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Applied Physics Letters

An inverse ac Josephson effect voltage standard

Mogens T. Levinsen, R. Y. Chiao, M. J. Feldman, B. A. Tucker

Published Dec 1, 1977• 154 citations
Publisher

Abstract

An unbiased Josephson tunnel junction, irradiated with microwaves, can spontaneously develop quantized dc voltages. We explain this effect with reference to the shunted junction model and to analog experiments. This effect may be utilized to significantly improve both the accuracy and the simplicity of the Josephson voltage standard.
DOI
10.1063/1.89520

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We have studied the power dependence of the microwave-induced dc voltages across "unbiased" Pb---Pb oxide---Pb Josephson tunnel junctions and found a systematic dependence. We have also found that the Josephson effect in the form of induced quantum voltages was observable in a large dc magnetic field as high as 0.5 kG, about one-half of the Hc2{H}_{c2}Hc2​ of the superconducting Pb film.
The DC voltage across a Josephson junction is exactly determined by the number of single flux quanta Φ0passing the junction per second. By locking this flux train to an external sinusoidal microwave with the frequency f or a pulse train with the pulse rate f in such a way that one flux quantum is transferred per microwave period or per pulse respectively, the junction DC voltage becomes V=Φ0f in the simplest case. The precision of V is only determined by the uncertainty of the frequency control. As the output voltage is relatively small (V=140μV for f=70GHz), large series arrays of n Josephson junctions must be used to increase the voltage to practical levels V=nΦ0f. With a sinusoidal 70 GHz microwave drive and series arrays of up to 14000 SIS tunnel junctions modern DC voltage standards were developed in the past which may reach a reproducibility of a few parts in 10-10. These standards are commercially available and form the basis of the legal voltage metrology of most of the national laboratories worldwide. Because the reference voltages of these standards are widely overlapping it is difficult to rapidly adjust the desired voltage. It was therefore impossible to use these quantum voltmeters for the precise analysis of AC voltages. For this purpose the arrays had to be modified in many respects. The direct way to generate arbitrary Josephson waveforms V(t) is to rapidly alter the frequency f(t) with respect to the desired waveform V(t)=nf(t)Φ0. It requires a precise flux transfer control over a very wide frequency range.
Chapter deals with Josephson effects, Feynman's derivation of DC and AC Josephson effects, Josephson effects in superfluid helium, calibration invariance, influence of DC magnetic field, temperature dependence of critical current, phase difference electrodynamics in the junction, RCSJ model, voltage-current characteristics, microwave irradiated junction, macroscopic quantum interference, technology, DC voltage standard, sub mm radiation receivers, microwave generators, SQUIDS and its applications.
A theory is presented for the nonequilibrium voltage states of an irradiated Josephson junction shunted by an external resistor but with no external current or voltage biasing. This device, referred to as a free-running Josephson junction, is modeled in a small--radiation-amplitude, deterministic regime extending the previous work of Shenoy and Agarwal. The time-averaged induced voltage is treated as a dynamical variable, the external radiation is modeled as a current source, and the induced junction-radiation vector potential, with and without a mode structure, is treated to first order in the driving currents. A dynamical equation for the time-averaged induced voltage yields a (nonequilibrium) steady-state relation between the time-averaged induced voltage and the incident radiation amplitude valid for a wide range of voltages, including zero. Regions of bistability occur in the voltage--versus--incident-amplitude curves, some of which are dependent on the external resistor. The zero-voltage state breaks down, as the external radiation amplitude is increased, at a critical value of the incident-radiation amplitude inversely proportional to the external resistance.
The unique ability of a Josephson junction to control the flow of magnetic flux quanta leads to a perfect relationship between frequency and voltage. Over the last 30 years, metrology laboratories have used this effect to greatly improve the accuracy of dc voltage standards. More recent research is focused on combining the ideas of digital signal processing with quantum voltage pulses to achieve similar gains in ac voltage metrology. The integrated circuits that implement these ideas are the only complex superconducting electronic devices that have found wide commercial application.