to a test for the more well known Hawking radiation. This related effect is Superradiance, a result of the reflection of an incoming scalar field with appropriate angular characteristics from the ergoregion of a massive rotating body such as a black hole. An ergoregion is a region around a rotating black hole or supermassive rotating star within which it is impossible to remain stationary with respect to an observer at infinity without exceeding the speed of light. Before an experiment can be designed to test for superradiance in a BEC it is necessary to establish whether the theory describing Bose-Einstein Condensates predicts that it will actually occur. Work on this problem thus far has either failed to consider whether the effect occurs, and instead focused on the consequences it would have, or has involved approximations that are not strictly valid. Here therefore, after an overview of both the analogy between fluid and gravitational systems and the specific theory related to Bose Einstein Condensates is an analysis using the full quantum theory of BECs. The initial consideration is analytic in character, but the equations do not allow for an exact solution within the approximations attempted that predict superradiance, so a change is made to a numerical simulation using the XMDS numerical simulation package. Unfortunately, this attempt also fails, since ongoing problems encountered in running the simulation consumed all the time available. A discussion of these problems is included.
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.