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Quantized current steps due to the a.c. coherent quantum phase-slip effect


The a.c. Josephson effect predicted in 19621 and observed experimentally in 19632 as quantized ‘voltage steps’ (the Shapiro steps) from photon-assisted tunnelling of Cooper pairs is among the most fundamental phenomena of quantum mechanics and is vital for metrological quantum voltage standards. The physically dual effect, the a.c. coherent quantum phase slip (CQPS), photon-assisted tunnelling of magnetic fluxes through a superconducting nanowire, is envisaged to reveal itself as quantized ‘current steps’3,4. The basic physical significance of the a.c. CQPS is also complemented by practical importance in future current standards, a missing element for closing the quantum metrology triangle5,6. In 2012, the CQPS was demonstrated as superposition of magnetic flux quanta in superconducting nanowires 7. However, the direct flat current steps in superconductors, the only unavailable basic effect of superconductivity to date, was unattainable due to lack of appropriate materials and challenges in circuit engineering. Here we report the direct observation of the dual Shapiro steps in a superconducting nanowire. The sharp steps are clear up to 26 GHz frequency with current values 8.3 nA and limited by the present set-up bandwidth. The current steps were theoretically predicted in small Josephson junctions 30 years ago5. However, unavoidable broadening in Josephson junctions prevents their direct experimental observation8,9. We solve this problem by placing a thin NbN nanowire in an inductive environment.

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Fig. 1: Principles of the microwave-induced transport in dual circuits.
Fig. 2: Device and transport.
Fig. 3: Inverse Shapiro steps in four-probe IV measurements.
Fig. 4: Oscillations of dV/dI peaks.

Data availability

The datasets used to produce the plots are available in the Open Science Framework (OSF) repository,


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This work was supported by European Union’s Horizon 2020 Research and Innovation Programme under grant agreement no. 862660/QUANTUM E-LEAPS and Engineering and Physical Sciences Research Council (EPSRC) grant no. EP/T004088/1.

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Authors and Affiliations



O.V.A. proposed, simulated and planned the experiment and circuit design and analysed data. R.S.S. made the major contribution to the design and fabrication of various samples, planned the experiment and analysed data. R.S.S. made the experiments with an important contribution from K.H.K. J.W.D., I.V.A., V.N.A. and K.H.K. designed and fabricated samples, analysed data and prepared figures. S.L., M.Z. and E.V.I. developed technology and M.Z. and S.L. fabricated NbN films. D.S.G. provided theory and simulations of the experiment. O.V.A., E.V.I., D.S.G. and V.N.A. wrote the manuscript.

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Correspondence to Oleg V. Astafiev.

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Shaikhaidarov, R.S., Kim, K.H., Dunstan, J.W. et al. Quantized current steps due to the a.c. coherent quantum phase-slip effect. Nature 608, 45–49 (2022).

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