Information recycling beam-splitters for atom-interferometry with enhanced sensitivity

We propose a scheme to significantly enhance the sensitivity of atom-interferometry performed with Bose-Einstein condensates. When a two-photon Raman transition is used to split the condensate into two modes, some information about the number of atoms in one of the modes is transferred to one of the optical modes. We introduce a simple model to describe this process, and find that by processing this information in an appropriate way, the sensitivity of atom interferometry can be enhanced by more than a factor of 10 for realistic parameters.