We consider the collision of two Bose Einstein condensates at supersonic velocities and focus on the halo of scattered atoms. This halo is the most important feature for experiments and is also an excellent testing ground for various theoretical appr
oaches. In particular we find that the typical reduced Bogoliubov description, commonly used, is often not accurate in the region of parameters where experiments are performed. Surprisingly, besides the halo pair creation terms, one should take into account the evolving mean field of the remaining condensate and on-condensate pair creation. We present examples where the difference is clearly seen, and where the reduced description still holds.
We apply an analytical model for anisotropic, colliding Bose-Einstein condensates in a spontaneous four wave mixing geometry to evaluate the second order correlation function of the field of scattered atoms. Our approach uses quantized scattering mod
es and the equivalent of a classical, undepleted pump approximation. Results to lowest order in perturbation theory are compared with a recent experiment and with other theoretical approaches.
