Mach-Zehnder interferometry at the heisenberg limit with coherent and squeezed-vacuum light

We show that the phase sensitivity Delta theta 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 Delta theta similar to 1/N-T, where N-T is the average number of input particles. We also demonstrate that the Cramer-Rao lower bound of phase sensitivity, Delta theta similar to 1/root|alpha|(2)e(2r)+sinh(2)r, can be saturated for arbitrary values of the squeezing parameter r and the amplitude of the coherent mode alpha by using a Bayesian phase inference protocol.