Shaping dual Shapiro steps in Josephson junctions using tailored drives

Recent experimental results have validated a prediction made almost four decades ago, affirming the existence of quantized current steps in Josephson junctions and superconducting nanowires, referred to as dual Shapiro steps[1, 2, 3]. These dual Shapiro steps have potential as a new current standard and, thus, might also allow to close the quantum metrological triangle. This is due to the fact that these steps are spaced apart by 2ef, with e being the elementary charge and f the frequency of the rf drive.

We integrate a dc-SQUID into a high-impedance environment composed of granular aluminum and oxidized titanium to suppress the quantum fluctuations of charge, which would otherwise prevent the occurrence of quantized current steps. First, we demonstrate dual Shapiro steps using an external rf drive with frequencies up to 6 GHz, resulting in current steps up to 2ef ≈ 2 nA. By applying a sawtooth waveform instead of the initially used sinusoidal one the first dual Shapiro step is either enhanced or suppressed, depending on the sign of the sawtooth. When comparing the differential resistance R_diff of the enhanced dual Shapiro step with a step generated by a sinusoidal drive, we observe an increase of R_diff by a factor of ≈ 2.

[1] K. K. Likharev and A. B. Zorin, J. Low Temp. Phys. 59, 347 (1985).

[2] R. S. Shaikhaidarov et al., Nature 608, 45–49 (2022).

[3] N. Crescini et al., Nat. Phys. 19, 851–856 (2023).