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Superconductor Science and Technology

The dynamics of high-frequency DC RSQUID oscillators

Colin M. Pegrum

Published May 14, 2009• 6 citations
Publisher

Abstract

Josephson circuit simulation software has been used to study the properties of a range of two-junction DC RSQUIDs configured as current-controlled heterodyne oscillators. We find that, if the loop inductance is small, their current–voltage curves are modified substantially due to self-induced Shapiro steps. When the heterodyne frequency is comparable with the Josephson frequency of the junctions the step amplitude becomes very large and additional features are seen, including sub-harmonic steps and step tails. We point out that conventional DC RSQUIDs generally have too large a loop inductance for some of these effects to be seen in the I–V curves, and we suggest that nanofabrication techniques could be used to make novel low-inductance RSQUIDs. We have also demonstrated that by applying a sinusoidally varying RF flux to a DC RSQUID it is possible to phase-modulate the heterodyne oscillation, which could have useful practical applications.

DOI
10.1088/0953-2048/22/6/064004

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Josephson circuit simulation software has been used to study the properties of a range of two-junction DC RSQUIDs configured as current-controlled heterodyne oscillators. We find that, if the loop inductance is small, their current–voltage curves are modified substantially due to self-induced Shapiro steps. When the heterodyne frequency is comparable with the Josephson frequency of the junctions the step amplitude becomes very large and additional features are seen, including sub-harmonic steps and step tails. We point out that conventional DC RSQUIDs generally have too large a loop inductance for some of these effects to be seen in the I–V curves, and we suggest that nanofabrication techniques could be used to make novel low-inductance RSQUIDs. We have also demonstrated that by applying a sinusoidally varying RF flux to a DC RSQUID it is possible to phase-modulate the heterodyne oscillation, which could have useful practical applications.
Resistive two-junction SQUIDs (RSQUIDs) made from high-temperature superconductors are being developed as narrow-linewidth tunable oscillators in the GHz frequency range. We present here the results of numerical simulation of RSQUIDs of this type. These studies have identified conditions where sub-harmonic steps and other features are apparent in the current-voltage characteristics, driven by the internally-generated heterodyne frequency. The behavior is sensitive to the frequency (set by the voltage across the resistive element in the RSQUID), the temperature and also the loop inductance. We have studied the effects of thermal noise on these features. We also assess how these effects might be observed, and consider how they might affect practical applications of high frequency heterodyne RSQUID oscillators.
We report continuing investigations into practical applications of the AC Josephson effect as the basis for a voltage-tunable radio-frequency oscillator. We have previously demonstrated experimentally that useful power levels (10 s of nW) and linewidths of a few kHz can be achieved in the heterodyne output from a high-temperature-superconducting resistive SQUID (HTS-RSQUID) operating in the frequency range 1-50 MHz. Those results were achieved with 2-junction R-SQUIDs incorporating current-biased shunt resistors of a few micro-ohms. We have now modified the fabrication procedures, and adjusted the shunt resistors and bias current values so that higher frequencies can be achieved. The Josephson junctions are of step-edge type, rather than the bi-crystal type used in our earlier work. The step-edge technique permits much more flexibility in the geometrical lay-out and utilizes the more cost-effective single-crystal MgO substrates. In the present paper, we report numerical simulations and experimental measurements on these devices in the frequency range up to 2 GHz.
Experimental evaluation of a high-temperature superconducting Josephson heterodyne mixer based on a 'resistive-SQUID' configuration is reported. The device consists of two YBa 2 Cu 3 O 7− x step-edge Josephson junctions connected via a small resistor in an otherwise superconducting loop. It has been previously shown to generate a heterodyne oscillation, which is frequency-tunable by a control current through the resistor. Under certain conditions, this device can operate as a frequency-tunable heterodyne mixer (down-converter) in the presence of an RF signal. In this paper, we describe the operation of the autonomous Josephson mixer–local oscillator device and present the experimental results on the mixer performances in terms of the junction current–voltage characteristics, the frequency tunability, linearity, and dynamic range as well as their temperature dependence for signal frequencies from 1 to 5 GHz.
The shunt resistors used in many Josephson junction circuits contain an inductive component that can significantly degrade high-frequency performance. Numerical simulations reveal complex dynamical behaviour, including relaxation oscillations, period-doubling sequences, and chaos, all of which are serious problems for applications as high-frequency sources and detectors. This complex AC behaviour creates features in the simulated DC current-voltage characteristics. Since these simulations closely match experimental data, they can be used to investigate the high-frequency AC behaviour of real junctions. Thus, we are able to use simple DC measurements to observe evidence of complex high-frequency dynamics. The inductance of the shunt branch can be accurately determined by comparing simulations to measurements. Simulations also allow us to map regions of the parameter space which exhibit complicated behaviour. These regions should be avoided when a nearly sinusoidal voltage waveform is desired, as is the case for Josephson junction-based oscillators.
Both resonant and microwave-induced steps in the V-I characteristics of four-Josephson-junction loop with a small junction-parameter spread have been investigated. An rf current was superimposed onto a dc current and the radio frequency was tuned to the resonance frequency of the loop. In the high-Q region, the rf-power dependence of the step amplitude was similar to that of a single junction. However, we obtained V-I characteristics which indicated that the behavior of the junction in the loop was coherent in the low-Q region.
The current height of RF-induced voltage steps in nonhysteretic single Josephson junctions is usually a small fraction of the critical current. It is demonstrated that when a resistively shunted DC superconducting quantum interference device (SQUID) is subjected to an RF magnetic flux, a voltage step with a large current height is obtained. In contrast to weak selection rules for single Josephson junctions, strong selection of the step harmonic number occurs in a shunted DC SQUID for appropriate choice of RF amplitude and DC flux offset, with odd harmonic numbers selected by half-integer flux quantum offsets and even harmonic numbers by integer flux quantum offsets. This pronounced effect has immediate implications for voltage standards and fast, high-precision digital-to-analog converters.>