Evidence of dual Shapiro steps in a Josephson junction array

The modern primary voltage standard is based on the a.c. Josephson effect and the ensuing Shapiro steps, where a microwave tone applied to a Josephson junction yields a constant voltage h f /2 e determined by only the microwave frequency f , Planck’s constant h and the electron charge e . Duality arguments for current and voltage have long suggested the possibility of dual Shapiro steps—that a Josephson junction device could produce current steps with heights determined only by the applied frequency. Here we embed an ultrasmall Josephson junction in a high impedance array of larger junctions to reveal dual Shapiro steps. For multiple frequencies, we detect that the a.c. response of the circuit is synchronized with the microwave tone at frequency f , and the corresponding emergence of flat steps in the d.c. response with current 2 e f , equal to the transport of a Cooper pair per tone period. This work extends phase–charge duality to Josephson circuits, which opens a broad range of possibilities in the field of circuit quantum electrodynamics and is an important step towards the long-sought closure of the quantum metrology electrical triangle.