Quantum analysis of a nonlinear microwave cavity-embedded dc SQUID displacement detector

TL;DR

This paper presents a quantum analysis of a nonlinear microwave cavity with an embedded dc SQUID, demonstrating enhanced displacement detection and cooling capabilities near the quantum limit.

Contribution

It introduces a model incorporating nonlinear Duffing self-interaction in a SQUID-based microwave resonator for improved quantum displacement detection.

Findings

Closer approach to the standard quantum limit

Enhanced cooling near the ground state

Nonlinear Duffing interaction improves sensitivity

Abstract

We carry out a quantum analysis of a dc SQUID mechanical displacement detector, comprising a SQUID with mechanically compliant loop segment, which is embedded in a microwave transmission line resonator. The SQUID is approximated as a nonlinear, current dependent inductance, inducing an external flux tunable, nonlinear Duffing self-interaction term in the microwave resonator mode equation. Motion of the compliant SQUID loop segment is transduced inductively through changes in the external flux threading SQUID loop, giving a ponderomotive, radiation pressure type coupling between the microwave and mechanical resonator modes. Expressions are derived for the detector signal response and noise, and it is found that a soft-spring Duffing self-interaction enables a closer approach to the displacement detection standard quantum limit, as well as cooling closer to the ground state.