Frequency Pulling and Mixing of Relaxation Oscillations in Superconducting Nanowires

Emily Toomey, Qing-Yuan Zhao, Adam N. McCaughan, and Karl K. Berggren

Phys. Rev. Applied 9, 064021 – Published 14 June 2018

Abstract

Many superconducting technologies such as rapid single-flux quantum computing and superconducting quantum-interference devices rely on the modulation of nonlinear dynamics in Josephson junctions for functionality. More recently, however, superconducting devices have been developed based on the switching and thermal heating of nanowires for use in fields such as single-photon detection and digital logic. In this paper, we use resistive shunting to control the nonlinear heating of a superconducting nanowire and compare the resulting dynamics to those observed in Josephson junctions. We show that interaction of the hotspot-impedance with an external shunt produces high-frequency relaxation oscillations with similar behavior to that observed in Josephson junctions due to their ability to be modulated by a weak periodic signal. In particular, we use a microwave drive to pull and mix the oscillation frequency, resulting in phase-locked features that resemble the Shapiro steps observed in the ac Josephson effect. Microwave nanowire devices based on these conclusions have promising applications in fields such as parametric amplification and frequency mixing.

Received 28 September 2017
Revised 21 March 2018

DOI:https://doi.org/10.1103/PhysRevApplied.9.064021

Physics Subject Headings (PhySH)

Josephson effect Optoelectronics Superconducting RF

Low-temperature superconductors Nanowires Thin films

Chaos & nonlinear dynamics Microwave techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Emily Toomey¹, Qing-Yuan Zhao¹, Adam N. McCaughan^1,2, and Karl K. Berggren^1,*

¹Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
²National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA

^*Corresponding author. berggren@mit.edu

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 9, Iss. 6 — June 2018

Subject Areas

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) rf voltage output of the shunted nanowire ( $R_{s} = 10 Ω$ ) when a bias-current ramp is applied. The blue trace corresponds to experimental data, and the red trace is the output of electrothermal simulations. (b) Scanning electron micrograph of the tapered nanowire. (c) Illustration of a basic relaxation model. The bias current is first diverted to the shunt after the nanowire switches to the normal state and then returns to the nanowire once superconductivity is restored. The total inductance $L$ is the sum of the nanowire’s kinetic inductance $L_{k}$ and the inductance of the wire bond connections $L_{w}$ . In our experimental setup, $L_{w}$ dominates the total inductance.
Reuse & Permissions
Figure 2
Relationship between $i_{bias}$ and the oscillation frequency for two different series inductances (red and black curves). The experimental data are compared to both electrothermal simulations and the basic relaxation oscillation model in Eq. (1). Parameters used to fit the red curve: $L = 20 nH$ (basic model), $L = 25 nH$ (simulation). Parameters used to fit the black curve: $L = 15.3 nH$ (basic model), $L = 18.75 nH$ (simulation). For all fits, $R_{s} = 10 Ω$ and $R_{w} = 500 Ω$ .
Reuse & Permissions
Figure 3
(a) Current-voltage characteristics of the unshunted nanowire. (b) Current-voltage characteristics of the nanowire when it is shunted with $R_{s} = 10 Ω$ . The red curve is a fit to an overdamped Josephson-junction model [Eq. (1)] with $I_{c} = 38.5 μ A$ and $R = 7.8 Ω$ . (c) Shunting the nanowire results in an increase in the mean and a narrowing in the width of the switching current distribution.
Reuse & Permissions
Figure 4
(a) Steps appearing in the current-voltage characteristics with 180-MHz radiation at two different powers. (b) Amplitudes of the first four current steps as a function of the modulation power. Amplitudes are scaled relative to $I_{c}$ , the magnitude of the $n_{0}$ step when no radiation is applied. The solid black curve shows fits to dynamical solutions for a Josephson junction following the expression $| J_{n} (2 e α V / h f) |$ as described in Ref. [26], where $α = 1 \times 10^{- 4}$ .
Reuse & Permissions
Figure 5
(a) FFT of the voltage output with an applied radiation of 320 MHz and a constant bias current of $60 μ A$ . Peaks indicate the resonance of the relaxation oscillations and the driving frequency, as well as their mixing products. (b) Enlarged view of the frequency spectrum while varying the applied microwave power. As the power increases, the relaxation oscillation frequency is pulled toward the driving frequency.
Reuse & Permissions

Physical Review Applied