Optimal phase measurements in a lossy Mach-Zehnder interferometer

TL;DR

This paper presents optimized phase measurement techniques for lossy Mach-Zehnder interferometers that achieve the standard interferometric limit by adjusting parameters, with experimental validation showing significant sensitivity improvements even at high loss rates.

Contribution

The work introduces two phase-measurement methods optimized for internal losses in MZIs and demonstrates their effectiveness both theoretically and experimentally, reaching the fundamental precision bound.

Findings

Theoretical phase sensitivity reaches the standard interferometric limit under optimized conditions.

Experimental results confirm sensitivity improvements up to 2.5 dB at high loss rates.

Optimization of reflectivities significantly enhances phase measurement precision.

Abstract

In this work, we discuss two phase-measurement methods for the Mach-Zehnder interferometer (MZI) in the presence of internal losses and give the corresponding optimum conditions. We find theoretically that when the core parameters (reflectivities, phase difference) are optimized, the phase sensitivity of the two methods can reach a generalized bound on precision: standard interferometric limit (SIL). In the experiment, we design an MZI with adjustable beam splitting ratios and losses to verify phase sensitivity optimization. The sensitivity improvements at loss rates from 0.4 to 0.998 are demonstrated based on difference-intensity detection, matching the theoretical results well. With a loss up to 0.998 in one arm, we achieve a sensitivity improvement of 2.5 dB by optimizing reflectivity, which equates to a 5.5 dB sensitivity improvement in single-intensity detection. Such optimal phase measurement methods provide practical solutions for the correct use of resources in lossy interferometry.