Atomic Interactions in Precision Interferometry Using Bose-Einstein Condensates

TL;DR

This paper develops theoretical methods to predict and mitigate atomic interaction effects in Bose-Einstein condensate interferometry, enabling high-precision measurements such as the fine structure constant.

Contribution

It introduces a scaling solution for the Gross-Pitaevskii equation and a generalized envelope reduction to improve modeling of BEC interferometry.

Findings

Agreement with experimental results for measuring the fine structure constant

Atomic interactions do not prevent achieving part-per-billion measurement accuracy

Tools enable broader application of BEC interferometry in precision measurements

Abstract

We present theoretical tools for predicting and reducing the effects of atomic interactions in Bose-Einstein condensate (BEC) interferometry experiments. To address mean-field shifts during free propagation, we derive a robust scaling solution that reduces the three-dimensional Gross-Pitaevskii equation to a set of three simple differential equations valid for any interaction strength. To model the other common components of a BEC interferometer---condensate splitting, manipulation, and recombination---we generalize the slowly-varying envelope reduction, providing both analytic handles and dramatically improved simulations. Applying these tools to a BEC interferometer to measure the fine structure constant (Gupta, et al., 2002), we find agreement with the results of the original experiment and demonstrate that atomic interactions do not preclude measurement to better than part-per-billion accuracy, even for atomic species with relatively large scattering lengths. These tools help make BEC interferometry a viable choice for a broad class of precision measurements.