Transconductance quantization in a topological Josephson tunnel junction circuit

L Peyruchat,J Griesmar,J.-D Pillet,Ç Ö Girit

doi:10.1103/physrevresearch.3.013289

Abstract

Superconducting circuits incorporating Josephson tunnel junctions are widely used for fundamental research as well as for applications in fields such as quantum information and magnetometry. The quantum coherent nature of Josephson junctions makes them especially suitable for metrology applications. Josephson junctions suffice to form two sides of the quantum metrology triangle, relating frequency to either voltage or current, but not its base, which directly links voltage to current. We propose a five Josephson tunnel junction circuit in which simultaneous pumping of flux and charge results in quantized transconductance in units 4e2/h=2e/Φ0, the ratio between the Cooper pair charge and the flux quantum. The Josephson quantized Hall conductance device (JHD) is explained in terms of intertwined Cooper pair pumps driven by the AC Josephson effect. We describe an experimental implementation of the device and discuss the optimal configuration of external parameters and possible sources of error. The JHD has a rich topological structure and demonstrates that Josephson tunnel junctions are universal, capable of interrelating frequency, voltage, and current via fundamental constants.1 MoreReceived 25 September 2020Revised 1 February 2021Accepted 2 February 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.013289Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectrical conductivityGeometric & topological phasesJosephson effectQuantum metrologyQuantum transportTopological materialsTopological phase transitionPhysical SystemsJosephson junctionsSuperconducting devicesCondensed Matter, Materials & Applied PhysicsQuantum Information

Highlights

Among quantum coherent electronic components, the most prominent are Josephson junctions and quantum Hall systems
The topology of the Josephson quantized Hall conductance device (JHD) and isolated Cooper pair pump (CPP) can be compared to understand why flux and charge are pumped in the JHD and only charge is pumped in the CPP
The JHD bias voltages VL,R result in both parameters φL, φR crossing the Brillouin zone boundary

Summary

INTRODUCTION

Among quantum coherent electronic components, the most prominent are Josephson junctions and quantum Hall systems. Due to their nonlinearity, serve as the qubit building blocks of superconducting quantum computers [1] and sensitive magnetometers [2] In metrology, this nonlinearity, the Josephson relation, allows employing such junctions to define the voltage standard, with an accuracy much better than parts per billion [3,4]. With recent graphene-based standards, it is possible to reduce the required magnetic field to several tesla and increase the operating temperature up to 10 k [9] In these semiconducting systems, the relevant resistance is the von Klitzing constant RK = h/e2, and is quantized on the order of parts per billion. Is the Hamiltonian for our device completely different from that of Andreev-based systems, engineering the circuit is relatively easy as the required technology is mature, there are less constraints on the circuit dimensions, no junction requires more than two terminals, and the junction transparencies may be small

FLUX AND CHARGE QUANTIZATION

DISCUSSION