Evidence of dual Shapiro steps in a Josephson junctions array

Abstract

The modern primary voltage standard is based on the AC Josephson effect and the ensuing Shapiro steps, where a microwave tone applied to a Josephson junction yields a constant voltage hf /2e (h is Planck's constant and e the electron charge) determined by only the microwave frequency f and fundamental constants 1,2 . Duality arguments for current and voltage 3-9 have long suggested the possibility of dual Shapiro steps-that a Josephson junction device could produce current steps with heights determined only on the applied frequency [10][11][12][13] . In this report, we embed an ultrasmall Josephson junction in a high impedance array of larger junctions to reveal dual Shapiro steps 8 . For multiple frequencies, we detect that the AC response of the circuit is synchronised with the microwave tone at frequency f , and the corresponding emergence of flat steps in the DC response with current 2ef , equal to the tunnelling of a Cooper pair per tone period. This work sheds new light on phase-charge duality, omnipresent in condensed matter physics 14,15 , and extends it to Josephson circuits. Looking forward, it opens a broad range of possibilities for new experiments in the field of circuit quantum electrodynamics 16,17 and is an important step towards the long-sought closure of the quantum metrology electrical triangle [18][19][20] .

Observation of Josephson Harmonics in Tunnel Junctions

“…Tunnel Josephson junctions (JJs), formed by two overlapping superconducting films separated by a thin insulating barrier, have enabled superconducting hardware to become one of the leading platforms for the realization of fault-tolerant quantum computers [1][2][3][4]. JJs are also at the heart of metrological applications [5], such as the definition of the voltage [6] and current standard [7], quantum limited amplification [8], and they enable quantum detectors such as the microwave photon counter [9]. The Josephson current-phase relation (CϕR) constitutes a unique source of lossless non-linearity.…”

“…In general, we expect the inclusion of the harmonics will refine the understanding of superconducting artificial atoms and will directly benefit, among others, qubit gates which rely on higher levels [48], quantum-non-demolition readout [49], and frequency crowding mitigation in quantum processors [50]. Josephson harmonics will probably also have to be accounted for in topological JJ circuits [51][52][53], in parametric pumping schemes employed in microwave amplifiers and bosonic codes [54,55], and in JJ metrological devices [5][6][7][8]. As devices become increasingly sophisticated with progressively smaller error margins, higher-order Josephson harmonics will need to be either engineered and included as an integral part of the device physics, or suppressed via the development of highly uniform and low transparency barriers.…”