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

TL;DR

This paper demonstrates that a Mach-Zehnder interferometer with coherent and squeezed-vacuum inputs can achieve phase sensitivity at the Heisenberg limit, independent of the phase shift, using Bayesian inference.

Contribution

It shows that the interferometer's phase sensitivity can reach the Heisenberg limit with a Bayesian protocol, regardless of the squeezing and coherent state parameters.

Findings

Phase sensitivity is independent of the true phase shift.

Sensitivity can reach the Heisenberg limit proportional to 1/N_T.

Cramer-Rao bound can be saturated for all squeezing and coherent amplitudes.

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, $\Delta \theta \propto 1/ \sqrt{|\alpha|^2 e^{2r} + \sinh^2r}$, 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.