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.
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