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arXiv:1709.06598 · Physical Review Applied

Frequency Pulling and Mixing of Relaxation Oscillations in Superconducting Nanowires

Emily Toomey, Qingyuan Zhao, Adam N. McCaughan, Karl K. Berggren

Published Jun 14, 2018• 24 citations
arXivHTMLPDF

Abstract

The electromagnetic response of a superconducting nanowire exhibits relaxation oscillations, due to strong electrothermal nonlinearity. Resultant technology has been limited, though, by a lack of understanding of how the nonlinear behavior can be externally modulated. This study of electrothermal oscillations in superconducting nanowires uses microwave modulation to show that the oscillations mix with an external microwave drive, and lock to its frequency. This interaction is reminiscent of the ac Josephson effect, despite its thermal origin. Nanowire devices based on these phenomena could see use in microwave applications like frequency mixing and parametric amplification.

DOI
10.1103/physrevapplied.9.064021

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The electromagnetic response of a superconducting nanowire exhibits relaxation oscillations, due to strong electrothermal nonlinearity. Resultant technology has been limited, though, by a lack of understanding of how the nonlinear behavior can be externally modulated. This study of electrothermal oscillations in superconducting nanowires uses microwave modulation to show that the oscillations mix with an external microwave drive, and lock to its frequency. This interaction is reminiscent of the ac Josephson effect, despite its thermal origin. Nanowire devices based on these phenomena could see use in microwave applications like frequency mixing and parametric amplification.
We propose a superconducting microwave relaxation oscillator based on a nanowire shunted by a resistor and an inductor controlled by quasiparticle injection from a tunnel junction positioned on it: the QUISTRON. This device exhibits relaxation oscillator behavior with dc voltage--controlled frequency tuning and dc bias. The device frequency is modulated via the tunnel junction, which induces localized heating by injecting quasiparticles. This heating mechanism modulates the nanowire switching current, enabling relaxation oscillations when it falls below the bias current. We simulate the device operating principles and its performance across various parameters, including different choices of shunt resistor, shunt inductance, and bath temperature ranging from 20 mK to 1 K. The device showed oscillation with a frequency range approximately between 1 and 10 GHz and total energy dissipation per cycle of approximately 100100100 zJ. Our results suggest that this design offers a promising platform for compact, tunable superconducting oscillators in the microwave spectrum with potential applications in quantum information processing, microwave technology, and ultralow-power electronics. The straightforward frequency control mechanism and integration potential make this device an attractive candidate for superconducting microwave local oscillators.
Niobium nitride nanowires show considerable promise as high-speed single-photon detectors. We report the observation of an anomalous low-frequency (∼10MHz) response in long, superconducting NbN nanowires (100nm wide, 4nm thick, and 500μm long). This behavior, although strikingly reminiscent of the ac Josephson effect, can be explained by a relaxation oscillation resulting from the high kinetic inductance of the type II nanowire. We simulate all of the observed effects using a simple resistive-hotspot/series-inductor model. The voltage pulses observed are indistinguishable from the pulses induced by visible photons, and our observations suggest noise-induced relaxation oscillations are one mechanism for the dark counts in photon detectors.
We propose a superconducting microwave relaxation oscillator based on a nanowire shunted by a resistor and an inductor controlled by quasiparticle injection from a tunnel junction positioned on it: the QUISTRON. This device exhibits relaxation oscillator behavior with DC voltage-controlled frequency tuning and DC current bias. The device frequency is modulated via the tunnel junction, which induces localized heating by injecting quasiparticles. This heating mechanism modulates the nanowire switching current, enabling relaxation oscillations when it falls below the bias current. We demonstrate the device operating principles and characterize its performance across various parameters, including different choices of shunt resistor, shunt inductance, and bath temperature ranging from 20 mK to 1 K. The device showed oscillation with a frequency range approximately between 1 GHz and 10 GHz and total energy dissipation per cycle of ∼100\sim100∼100 zJ. Our results suggest that this design offers a promising platform for compact, tunable superconducting oscillators in the microwave spectrum with potential applications in quantum information processing, microwave technology, and ultra-low-power electronics. The straightforward frequency control mechanism and integration potential make this device an attractive candidate for superconducting microwave local oscillators.
We report microwave transmission measurements of superconducting Fabry-Perot resonators, having a superconducting nanowire placed at a supercurrent antinode. As the plasma oscillation is excited, the supercurrent is forced to flow through the nanowire. The microwave transmission of the resonator-nanowire device shows a nonlinear resonance behavior, significantly dependent on the amplitude of the supercurrent oscillation. We show that such amplitude-dependent response is due to the nonlinearity of the current-phase relationship of the nanowire. The results are explained within a nonlinear oscillator model of the Duffing oscillator, in which the nanowire acts as a purely inductive element, in the limit of low temperatures and low amplitudes. The low-quality factor sample exhibits a ``crater'' at the resonance peak at higher driving power, which is due to dissipation. We observe a hysteretic bifurcation behavior of the transmission response to frequency sweep in a sample with a higher quality factor. The Duffing model is used to explain the Duffing bistability diagram. We also propose a concept of a nanowire-based qubit that relies on the current dependence of the kinetic inductance of a superconducting nanowire.
Superconducting optomechanical circuits enable frequency mixing of optical and mechanical modes, facilitating the generation of microwave frequency combs. However, such optomechanical combs suffer from frequency fluctuations, requiring their stabilization for applications in precision sensing and signal processing. Here, we investigate the sideband injection locking of microwave frequency combs in a niobium-based superconducting optomechanical circuit. By strongly driving the device with a blue-detuned pump to induce parametric instability and introducing an additional tone near individual comb peaks, we study how the locking range varies with the power, the frequency position, and the sweep direction of the injection tone. The locking responses show interesting features such as injection hysteresis, which cannot be explained by existing models. Numerical simulations of the classical optomechanical equations implementing a cubic mechanical nonlinearity show that the nonlinearity contributes to broadening the locking range. We also characterize the Allan deviations and phase noise of the injection-locked combs for different injection frequencies, demonstrating enhanced stability performance. Our results lay the foundation for the utilization of optomechanical combs for applications in nanomechanical sensing and cryogenic microwave pulse generation.
We demonstrate the controllable nonlinear microwave modulation in a cyclically driven three-level superconducting Josephson system. By designing two subtle matched conditions in the △-type atom-field configuration, a new physical mechanism – combined action of nonlinear wave mixing and wave interference – is developed and leads to not only amplification but also attenuation for two microwave signals. Our results show that such a nonlinear manipulation of the signal transition from enhancement to damping can be tuned in a large scope by controlling the relative phase and the driving-field frequency and thus the solid-state Josephson system can act as a phase- and frequency-controlled amplitude modulator. Our study opens up a fascinating perspective for its widespread applications in nonlinear optics and quantum information science.