Information-Recycling Beam Splitters for Quantum Enhanced Atom Interferometry

We propose a scheme to significantly enhance the sensitivity of atom interferometry performed with Bose-Einstein condensates. When an optical 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 contained in 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 phase sensitivity of atom interferometry can be enhanced by more than a factor of 10 for realistic parameters.