Non-Abelian monopoles in the multiterminal Josephson effect

TL;DR

This paper provides a theoretical analysis of Andreev bound states in multiterminal Josephson junctions, revealing non-Abelian monopoles with potential applications in topological quantum computing.

Contribution

It introduces a symmetry-constrained scattering matrix approach to identify non-Abelian SU(2) monopoles in the spectral properties of these junctions, linking topology and quantum states.

Findings

Identification of non-Abelian SU(2) monopoles in Andreev band crossings

Proposal for detecting topological defects via nonlinear current autocorrelation measurements

Multiterminal Josephson devices as platforms for holonomic quantum computation

Abstract

In this work we present a detailed theoretical analysis for the spectral properties of Andreev bound states in the multiterminal Josephson junctions by employing a symmetry-constrained scattering matrix approach. We find that in the synthetic multidimensional space of superconducting phases, crossings of Andreev bands may support non-Abelian SU(2) monopoles with a topological charge characterized by the second class Chern number. We propose that these topological defects can be detected via a nonlinear response measurement of the current autocorrelations. In addition, multiterminal Josephson junction devices can be tested as a hardware platform for realizing holonomic quantum computation.