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

P. D. Nation; M. P. Blencowe; E. Buks

doi:10.1103/PhysRevB.78.104516

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

P. D. Nation, M. P. Blencowe, E. Buks

DOI 10.1103/PhysRevB.78.104516 · Physical Review B

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Abstract

We carry out a quantum analysis of a dc superconducting quantum interference device (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.