The phase sensitivity of a fully quantum three-mode nonlinear interferometer

TL;DR

This paper investigates a fully quantum three-mode nonlinear interferometer, revealing phase uncertainty behaviors, including oscillations, saturation, and Heisenberg scaling, when all optical fields are treated quantum mechanically.

Contribution

It introduces a comprehensive quantum model of the interferometer that accounts for pump depletion and quantum effects, showing new phase sensitivity behaviors.

Findings

Phase uncertainty oscillates around a saturation level with increasing pump photons.

Achieves phase uncertainty below shot-noise level at optimal interaction strengths.

Demonstrates Heisenberg scaling of phase uncertainty as 1/N.

Abstract

We study a nonlinear interferometer consisting of two consecutive parametric amplifiers, where all three optical fields (pump, signal and idler) are treated quantum mechanically, allowing for pump depletion and other quantum phenomena. The interaction of all three fields in the final amplifier leads to an interference pattern from which we extract the phase uncertainty. We find that the phase uncertainty oscillates around a saturation level that decreases as the mean number $N$ of input pump photons increases. For optimal interaction strengths, we also find a phase uncertainty below the shot-noise level and obtain a Heisenberg scaling $1/N$. This is in contrast to the conventional treatment within the parametric approximation, where the Heisenberg scaling is observed as a function of the number of down-converted photons inside the interferometer.