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arXiv:1405.6991 · Physical Review B

Multistability of a Josephson parametric amplifier coupled to a mechanical resonator

Olga Shevchuk, Rosario Fazio, Yaroslav M. Blanter

Published Nov 11, 2014• 4 citations
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Abstract

We study the dynamics of a Josephson parametric amplifier (JPA) coupled to a mechanical oscillator, as realized with a dc superconducting quantum interference device (SQUID) with an embedded movable arm. We analyze this system in the regime when the frequency of the mechanical oscillator is comparable in magnitude to the plasma oscillation of the SQUID. When the nanomechanical resonator is driven, it strongly affects the dynamics of the JPA. We show that this coupling can considerably modify the dynamics of the JPA and induce its multistability rather than common bistability. This analysis is relevant if one considers a JPA for detection of mechanical motion.

DOI
10.1103/physrevb.90.205411

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We study the dynamics of a Josephson parametric amplifier (JPA) coupled to a mechanical oscillator, as realized with a dc superconducting quantum interference device (SQUID) with an embedded movable arm. We analyze this system in the regime when the frequency of the mechanical oscillator is comparable in magnitude to the plasma oscillation of the SQUID. When the nanomechanical resonator is driven, it strongly affects the dynamics of the JPA. We show that this coupling can considerably modify the dynamics of the JPA and induce its multistability rather than common bistability. This analysis is relevant if one considers a JPA for detection of mechanical motion.
We investigate the dynamics of a superconducting rectifying circuit, namely, a three-junction superconducting quantum interference device (SQUID), where one arm of the superconducting loop consists of a nanomechanical resonator. We find that the dc characteristic curve of the system displays features that are directly related to the frequency and amplitude of the mechanical oscillations; these effects can be further enhanced by biasing the SQUID with an ac current. We discuss potential future developments of this idea in the field of ultrasensitive position detection, and assess their feasibility in current setups.
We have developed a Josephson parametric amplifier comprising a superconducting coplanar-waveguide resonator terminated by a dc superconducting quantum interference device (SQUID). An external field (the pump, ∼20 GHz) modulates the flux threading of the dc SQUID and, therefore, the resonant frequency of the cavity field (the signal, ∼10 GHz), which leads to the parametric signal amplification. We operated the amplifier at different band centers and observed amplification (17 dB at maximum) and deamplification depending on the relative phase between the pump and the signal. The noise temperature is estimated to be less than 0.87 K.
We have developed a Josephson parametric amplifier, comprising a superconducting coplanar waveguide resonator terminated by a dc SQUID (superconducting quantum interference device). An external field (the pump, ∼20\sim 20∼20 GHz) modulates the flux threading the dc SQUID, and, thereby, the resonant frequency of the cavity field (the signal, ∼10\sim 10∼10 GHz), which leads to parametric signal amplification. We operated the amplifier at different band centers, and observed amplification (17 dB at maximum) and deamplification depending on the relative phase between the pump and the signal. The noise temperature is estimated to be less than 0.87 K.
Abstract A Josephson parametric amplifier (JPA) is executed in a three-dimensional (3D) microwave cavity by coupling it to a superconducting quantum interference device (SQUID) that is embedded in a two-dimensional resonator. The JPA is activated in a three-wave mixing configuration by injecting ac magnetic flux, at twice the 3D cavity frequency, into the SQUID. An 8.3 GHz cavity is measured in a non-degenerate phase-insensitive configuration which yields gains in excess of 40 dB, where a 20 dB gain results in an operational bandwidth of 0.4 MHz, a 1 dB compression point of −115 dBm with half a quantum of added noise.
We study microwave response of a Josephson parametric oscillator consisting of a superconducting transmission-line resonator with an embedded DC-superconducting quantum interference device (-SQUID). The DC-SQUID allows to control the magnitude of a Kerr nonlinearity over the ranges where it is smaller or larger than the photon loss rate. Spectroscopy measurements reveal the change in the microwave response from a classical Duffing oscillator to a Kerr parametric oscillator in a single device. In the single-photon Kerr regime, we observe parametric oscillations with a well-defined phase of either 0 or $\ensuremath{\pi}$, whose probability can be controlled by an externally injected signal.
The coupled dynamics of a nanomechanical resonator and superconducting quantum circuits are studied in three experiments, in the context of studying the quantum limit for force detection and quantum physics of macroscopic objects. In the first experiment, the dispersive mechanical resonance shift from the interaction with a Cooper-pair box qubit is studied. The measured coupling strength is large enough to satisfy one of the conditions required to perform many of the proposed quantum nanomechanical measurements. The resonance shift also probes the microwave-driven response of the qubit, showing Rabi oscillation and Landau-Zener tunneling, proving the coherent dynamics of the qubit. Second, the parametric excitation of nanomechanical motion is studied via experiments with a driven qubit. Degenerate parametric amplification and oscillation are demonstrated, with a new observation of nonlinear dissipation. The squeezing of the back-action noise from the detection amplifier is also observed, up to 4dB. It is the first demonstration using a qubit as an auxiliary system to modify the nanomechanical dynamics, showing a possible route for generation of nanomechanical quantum states. Finally, back-action cooling of nanomechanical motion has been investigated, which is implemented by capacitively coupling a high-Q coplanar waveguide microwave resonator to a nanomechanical resonator. The thermal state with 7.5 mechanical quanta on average is reached, a result that is ultimately limited due to increased bath heating with microwave power. The heating is consistent with a model based on two-level systems resonantly coupled to the nanomechanical mode. This additional heating suggests future efforts to improve coupling and for reducing two-level system density in materials employed to reach the motional ground state via back-action cooling.