Effects of photon losses on phase estimation near the Heisenberg limit using coherent light and squeezed vacuum

TL;DR

This paper analyzes how photon losses affect phase estimation near the Heisenberg limit using coherent and squeezed vacuum states, proposing methods to optimize robustness against such losses.

Contribution

It provides an experimental approach to achieve phase sensitivity bounds in lossy environments and derives an optimized squeezing fraction to mitigate loss effects.

Findings

Phase sensitivity can be achieved with photon counting and a weak local oscillator.

Losses reduce Fisher information, but optimization of squeezing fraction can improve robustness.

Maximum improvement in loss tolerance is about a factor of two at high losses.

Abstract

Two path interferometry with coherent states and squeezed vacuum can achieve phase sensitivities close to the Heisenberg limit when the average photon number of the squeezed vacuum is close to the average photon number of the coherent light. Here, we investigate the phase sensitivity of such states in the presence of photon losses. It is shown that the Cramer-Rao bound of phase sensitivity can be achieved experimentally by using a weak local oscillator and photon counting in the output. The phase sensitivity is then given by the Fisher information F of the state. In the limit of high squeezing, the ratio (F-N)/N^2 of Fisher information above shot noise to the square of the average photon number N depends only on the average number of photons lost, n_loss, and the fraction of squeezed vacuum photons mu. For mu=1/2, the effect of losses is given by (F-N)/N^2=1/(1+2 n_loss). The possibility of increasing the robustness against losses by lowering the squeezing fraction mu is considered and an optimized result is derived. However, the improvements are rather small, with a maximal improvement by a factor of two at high losses.