Demonstration of dual Shapiro steps in small Josephson junctions

Bloch oscillations in small Josephson junctions were predicted theoretically as the quantum dual to Josephson oscillations. A significant consequence of this prediction is the emergence of quantized current steps, so-called dual Shapiro steps, when synchronizing Bloch oscillations to an external microwave signal. These steps potentially enable a fundamental standard of current I, defined via the frequency f of the external signal and the elementary charge e, I = +/- n x 2ef, where n is a natural number. Here, we realize this fundamental relation by synchronizing the Bloch oscillations in small Al/AlOx/Al Josephson junctions to sinusoidal drives with frequencies from 1 to 6 GHz and observe dual Shapiro steps up to I approximate to 3 nA. Inspired by today's voltage standards and to further confirm the duality relation, we investigate a pulsed drive regime and observe an asymmetric pattern of dual Shapiro steps. This work confirms quantum duality effects in Josephson junctions and paves the way towards a range of applications in quantum metrology based on well-established fabrication techniques and straightforward circuit design. Biasing a Josephson junction embedded in a high impedance environment with a dc-current results in small voltage oscillations. Here, the authors demonstrate that when those oscillations are locked to an external rf-signal, it results in the creation of quantized current steps, the so-called dual Shapiro steps.