# Versatile Super-Sensitive Metrology Using Induced Coherence

## TL;DR

This paper presents a theoretical analysis of a hybrid interferometer that achieves super-sensitive phase measurements using induced coherence, surpassing shot noise limits, with practical advantages like subtracted intensity detection.

## Contribution

It introduces a novel hybrid interferometer setup that combines linear and non-linear elements, enabling bright-light super-sensitivity with practical detection methods and specific gain configurations.

## Key findings

- Scaling below shot noise limit achieved with seeding
- Super-sensitivity depends on specific gain imbalance and non-monotonic behavior
- Subtracted intensity measurements enable practical phase estimation

## Abstract

We theoretically analyze the phase sensitivity of the Induced-Coherence (Mandel-Type) Interferometer, including the case where the sensitivity is "boosted" into the bright input regime with coherent-light seeding. We find scaling which reaches below the shot noise limit, even when seeding the spatial mode which does not interact with the sample - or when seeding the undetected mode. It is a hybrid of a linear and a non-linear (Yurke-Type) interferometer, and aside from the supersensitivity, is distinguished from other systems by "preferring" an imbalance in the gains of the two non-linearities (with the second gain being optimal at low values), and non-monotonic behavior of the sensitivity as a function of the gain of the second non-linearity. Furthermore, the setup allows use of subtracted intensity measurements, instead of direct (additive) or homodyne measurements - a significant practical advantage. Bright, super-sensitive phase estimation of an object with different light fields for interaction and detection is possible, with various potential applications, especially in cases where the sample may be sensitive to light, or is most interesting in frequency domains outside what is easily detected, or when desiring bright-light phase estimation with sensitive/delicate detectors. We use an analysis in terms of general squeezing and discover that super-sensitivity occurs only in this case - that is, the effect is not present with the spontaneous-parametric-down-conversion approximation, which many previous analyses and experiments have focused on.