Deterministic super-resolved estimation towards angular displacements based upon a Sagnac interferometer and parity measurement

TL;DR

This paper presents an experimentally demonstrated protocol for super-resolved angular displacement estimation using a coherent state with orbital angular momentum and parity measurement, achieving near shot-noise-limited sensitivity and super-resolution.

Contribution

The work introduces a new protocol combining orbital angular momentum and parity measurement for super-resolved angular displacement estimation with experimental validation.

Findings

Achieved a super-resolution factor of 7.88 with mean photon number 2.297 and angular momentum quantum number 1.

The protocol theoretically reaches 4ℓ-fold super-resolution and saturates the quantum Cramér-Rao bound in ideal conditions.

Experimental results show near shot-noise-limited sensitivity despite realistic imperfections.

Abstract

Super-resolved angular displacement estimation is of crucial significances for quantum information process and optical lithography. Here we report on and experimentally demonstrate a protocol for angular displacement estimation based on a coherent state containing orbital angular momentum. In the lossless scenario, with using parity measurement, this protocol can theoretically achieve 4$\ell$-fold super-resolution with quantum number $\ell$, and shot-noise-limited sensitivity saturating the quantum Cram\'er-Rao bound. Several realistic factors and their effects are considered, including nonideal state preparation, photon loss, and imperfect detector. Finally, given mean photon number $\bar N=2.297$ and $\ell=1$, we show an angular displacement super-resolution effect with a factor of 7.88, and the sensitivity approaching shot-noise limit is reachable.