Frankfurt 2006 – scientific programme

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Q: Quantenoptik und Photonik

Q 8: Quantengase II

Q 8.2: Talk

Monday, March 13, 2006, 14:15–14:30, HVI

How correlation functions illuminate the frontiers of an extended mean-field theory in a quasi-1D Bose gas — •M. Eckart, R. Walser, and W. P. Schleich — Abteilung Quantenphysik, Universität Ulm, D-89069 Ulm, Germany

Quasi-1D systems have gained a lot of interest, because they have recently been experimentally realized in the context of ultracold gases and have always been a valuable playground for theorists due to the fact, that exact solutions exist for a reduced dimensionality. One of the most interesting questions is how to describe the cross-over from the Gross-Pitaevskii regime of weakly correlated bosons (γ ≪ 1) to the Tonks-Girardeau regime of strongly correlated bosons (γ ≫ 1). The most sensitive experimentally available observable that can be used to study this cross-over is the third-order correlation function which is proportional to the directly measurable three-body recombination rate.

Although the quasi-1D case is the harshest environment for a mean-field theory, we show how an extension, which also includes density fluctuations and pairing fields, can be used to describe the cross-over up to values of γ ≈ 1. As any mean-field theory is known to fail in the strongly correlated regime, we give a detailed analysis of how far an extended mean-field theory can be pushed. The benefit of our approach lies in the fact that correlation functions emerge naturally and that we obtain results for the homogeneous as well as the experimentally relevant trapped case. In the region where an extended mean-field theory is applicable we also present the first calculations of the full behavior (diagonal and off-diagonal) of correlation functions up to third order.