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IntroductionThe Josephson effect has revolutionised accurate electrical measurement. Practical systems based on arrays of junctions have provided calibration of dc voltage for 25 years. In this paper, we present the design of a system able to deliver quantum accurate measurements of not only dc voltage, but of arbitrary voltage waveforms in real time. This is achieved by utilising the property of a Josephson junction whereby a current pulse applied to the junction leads to a quantised voltage-time integral pulse. By averaging these pulses over a defined period of time, a quantum accurate voltage is obtained. We describe how by using a novel optoelectronic coupling to Josephson junctions arrays (JJAs), macroscopic voltage levels ( > 1V) will be achieved.

Quantum Electrical Metrology

Dissemination of quantum accurate dc voltage and resistance is routinely achieved via the Josephson effect and quantum Hall resistance respectively. Worldwide research effort (e.g. [1]) is underway to develop a quantum current standard to complete the quantum metrological triangle. However, ac voltage calibration is reliant on a classical thermal transfer method. There is increasing demand from industry to be able to provide ac voltage calibration of high performance A/D and D/A converters which requires a quantum accurate arbitrary voltage waveform.

AC voltage metrology: Method 1

Quantum accurate sinusoidal voltage waveforms have been demonstrated using programmable, binary segmented JJAs up to kHz frequencies [2]. A binary bias source switches on appropriate segments of the array to achieve the required voltage. However, this technology is not suitable for higher frequencies since the JJA takes several 100 ns to stabilise after switching.

AC voltage metrology: Method 2

The advantage of the pulse-driven JJAs, used here, is that they can operate at higher frequencies with hundreds of kHz being demonstrated (for a review see [3]). An arbitrary current pulse applied to the JJA generates a voltage pulse of quantised area (e.g. [4]). The desired quantum accurate voltage output is generated by applying an appropriate sequence of pulses to the JJA.

Array Design

JJAs are fabricated by Physikalisch-Technische Bundesanstalt (PTB), Germany. They consist of SNSNS junctions, where S is superconductor (Nb) and N is normal metal (NbSi), which are linked in a “double-stacked” design. These JJAs operate at 4.2 K in a liquid helium cryostat. Low pass filtering of the output is provided on-chip.

Novel optoelectronic coupling

An optoelectronic input, using a photodiode (PD) can be used to drive the JJA [5]. Several JJAs can then be connected in series to provide a larger (industrial level) output voltage whilst being driven in parallel. Optoelectronic coupling also reduces the electrical noise transmitted from the room temperature electronics.

Quantum Voltage Digitiser

The quantum voltage digitiser uses a delta sigma control loop to measure an arbitrary voltage waveform in terms of the JJA output. The comparator output is used to generate a pulse stream which drives a Mach-Zehnder modulator, creating a GHz rate pulse stream of optical pulses which provide the JJA drive via a photodiode located inside the cryostat. The resultant output (fast, quantised-area voltage pulses) are fed back around the loop via a low pass filter.

Preliminary Data

The temporal response of a commercial InGaAs photodiode was characterised at room temperature under a variety of conditions (spot size, spot position, over-filled mode, under-filled mode, power levels, and frequency) and was found to be suitable for driving the JJAs.

AcknowledgmentsThis work was co-funded by the European Union within the European Metrology Research Program (EMRP) joint research project SIB59 Q-WAVE and by the UK National Measurement Office Electromagnetics and Time Program. The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union.

References[1] S. P. Giblin, M. Kataoka, J. D. Fletcher, P. See, T. J. B. M. Janssen, J. P. Griffiths, G. A. C. Jones, I. Farrer, D. A. Ritchie, “Towards a quantum representation of the ampere using single electron pumps.,” Nat. Commun., 3:930 doi: 10.1038/ncomms1935 (2012).

[2] J. M. Williams, D. Henderson, J. Pickering, R. Behr, F. Muller and P. Scheibenreiter, “Quantum-referenced voltage waveform synthesizer,” IET Sci. Meas. Technol., Vol. 5, no. 5, pp. 163 – 174 (2011).

[3] R. Behr, O. Kieler, J. Kohlmann, F. Müller and L. Palafox, “Development and metrological applications of Josephson arrays at PTB,” Meas. Sci. Technol., Vol. 23, no. 12, 124002 (19 pp.) (2012).

[4] S. P. Benz, P. D. Dresselhaus, A. Rüfenacht, N. F. Bergren, J. R. Kinard and R. Landim, “Progress toward a 1 V pulse-driven AC Josephson voltage standard,” IEEE Trans. Instrum. Meas., Vol. 58, no. 4, pp. 838 – 843 (2009).

[5] J. M. Williams, T. J. B. M. Janssen, L. Palafox, D. A. Humphreys, R. Behr, J. Kohlmann and F. Muller, “The simulation and measurement of the response of Josephson junctions to optoelectronically generated short pulses”, Supercond. Sci. Technol., Vol. 17, no. 6, pp. 815 – 818 (2004).

Quantum Accurate Measurement of Arbitrary Voltage Waveforms Using Pulse-Driven

Josephson Junction ArraysJane Ireland1, Jonathan Williams1, Oliver Kieler2, Johannes Kohlmann2,

Ralf Behr2, Jarle Gran3, Helge Malmbekk3, Kåre Lind3 and Chi Kwong Tang3

1 National Physical Laboratory, Queens Road, Teddington, Middlesex, TW11 0LW, UK 2 Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany

3 Justervesenet, P.O. Box 170, NO-2027 Kjeller, Norway

jane.ireland@npl.co.uk