Non-Linear Beam Splitter in Bose-Einstein Condensate Interferometers

A beam splitter is an important component of an atomic/optical Mach-Zehnder interferometer. Here we study a Bose Einstein Condensate beam splitter, realized with a double well potential of tunable height. We analyze how the sensitivity of a Mach Zehnder interferometer is degraded by the non-linear particle-particle interaction during the splitting dynamics. We distinguish three regimes, Rabi, Josephson and Fock, and associate to them a different scaling of the phase sensitivity with the total number of particles.