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Comptes Rendus Physique

dc SQUIDs as linear displacement detectors for embedded micromechanical resonators

Samir Etaki, Menno Poot, Koji Onomitsu, Hiroshi Yamaguchi, Herre S. J. van der Zant

Published Nov 9, 2011• 14 citations
Publisher

Abstract

Superconducting quantum interference devices (SQUIDs) can detect tiny amounts of magnetic flux and are also used to study macroscopic quantum effects. We employ a dc SQUID as a linear detector of the displacement of an embedded micromechanical resonator with a femtometer sensitivity. We discuss the measurement method, including operation in high magnetic field and a cryogenic amplification scheme which allows us to reach a resolution which is only a factor 4.4 above the standard quantum limit.

DOI
10.1016/j.crhy.2011.10.005

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Superconducting quantum interference devices (SQUIDs) can detect tiny amounts of magnetic flux and are also used to study macroscopic quantum effects. We employ a dc SQUID as a linear detector of the displacement of an embedded micromechanical resonator with a femtometer sensitivity. We discuss the measurement method, including operation in high magnetic field and a cryogenic amplification scheme which allows us to reach a resolution which is only a factor 4.4 above the standard quantum limit.
We have measured the backaction of a dc superconducting quantum interference device (SQUID) position detector on an integrated 1 MHz flexural resonator. The frequency and quality factor of the micromechanical resonator can be tuned with bias current and applied magnetic flux. The backaction is caused by the Lorentz force due to the change in circulating current when the resonator displaces. The experimental features are reproduced by numerical calculations using the resistively and capacitively shunted junction model.
We demonstrate a superconducting inductive technique to measure the displacement of a micromechanical resonator. In our scheme, a type I superconducting microsphere is attached to the free end of a microcantilever and approached to the loop of a dc Superconducting Quantum Interference Device (SQUID) microsusceptometer. A local magnetic field as low as 100 μT, generated by a field coil concentric to the SQUID, enables detection of the cantilever thermomechanical noise at 4.2 K. The magnetomechanical coupling and the magnetic spring are in good agreement with image method calculations assuming pure Meissner effect. These measurements are relevant to recent proposals of quantum magnetomechanics experiments based on levitating superconducting microparticles.
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.
We present a study of the controllable nonlinear dynamics of a micromechanical beam coupled to a dc-SQUID (superconducting quantum interference device). The coupling between these systems places the modes of the beam in a highly nonlinear potential, whose shape can be altered by varying the control parameters of the SQUID. We detect the position of the beam by placing it in an optical cavity, which frees the SQUID to be used solely for actuation. This enables us to probe the previously unexplored full parameter space of this device. We measure the frequency response of the beam and find that it displays a periodic dependence on applied magnetic flux. To account for this, we develop a model based on the standard theory for SQUID dynamics. In addition, with the aim of understanding if the device can reach nonlinearity at the single phonon level, we use this model to show that the responsivity of the current circulating in the SQUID to the position of the beam can become divergent, with its magnitude limited only by noise. This suggests a direction for the generation of macroscopically distinguishable superposition states of the beam.
We present a study of the controllable nonlinear dynamics of a micromechanical beam coupled to a dc-SQUID (superconducting quantum interference device). The coupling between these systems places the modes of the beam in a highly nonlinear potential, whose shape can be altered by varying the bias current and applied flux of the SQUID. We detect the position of the beam by placing it in an optical cavity, which sets free the SQUID to be used solely for actuation. This enables us to probe the previously unexplored full parameter space of this device. We measure the frequency response of the beam and find that it displays a Duffing oscillator behavior which is periodic in the applied magnetic flux. To account for this, we develop a model based on the standard theory for SQUID dynamics. In addition, with the aim of understanding if the device can reach nonlinearity at the single phonon level, we use this model to show that the responsivity of the current circulating in the SQUID to the position of the beam can become divergent, with its magnitude limited only by noise. This suggests a direction for the generation of macroscopically distinguishable superposition states of the beam.
We provide a quantum analysis of a dc SQUID mechanical displacement detector within the subcritical 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 detector back reaction.