Microwave signatures of $\mathbb{Z}_{2}$ and $\mathbb{Z}_{4}$ fractional Josephson effects

TL;DR

This paper uses exact diagonalization to study fractional Josephson effects in Kitaev chain junctions, predicting microwave signatures observable in circuit QED setups, with implications for topological quantum systems.

Contribution

It provides a detailed numerical analysis of $ ext{Z}_2$ and $ ext{Z}_4$ fractional Josephson effects in interacting Kitaev chains and predicts measurable microwave signatures.

Findings

Fractional Josephson effects influence cavity frequency shifts.

Time-resolved reflectivity reveals signatures of fractional effects.

Effective theory matches that of quantum spin-Hall edge junctions.

Abstract

We present a many-body exact diagonalization study of the $\mathbb{Z}_2$ and $\mathbb{Z}_4$ Josephson effects in circuit quantum electrodynamics architectures. Numerical simulations are conducted on Kitaev chain Josephson junctions hosting nearest-neighbor Coulomb interactions. The low-energy effective theory of highly transparent Kitaev chain junctions is shown to be identical to that of junctions created at the edge of a quantum spin-Hall insulator. By capacitively coupling the interacting junction to a microwave resonator, we predict signatures of the fractional Josephson effects on the cavity frequency and on time-resolved reflectivity measurements.