Sub-shot-noise interferometry with two-mode quantum states

TL;DR

This paper investigates the potential for sub-shot-noise phase measurements using twin-Fock and two-mode squeezed vacuum states despite detector imperfections, providing analytical tools and thresholds for surpassing classical limits.

Contribution

It derives analytical expressions for phase uncertainty in sub-shot-noise interferometry with imperfect detectors and offers accessible software tools for practical implementation.

Findings

Phase measurements below the standard quantum limit are achievable with low enough losses.

Analytical formulas for phase uncertainty are provided and validated.

The phase must be close to an optimal value for sub-shot-noise performance.

Abstract

We study the feasibility of sub-shot-noise interferometry with imperfect detectors, starting from twin-Fock states and two mode squeezed vacuum states. We derive analytical expressions for the corresponding phase uncertainty. We find that one can achieve phase shift measurements below the standard quantum limit, as long as the losses are smaller than a given threshold, and that the measured phase is close enough to an optimal value. We provide our analytical formulae in a Python package, accessible online.