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

Figure 1

(Color online) Momentum widths of the BB and CL correlations relative to the width of the source BEC in $x$, $y$, and $z$ directions as a function of time. The solid and dashed curves with marks are the results of the positive-$P$ simulations for ${}^{23}\mathrm{Na}$ BECs as in Ref. 9. The horizontal solid and dashed lines are the corresponding correlation widths from Eqs. (12, 13).