Mach-Zehnder Interferometry at the Heisenberg Limit with Coherent and Squeezed-Vacuum Light

We show that the phase sensitivity Δθ of a Mach-Zehnder interferometer illuminated by a coherent state in one input port and a squeezed-vacuum state in the other port is (i) independent of the true value of the phase shift and (ii) can reach the Heisenberg limit Δθ~1/NT, where NT is the average number of input particles. We also demonstrate that the Cramer-Rao lower bound of phase sensitivity, Δθ~0ex0ex1/√|α|²e²ʳ+sinh²r, can be saturated for arbitrary values of the squeezing parameter r and the amplitude of the coherent mode α by using a Bayesian phase inference protocol.