Atom-atom correlations in colliding Bose-Einstein condensates

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 [Phys. Rev. Lett. 99, 150405 (2007)]. For long collision durations, we predict that the BB correlation becomes broader than the CL correlation.