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arXiv:quant-ph/0606147 · Physical Review A

Theory for a Hanbury Brown Twiss experiment with a ballistically expanding cloud of cold atoms

José Viana‐Gomes, A. Perrin, M. Schellekens, Denis Boiron, Christoph Ira Westbrook, Michael Scott Belsley

Published Nov 7, 2006• 51 citations
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Abstract

We have studied one-body and two-body correlation functions in a ballistically expanding, noninteracting atomic cloud in the presence of gravity. We find that the correlation functions are equivalent to those at thermal equilibrium in the trap with an appropriate rescaling of the coordinates. We derive simple expressions for the correlation lengths and give some physical interpretations. Finally a simple model to take into account finite detector resolution is discussed.

DOI
10.1103/physreva.74.053607

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We have studied one-body and two-body correlation functions in a ballistically expanding, noninteracting atomic cloud in the presence of gravity. We find that the correlation functions are equivalent to those at thermal equilibrium in the trap with an appropriate rescaling of the coordinates. We derive simple expressions for the correlation lengths and give some physical interpretations. Finally a simple model to take into account finite detector resolution is discussed.
We consider the ballistic expansion of a cloud of trapped atoms falling under the influence of gravity. Using a simple coordinate transformation, we derive an analytical expression for the time-of-flight signal. The properties of the signal can be used to infer the initial temperature of the cloud. We first assume a point size cloud with an isotropic velocity distribution to explain the physical basis of the calculation. The treatment is then generalized to include a finite-size cloud with an anisotropic velocity distribution, and an exact result for the signal is derived. The properties of the signal are discussed, and an intuitive picture is presented to explain how initial conditions determine the features of the signal.
The pair correlation function of an expanding gas is investigated with an emphasis on the BEC-BCS crossover of a superfluid Fermi gas at zero temperature. At unitarity quantum Monte Carlo simulations reveal the occurrence of a sizable bunching effect due to interactions in the spin up-down channel which, at short distances, is larger than that exhibited by thermal bosons in the Hanbury-Brown-Twiss effect. We propose a local equilibrium ansatz for the pair correlation function which we predict will remain isotropic during the expansion even if the trapping potential is anisotropic, in contrast with the behavior of the density. The isotropy of the pair correlation function is an experimentally accessible signature, which makes a clear distinction with respect to the case of noninteracting gases and can be understood as a consequence of the violation of scaling.