Interferometric determination of the s- and d-wave scattering amplitudes in $^{87}$Rb

TL;DR

This paper introduces an interference-based method to accurately measure low-energy s- and d-wave scattering amplitudes in ultracold $^{87}$Rb gases, enabling precise characterization of atomic interactions without requiring density measurements.

Contribution

The authors develop a novel interference technique to determine scattering phase shifts and amplitudes directly from collision patterns, improving accuracy and simplifying experimental requirements.

Findings

Successfully measured s- and d-wave phase shifts up to 1.2 mK.

Achieved 6% accuracy in scattering length for $^{87}$Rb.

Reproduced scattering amplitudes using only Van der Waals coefficient.

Abstract

We demonstrate an interference method to determine the low-energy elastic scattering amplitudes of a quantum gas. We linearly accelerate two ultracold atomic clouds up to energies of 1.2 mK and observe the collision halo by direct imaging in free space. From the interference between $s$- and $d$- partial waves in the differential scattering pattern we extract the corresponding phase shifts. The method does not require knowledge of the atomic density. This allows us to infer accurate values for the $s$- and d-wave scattering amplitudes from the zero-energy limit up to the first Ramsauer minimum using only the Van der Waals $C_{6}$ coefficient as theoretical input. For the $^{87}$Rb triplet potential, the method reproduces the scattering length with an accuracy of 6%.