Adiabatic Mach-Zehnder interferometry on a quantized Bose-Josephson junction

We propose a scheme to achieve Mach-Zehnder interferometry using a quantized Bose-Josephson junction with a negative charging energy. The quantum adiabatic evolution through a dynamical bifurcation is used to accomplish the beam splitting and recombination. The negative charging energy ensures the existence of a path-entangled state which enhances the phase measurement precision to the Heisenberg limit. A feasible detection procedure is also presented. The scheme should be realizable with current technology.