Optimal phase sensitivity of an unbalanced Mach-Zehnder interferometer

TL;DR

This paper derives optimal configurations for an unbalanced Mach-Zehnder interferometer to maximize phase sensitivity, considering different detection schemes and input states, demonstrating potential advantages over balanced setups.

Contribution

It provides analytic solutions for the second beam splitter's transmission coefficient tailored to various detection schemes, enhancing interferometer optimization methods.

Findings

Unbalanced interferometers can outperform balanced ones in phase sensitivity.

Analytic solutions for optimal second beam splitter transmission are provided.

Performance depends on input state type and detection scheme.

Abstract

In this paper we address the problem of optimizing an unbalanced Mach-Zehnder interferometer, for a given pure input state and considering a specific detection scheme. While the optimum transmission coefficient of the first beam splitter can be uniquely determined via the quantum Fisher information only [Phys. Rev. A 105, 012604 (2022)], the second beam splitter transmission coefficient is detection-scheme dependent, too. We systematically give analytic solutions for the optimum transmission coefficient of the second beam splitter for three types of widely used detection schemes. We provide detailed examples including both Gaussian and non-Gaussian input states, showing when an unbalanced Mach-Zehnder interferometer can outperform its balanced counterpart in terms of phase sensitivity.