Bogoliubov theory for atom scattering into separate regions

Abstract

We review the Bogoliubov theory in the context of recent experiments, where\natoms are scattered from a Bose-Einstein Condensate into two well-separated\nregions. We find the full dynamics of the pair-production process, calculate\nthe first and second order correlation functions and show that the system is\nideally number-squeezed. We calculate the Fisher information to show how the\nentanglement between the atoms from the two regions changes in time. We also\nprovide a simple expression for the lower bound of the useful entanglement in\nthe system in terms of the average number of scattered atoms and the number of\nmodes they occupy. We then apply our theory to a recent "twin-beam" experiment\n[R. B\\"ucker {\\it et al.}, Nat. Phys. {\\bf 7}, 608 (2011)]. The only numerical\nstep of our semi-analytical description can be easily solved and does not\nrequire implementation of any stochastic methods.\n