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

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.

References in corpus (31)

• Strong dispersive coupling of a high finesse cavity to a micromechanical membrane
• Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion
• Theory of ground state cooling of a mechanical oscillator using dynamical back-action
• Radiation-pressure cooling and optomechanical instability of a micro-mirror
• Self-cooling of a micro-mirror by radiation pressure
• Cavity Optomechanics
• Cooling of a micro-mechanical oscillator using radiation pressure induced dynamical back-action
• Dynamical multistability in high-finesse micromechanical optical cavities
• An RF-Driven Josephson Bifurcation Amplifier for Quantum Measurements
• Noise-enabled precision measurements of a Duffing nanomechanical resonator
• Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK
• Performance of cavity-parametric amplifiers, employing Kerr nonlinearites, in the presence of two-photon loss
• High-contrast dispersive readout of a superconducting flux qubit using a nonlinear resonator
• Quantum-Limited Position Detection and Amplification: A Linear Response Perspective
• Classical to Quantum Transition of a Driven Nonlinear Nanomechanical Resonator
• Nonlinearities and Parametric Amplification in Superconducting Coplanar Waveguide Resonators
• Signal amplification in a nanomechanical Duffing resonator via stochastic resonance
• Controllable Coupling between Flux Qubit and Nanomechanical Resonator by Magnetic Field
• Critical exponents in metastable decay via quantum activation
• Nanomechanical resonators operating as charge detectors in the nonlinear regime
• Measuring the Decoherence of a Quantronium Qubit with the Cavity Bifurcation Amplifier
• Cooling a Micromechanical Beam by Coupling it to a Transmission Line
• Quantum noise in the position measurement of a cavity mirror undergoing Brownian motion
• Quantum analysis of a linear DC SQUID mechanical displacement detector
• Decoherence and Recoherence in a Vibrating RF SQUID
• Dynamical tunneling in macroscopic systems
• Readout methods and devices for Josephson-junction-based solid-state qubits
• Scaling in activated escape of underdamped systems
• Displacement Detection with a Vibrating RF SQUID: Beating the Standard Linear Limit
• Nonlinear resonant behavior of the dispersive readout scheme for a superconducting flux qubit
• Scaling and crossovers in activated escape near a bifurcation point

Cited by in corpus (31)

• Mechanical systems in the quantum regime
• Optomechanical position detection enhanced by de-amplification using intracavity squeezing
• Coupling microwave photons to a mechanical resonator using quantum interference
• Nonclassical mechanical states in an optomechanical micromaser analogue
• Quantum heating of a parametrically modulated oscillator: spectral signatures
• Kerr enhanced backaction cooling in magnetomechanics
• Quantum limited amplification with a nonlinear cavity detector
• Nonlinear modal coupling in a high-stress doubly-clamped nanomechanical resonator
• Flux-mediated optomechanics with a transmon qubit in the single-photon ultrastrong-coupling regime
• Weak and strong measurement of a qubit using a switching-based detector
• Single-photon cooling in microwave magneto-mechanics
• Tunable backaction of a dc SQUID on an integrated micromechanical resonator
• Sideband-resolved resonator electromechanics on the single-photon level based on a nonlinear Josephson inductance
• Strong Single-Photon Coupling in Superconducting Quantum Magnetomechanics
• Four-wave-cooling to the single phonon level in Kerr optomechanics
• Ultra-Strong Optomechanics Incorporating the Dynamical Casimir Effect
• Emission spectrum of the driven nonlinear oscillator
• Synthesizing multi-phonon quantum superposition states using flux-mediated three-body interactions with superconducting qubits
• Dynamical Casimir effect in nonlinear vibrating cavities
• Intermittency in an Optomechanical Cavity Near a Subcritical Hopf Bifurcation
• Phase sensitive amplification in a superconducting stripline resonator integrated with a dc-SQUID
• Parametrically enhanced interactions and non-trivial bath dynamics in a photon-pressure Kerr amplifier
• Intermode Dephasing in a Superconducting Stripline Resonator - Supplementary Information
• Nonlinear dynamical Casimir effect at weak nonstationarity
• Feedback-induced nonlinearity and superconducting on-chip quantum optics
• Dissipative dynamics of a qubit coupled to a nonlinear oscillator
• The dissipative quantum Duffing oscillator: a comparison of Floquet-based approaches
• Kerr enhanced optomechanical cooling in the unresolved sideband regime
• Time Resolved Phase Space Tomography of an Optomechanical Cavity
• Optomechanical Backaction in the Bistable Regime
• Electromotive interference in a mechanically oscillating superconductor: generalized Josephson relations and self-sustained oscillations of a torsional SQUID