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arXiv:cond-mat/0412393 · Physical Review A

Resonant scattering properties close to a p -wave Feshbach resonance

Frédéric Chevy, E. G. M. van Kempen, Thomas Bourdel, J. Zhang, Lev Khaykovich, Martin Teichmann, Leticia Tarruell, S. J. J. M. F. Kokkelmans, Ch Salomon

Published Jun 22, 2005• 72 citations
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Abstract

We present a semianalytical treatment of both the elastic and inelastic collisional properties near a $p$-wave Feshbach resonance. Our model is based on a simple three-channel system that reproduces more elaborate coupled-channel calculations. We stress the main differences between $s$-wave and $p$-wave scattering. We show in particular that, for elastic and inelastic scattering close to a $p$-wave Feshbach resonance, resonant processes dominate over the low-energy behavior.

DOI
10.1103/physreva.71.062710

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We use the dressed potentials obtained in the adiabatic representation of two coupled channels to calculate sss-wave Feshbach resonances in a three-dimensional spherically symmetric potential with an open channel interacting with a closed channel. Analytic expressions for the sss-wave scattering length aaa and number of resonances are obtained for a piecewise constant model with a piecewise constant interaction of the open and closed channels near the origin. We show analytically and numerically that, for strong enough coupling strength, Feshbach resonances can exist even when the closed channel does not have a bound state.
In the absence of inelastic scattering, Feshbach resonances produce poles in scattering lengths and very large peaks in elastic cross-sections. However, inelastic scattering removes the poles. Whenever the resonant state is coupled comparably to the elastic and inelastic channels, the scattering length exhibits only a small oscillation and peaks in cross-sections are significantly suppressed. A resonant scattering length is defined to characterize the amplitude of the oscillation, and is shown to be small for many collisions of ultracold molecules. The results suggest that cross-sections for some ultracold collision processes will be much less sensitive to details of the potential than has been expected.