TY - JOUR

T1 - Demonstration of dual Shapiro steps in small Josephson junctions

AU - Kaap, Fabian

AU - Kissling, Christoph

AU - Gaydamachenko, Victor

AU - Grünhaupt, Lukas

AU - Lotkhov, Sergey

N1 - Publisher Copyright: © The Author(s) 2024.

PY - 2024/10/9

Y1 - 2024/10/9

N2 - 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 $e$, $I=\pm n \times 2ef$, where $n$ is a natural number. Here, we realize this fundamental relation by synchronizing the Bloch oscillations in small Al/AlO$_\mathrm{x}$/Al Josephson junctions to sinusoidal drives with frequencies varying from $1$ to $6\:\mathrm{GHz}$ and observe dual Shapiro steps up to $I\approx 3 \: \mathrm{nA}$. Inspired by today's voltage standards and to further confirm the duality relation, we investigate a pulsed drive regime, which is dual to the single flux quantum mode of Josephson oscillations, and observe a similar 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.

AB - 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 $e$, $I=\pm n \times 2ef$, where $n$ is a natural number. Here, we realize this fundamental relation by synchronizing the Bloch oscillations in small Al/AlO$_\mathrm{x}$/Al Josephson junctions to sinusoidal drives with frequencies varying from $1$ to $6\:\mathrm{GHz}$ and observe dual Shapiro steps up to $I\approx 3 \: \mathrm{nA}$. Inspired by today's voltage standards and to further confirm the duality relation, we investigate a pulsed drive regime, which is dual to the single flux quantum mode of Josephson oscillations, and observe a similar 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.

KW - cond-mat.mes-hall

KW - cond-mat.supr-con

KW - quant-ph

UR - http://www.scopus.com/inward/record.url?scp=85206065782&partnerID=8YFLogxK

U2 - 10.1038/s41467-024-53011-z

DO - 10.1038/s41467-024-53011-z

M3 - Article

VL - 15

JO - Nature Communications

JF - Nature Communications

SN - 2041-1723

IS - 1

M1 - 8726

ER -