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IEEE Transactions on Applied Superconductivity

Numerical simulation of quantized voltage steps in overdamped josephson junctions controlled by simple pulse codes

A. Takada

Published Dec 1, 2003• 0 citations
Publisher

Abstract

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.

DOI
10.1109/tasc.2003.820504

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In this paper, quantized voltage steps were observed by driving an overdamped Josephson junction array (JJA) with current pulse trains. The current pulse trains were generated by triggering a metal-semiconductor-metal photodetector installed close to JJA at 4.2 K with a mode-locked fiber laser. The intervals of the constant voltage steps were 10 muV, which agrees with the repetition frequency of the light source (49.7 MHz) and the number of Josephson junctions (100) in the JJA. This is the first step toward establishing an ac voltage standard at the National Institute of Advanced Industrial Science and Technology
On an asymmetric two-junction superconducting quantum interference device (2J-SQUID) driven by one sinusoidal rf signal, the observation of zero-crossing Shapiro steps have been reported. In this paper, the loop inductance, L and the ratio of critical currents of Josephson junctions of the 2J-SQUID were optimized by a simulation. Using three voltage states those this asymmetric 2J-SQUID has, the bipolar quantum voltage generator that has three asymmetric 2J-SQUIDs and two control lines, was designed based on obtained parameters. Within the bias current -voltage curves with seven different combinations of the control currents, seven quantized voltages were obtained at the zero bias current.
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.
Abstract Bloch oscillations in small Josephson junctions were predicted theoretically as the quantum dual to Josephson oscillations. A significant consequence of this prediction is the emergence of quantized current steps, so-called dual Shapiro steps, when synchronizing Bloch oscillations to an external microwave signal. These steps potentially enable a fundamental standard of current I, defined via the frequency f of the external signal and the elementary charge e, I = ± n × 2ef, where n is a natural number. Here, we realize this fundamental relation by synchronizing the Bloch oscillations in small Al/AlOx/Al Josephson junctions to sinusoidal drives with frequencies from 1 to 6 GHz and observe dual Shapiro steps up to I ≈ 3 nA. Inspired by today’s voltage standards and to further confirm the duality relation, we investigate a pulsed drive regime and observe an asymmetric pattern of dual Shapiro steps. This work confirms quantum duality effects in Josephson junctions and paves the way towards a range of applications in quantum metrology based on well-established fabrication techniques and straightforward circuit design.
We demonstrate a zero-crossing Shapiro step generated in a magnetically-coupled Josephson gate, where a long Josephson junction and a control line are placed in-line. The operation is based on the imbalanced evolution of the junction phases owing to the different amplitudes of the positive and negative critical current. A test circuit was fabricated using a Nb/AlOx/Nb junction technology. When we applied a rf signal of 15.2GHz, we observed a Shapiro step that crossed the zero-current axis at the voltage position of the 1st order. The experimental results were quantitatively reproduced by simulation.
We demonstrate a zero-crossing Shapiro step in a three-junction SQUID (3J-SQUID) coupled with two phase-shifted RF signals. The operation is based on periodic flux quantum transitions in the 3J-SQUID under the zero- and negatively-biasing conditions. A test circuit is fabricated using a Nb/AlO/sub x//Nb junction technology. When we feed RF signals up to 10.5 GHz, we observe a Shapiro step crossing the zero-current axis at the voltage position of the 1st order. The experimental current-voltage characteristics are quantitatively reproduced by simulation. Zero-crossing conditions for the DC offset flux and the RF power are obtained experimentally, which is also confirmed by simulation. A programmable Josephson voltage standard is discussed as one of the possible applications.