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arXiv:0705.0206 · Physical Review E

Displacement detection with a vibrating rf superconducting interference device: Beating the standard linear limit

Eyal Buks, Stav Zaitsev, Eran Segev, Baleegh Abdo, M. P. Blencowe

Published Aug 28, 2007• 22 citations
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Abstract

We study a configuration for displacement detection consisting of a nanomechanical resonator coupled to both a radio frequency superconducting interference device and to a superconducting stripline resonator. We employ an adiabatic approximation and rotating wave approximation and calculate the displacement sensitivity. We study the performance of such a displacement detector when the stripline resonator is driven into a region of nonlinear oscillations. In this region the system exhibits noise squeezing in the output signal when homodyne detection is employed for readout. We show that displacement sensitivity of the device in this region may exceed the upper bound imposed upon the sensitivity when operating in the linear region. On the other hand, we find that the high displacement sensitivity is accompanied by a slowing down of the response of the system, resulting in a limited bandwidth.

DOI
10.1103/physreve.76.026217

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We study a configuration for displacement detection consisting of a nanomechanical resonator coupled to both a radio frequency superconducting interference device and to a superconducting stripline resonator. We employ an adiabatic approximation and rotating wave approximation and calculate the displacement sensitivity. We study the performance of such a displacement detector when the stripline resonator is driven into a region of nonlinear oscillations. In this region the system exhibits noise squeezing in the output signal when homodyne detection is employed for readout. We show that displacement sensitivity of the device in this region may exceed the upper bound imposed upon the sensitivity when operating in the linear region. On the other hand, we find that the high displacement sensitivity is accompanied by a slowing down of the response of the system, resulting in a limited bandwidth.
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We study theoretically a radio frequency superconducting interference device integrated with both a nanomechanical resonator and an LC one. By applying adiabatic and rotating wave approximations, we obtain an effective Hamiltonian that governs the dynamics of the mechanical and LC resonators. Nonlinear terms in this Hamiltonian can be exploited for performing a quantum nondemolition measurement of Fock states of the nanomechanical resonator. We address the feasibility of experimental implementation and show that the nonlinear coupling can be made sufficiently strong to allow the detection of discrete mechanical Fock states.
The nonlinearity exhibited by the kinetic inductance of a superconducting stripline couples stripline resonator modes together in a manner suitable for quantum nondemolition measurement of the number of photons in a given resonator mode. Quantum nondemolition measurement is accomplished by coherently driving another resonator mode, referred to as the detector mode, and measuring its response. We show that the sensitivity of such a detection scheme is directly related to the dephasing rate induced by such an intermode coupling. We show that high sensitivity is expected when the detector mode is driven into the nonlinear regime and operated close to a point where critical slowing down occurs.
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.
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