Bose-Einstein condensate as a nonlinear Ramsey interferometer operating beyond the Heisenberg limit

We show that a dynamically evolving two-mode Bose-Einstein condensate (TBEC) with an adiabatic, time-varying Raman coupling maps exactly onto a Ramsey interferometer that includes a nonlinear medium. Assuming a realistic quantum state for the TBEC that has been achieved experimentally, we find that the measurement uncertainty of the "path-difference" phase shift scales as the standard quantum limit (1/N), where N is the number of atoms, while that for the interatomic scattering strength scales as 1/ N7/5, overcoming the conventional Heisenberg limit of 1/N.