Mach-Zehnder Interferometry at the Heisenberg Limit with coherent and squeezed-vacuum light

Abstract

We show that the phase sensitivity $\Delta \theta$ of a Mach-Zehnder interferometer fed by a coherent state in one input port and squeezed-vacuum in the other one is i) independent from the true value of the phase shift and ii) can reach the Heisenberg limit $\Delta \theta \sim 1/N_T$, where $N_T$ is the average number of particles of the input states. We also show that the Cramer-Rao lower bound, $\Delta \theta \propto 1/\sqrt{|\alpha {|}^2{e}^{2r}+{\sinh }^{2}r}$, can be saturated for arbitrary values of the squeezing parameter $r$ and the amplitude of the coherent mode $|\alpha |$ by a Bayesian phase inference protocol.

4 pages, 4 figures

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