The ac Josephson effect, realised in a tunnel junction between two superconductors separated by an insulating barrier, gives rise to an average voltage dependent only on the Planck constant, h, the electron charge, e and the frequency, f, of the microwave power used to bias the junction.

V­_J = hf / 2e

The constant of proportionality between voltage and frequency is called the Josephson constant so that

V_J = K_J^-1 f

This equation is used to maintain a representation of the SI Volt using an internationally agreed value

K­_J-90 = 483 597.9 GHz V^-1

Figure 1 Current-Voltage characteristic of four junctions connected in series when biased at 70 GHz

In operation, the Josephson junctions that we use are simultaneously biased with a microwave power at 70 GHz and a dc current.

If the dc current is varied, a current-voltage or I-V curve is produced (Figure 1).

Constant-voltage regions can be seen at zero and ±V_J.

This is an example of a damped Josephson junction and exhibits a single-valued I-V curve with no hysteresis.

Figure 2 Binary-divided array showing dc bias connections for waveform generation (microwave bias is not shown). Generated voltage appears at terminals b-c

The voltage across a single junction is only of the order 100 µV but can be increased by connecting several Josephson junctions in series. An array of 8192 junctions, when biased at a frequency of 70 GHz will produce an output of approximately 1.2 V.

If the array is sub-divided in a binary fashion, with individual taps for the dc bias currents, then a digital to analogue converter can be created with perfect linearity and quantum accuracy (Figure 2).

If a digital pattern is loaded into the bias source, then a waveform consisting of discrete levels can be generated.

This is the fundamental principle of our quantum voltage synthesizer.

People working on the project

• Jonathan Williams
• Dale Henderson

Recent publications

Application of a Josephson quantum voltage source to the measurement of microsecond timescale settling time on the Agilent 3458A 8.5 digit voltmeter
D. Henderson, J. M. Williams and T. Yamada
Meas. Sci. Technol. 23, 124006 (2012)

Quantum-referenced voltage waveform synthesiser
J. M. Williams, D. Henderson, J. Pickering, R. Behr, F. Muller, P. Scheibenreiter
IET Science Measurement & Technology 5, 163 (2011)

Development of a 60 Hz power standard using SNS programmable Josephson voltage standards
C. J. Burroughs, S. P. Benz, P. D. Dresselhaus, B. C. Waltrip, T. L. Nelson, Y. Chong, J. M. Williams, D. Henderson, P. Patel, L. Palafox, R. Behr
IEEE Transactions On Instrumentation And Measurement 56, 289 (2007)

Achieving sub-100-ns switching of programmable Josephson arrays
J. M. Williams, D. Henderson, P. Patel, R. Behr, L. Palafox
IEEE Transactions On Instrumentation And Measurement 56, 651 (2007)