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arXiv:physics/0104053 · Physical Review A

Improved characterization of elastic scattering near a Feshbach resonance in 85Rb

Jacob Roberts, James P. Burke, N. R. Claussen, Simon L. Cornish, Elizabeth A. Donley, Carl Wieman

Published Jul 5, 2001• 47 citations
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Abstract

We report extensions and corrections to the measurement of the Feshbach resonance in ${}^{85}\mathrm{Rb}$ cold atom collisions reported earlier [J. L. Roberts et al., Phys. Rev. Lett. 81, 5109 (1998)]. In addition to a better determination of the position of the resonance peak [154.9(4) G] and its width [11.0(4) G], improvements in our techniques now allow the measurement of the absolute size of the elastic-scattering rate. This provides a measure of the s-wave scattering length as a function of magnetic field near the Feshbach resonance and constrains the Rb-Rb interaction potential.

DOI
10.1103/physreva.64.024702

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We report extensions and corrections to the measurement of the Feshbach resonance in 85Rb{}^{85}\mathrm{Rb}85Rb cold atom collisions reported earlier [J. L. Roberts et al., Phys. Rev. Lett. 81, 5109 (1998)]. In addition to a better determination of the position of the resonance peak [154.9(4) G] and its width [11.0(4) G], improvements in our techniques now allow the measurement of the absolute size of the elastic-scattering rate. This provides a measure of the s-wave scattering length as a function of magnetic field near the Feshbach resonance and constrains the Rb-Rb interaction potential.
The s-wave scattering length for elastic collisions between 87Rb{}^{87}\mathrm{Rb}87Rb atoms in the state ∣f,mf〉=∣1,1〉|{f,m}_{f}〉=|1,1〉∣f,mf​〉=∣1,1〉 is measured in the vicinity of a Feshbach resonance near 1007 G. Experimentally, the scattering length is determined from the mean-field-driven expansion of a Bose-Einstein condensate in a homogeneous magnetic field. The scattering length is measured as a function of the magnetic field and agrees with the theoretical expectation. The width of the resonance is determined to be 0.20(3) G, the position of the zero crossing of the scattering length is found at 1007.60(3) G.
A magnetic field dependent Feshbach resonance has been observed in the elastic scattering collision rate between atoms in the F = 2, M = -2 state of 85 Rb. Changing the magnetic field by several Gauss caused the collision rate to vary by a factor of 10,000, and the sign of the scattering length could be reserved. The resonance peak is at 155.2(4) G and its width is 11.6(5) G. From these results we extract much improved values for the three quantities that characterize the interaction porential: the van der Waals coefficient C6, the singlet scattering length, and the triplet scattering length.
A magnetic field-dependent Feshbach resonance has been observed in the elastic scattering collision rate between atoms in the $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2,M\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}2$ state of 85Rb{}^{85}\mathrm{Rb}85Rb. Changing the magnetic field by several Gauss caused the collision rate to vary by a factor of 104{0}^{4}04, and the sign of the scattering length could be reversed. The resonance peak is at 155.2(4) G and its width is 11.6(5) G. From these results we extract much improved values for the three quantities that characterize the interaction potential: The van der Waals coefficient C6{C}_{6}C6​, the singlet scattering length aS{a}_{S}aS​, and the triplet scattering length aT{a}_{T}aT​.
We have measured the elastic-scattering cross section of 87Rb^{87}\mathrm{Rb}87Rb atoms in the \ensuremath{\Vert}F=1,mF{\mathit{m}}_{\mathit{F}}mF​=-1〉 ground state at 25 \ensuremath{\mu}K. The cross section is almost purely s wave at these temperatures and has a value of (5.4\ifmmode\pm\else\textpm\fi{}1.3)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ cm2{\mathrm{cm}}^{2}cm2. We have searched for the predicted Feshbach-type resonances in the elastic cross section [Tiesinga et al., Phys. Rev. A 46, 1167 (1992)] as a function of magnetic field. There are no resonances with a magnetic-field width \ensuremath{\ge}2 G over a magnetic-field range of 15--540 G.
Due to atomic interactions, a dilute gas Bose-Einstein condensate acquires a self- energy proportional to the two-body scattering length a. This self-energy strongly influences the stability, formation rate, size and shape, collective excitations, and other properties of a condensate. For a given atomic species at zero magnetic field, the scattering length is fixed, and this had led to a rather limited range of interaction strengths in experiments. However, it has been predicted that a magnetically tunable Feshbach resonance could be used to strongly modify scattering lengths [1]. We have observed such a Feshbach resonance in collisions of ultracold 85Rb(f =2, mf=−2) atoms in a magnetic field B. From our measured resonance position and width, we infer that the scattering length a2,−2 for collisions of these atoms has the dispersive resonance form.
More than 40 Feshbach resonances in rubidium 87 are observed in the magnetic-field range between 0.5 and 1260 G for various spin mixtures in the lower hyperfine ground state. The Feshbach resonances are observed by monitoring the atom loss, and their positions are determined with an accuracy of 30 mG. In a detailed analysis, the resonances are identified and an improved set of model parameters for the rubidium interatomic potential is deduced. The elastic width of the broadest resonance at 1007 G is predicted to be significantly larger than the magnetic-field resolution of the apparatus. This demonstrates the potential for applications based on tuning the scattering length.