# Quantum analysis of a linear DC SQUID mechanical displacement detector

## TL;DR

This paper presents a quantum analysis of a DC SQUID-based mechanical displacement detector, deriving its response and noise characteristics, and exploring its sensitivity and cooling capabilities for precise quantum measurements.

## Contribution

It introduces a quantum framework for analyzing a DC SQUID mechanical detector, including signal response, noise, and back reaction effects, advancing understanding of quantum-limited displacement detection.

## Key findings

- Derived expressions for detector response and noise
- Evaluated position and force detection sensitivities
- Investigated mechanical resonator cooling via back reaction noise

## Abstract

We provide a quantum analysis of a DC SQUID mechanical displacement detector within the sub-critical Josephson current regime. A segment of the SQUID loop forms the mechanical resonator and motion of the latter is transduced inductively through changes in the flux threading the loop. Expressions are derived for the detector signal response and noise, which are used to evaluate the position and force detection sensitivity. We also investigate cooling of the mechanical resonator due to back reaction noise from the detector.