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Journal of Applied Physics

Step width enhancement in a pulse-driven Josephson junction

Sabino Maggi

Published May 15, 1996• 12 citations
Publisher

Abstract

The response of an overdamped current biased Josephson junction to a pulsed rf drive has been investigated by both numerical and analog simulations. The rf signal was a periodic rectangular pulse of varying amplitude and duration. A considerable increase of the width of the rf-induced steps with respect to those of an equivalent junction driven by a sinusoidal signal has been obtained. In the limiting case of a pulse repetition frequency much lower than the junction RC cutoff frequency, all steps have a maximum width which is independent of the step order n and increases with decreasing pulse duration.

DOI
10.1063/1.362395

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The response of an overdamped current biased Josephson junction to a pulsed rf drive has been investigated by both numerical and analog simulations. The rf signal was a periodic rectangular pulse of varying amplitude and duration. A considerable increase of the width of the rf-induced steps with respect to those of an equivalent junction driven by a sinusoidal signal has been obtained. In the limiting case of a pulse repetition frequency much lower than the junction RC cutoff frequency, all steps have a maximum width which is independent of the step order n and increases with decreasing pulse duration.
Shapiro steps crossing the zero-current axis, i.e., zero-crossing steps, in the overdamped Josephson junction driven with a simple pulse code consisting of single and multiple pulses in each repetition period are studied based on numerical simulations. In this study, it is confirmed that the quantized voltage at which the zero-crossing step appears can be controlled by the number of the additional pulses without changing current bias range. The case in which the additional pulses having small fluctuations in phase is also considered. No visible effect of the fluctuations on the current position of the Shapiro steps is observed, so that the current range with respect to the phase lock between the Josephson oscillation and the pulse code is determined by the number of pulses.
We have designed and fabricated a Josephson voltage standard where the voltage can be rapidly and continuously programmed by changing the repetition frequency of a pulse drive. Simulations are made to optimize the operating margins of the circuit for different pulse waveforms. The response of a 1000-junction array of Nb-PdAu-Nb junctions is measured, and constant-voltage step heights are characterized as a function the pulse amplitude, pulse width, frequency. A DC bias range of 0.62 mA is demonstrated over a continuous voltage-tunable range from -6.2 mV to +6.5 mV.
We have investigated theoretically the amplitudes of RF- induced constant voltage steps in two-dimensional Josephson tunnel junctions, using both a first-order approximation and a numerical it- eration procedure to calculate the current density distribution in the junction. We use a planar resonator model to analyze the electromag- netic field in the microwave-driven junction. Integrating the local Jo- sephson current density over the junction area yields the total dc current on a chosen Shapiro step. Numerical calculations of the Sha- piro step amplitudes in two-dimensional resonant junctions show a qualitatively different behavior from that in one-dimensional resonant junctions. Depending on the dominant resonant mode, the microwave power dependence of the step amplitude gives a smooth curve without zeros. This behavior is advantageous for biasing the Josephson junc- tion in its maximum step amplitude. The main difference between the results of the first-order approximation and the full theory is that- using the iteration procedure-the Shapiro steps in resonant junctions become asymmetric with respect to the quasi-particle curve. This is due to consideration of the losses and the internal Josephson currents in the numerical iteration procedure of the full theory.
Abstract The dynamics of overdamped Josephson junctions under varying microwave-driving conditions have been studied through numerical simulations using the resistively-shunted junction model, with a focus on primary voltage metrology applications, where a significantly high number of series-connected junctions and stringent uniformity of their electrical parameters are required. The aim is to determine the optimal junction characteristics and external microwave (rf) parameters that maximize the width of quantum voltage levels (Shapiro steps) from order n = 0 to n > 1. Both the rf and dc power requirements, along with the junction parameter spread and power attenuation, are analyzed as key factors that need to be optimized for improved performance of the quantum device. This work aims to advance the development of next-generation programmable Josephson voltage standards with logic architectures that surpass the conventional binary and ternary codifications used in present quantum voltage arrays, while significantly reducing the overall number of junctions as well as the number of sub-arrays and bias lines. Existing technologies exploiting n = 0 and n = ± 1 voltage steps are first discussed and analyzed to verify the validity of the simulation model. They are then further investigated to extend their usability with multi-order quantum steps for n up to 3. From the simulation results, it follows that present junction technologies may be employed with no modifications for the simultaneous operation of quantum steps up to n = 2, although optimal power efficiency would require a retrimming of the junction’s electrical parameters. On the contrary, extending the highest step order to n = 3 strictly requires the junction’s characteristic parameters to be properly adjusted to maintain sustainable power levels as well as acceptable quantum-locking ranges.
We study the effects of thermal noise on the microwave-induced steps of a current-driven Josephson junction using the resistively shunted junction model for the junction. We generalize Stephen's method for calculating the width of the steps to the case of an underdamped junction, and to the case of a subharmonic step, provided that there is no overlapping of different steps. In order to treat the case of overlapping steps we introduce a new approach which enables us to calculate the distribution of fluctuations about as well as the transition rates out of the steps. All our results are usually in the form of explicit analytical expressions that facilitate a comparison with experiments.