Atom-atom correlations in colliding Bose-Einstein condensates

TL;DR

This paper develops an analytic approach to study atom-atom correlations in colliding Bose-Einstein condensates, providing insights into experimental observations and predicting how correlations evolve over time.

Contribution

It introduces a simple perturbative method to analytically compute atom-atom correlations in colliding condensates, aligning with simulations and experiments.

Findings

Analytic expressions for collinear and back-to-back correlations.

Agreement with positive-P simulation results in short time limit.

Prediction that back-to-back correlation broadens over long collision durations.

Abstract

We analyze atom-atom correlations in the s-wave scattering halo of two colliding condensates. By developing a simple perturbative approach, we obtain explicit analytic results for the collinear (CL) and back-to-back (BB) correlations corresponding to realistic density profiles of the colliding condensates with interactions. The results in the short time limit are in agreement with the first-principles simulations using the positive-$P$ representation and provide analytic insights into the experimental observations of Perrin et al. [Phys. Rev. Lett. 99, 150405 (2007)]. For long collision durations, we predict that the BB correlation becomes broader than the CL correlation.