# Light-matter quantum interferometry with homodyne detection

## TL;DR

This paper presents a light-matter interferometric scheme using homodyne detection to estimate Gaussian processes on matter systems, demonstrating high accuracy even with limited coupling and noise, advancing quantum metrology techniques.

## Contribution

The paper introduces a novel light-matter interferometric setup with homodyne detection for estimating Gaussian processes on matter systems, showing its superiority over non-interferometric methods.

## Key findings

- Interferometric setup outperforms non-interferometric schemes.
- Effective estimation with limited coupling strength and noise.
- Potential for future quantum metrology applications.

## Abstract

We investigated the estimation of an unknown Gaussian process (containing displacement, squeezing and phase-shift) applied to a matter system. The state of the matter system is not directly measured; instead, we measure an optical mode which interacts with the system. We propose an interferometric setup exploiting a beam-splitter-type of light-matter interaction with homodyne detectors and two methods of estimation. We demonstrate the superiority of the interferometric setup over alternative non-interferometric schemes. Importantly, we show that even limited coupling strength and a noisy matter system are sufficient for very good estimation. Our work opens the way to many future investigations of light-matter interferometry for experimental platforms in quantum metrology of matter systems.