# Spectral response of Josephson junctions with low-energy quasiparticles

## TL;DR

This paper investigates how low-energy quasiparticles, including Majorana modes, influence the spectral response of nanowire-based Josephson junctions, combining advanced numerical and analytical methods to inform experimental qubit research.

## Contribution

It extends existing models to include Majorana quasiparticles and provides detailed spectral analysis using matrix-product state techniques and perturbation theory.

## Key findings

- Low-energy quasiparticles significantly alter the junction's spectrum.
- Majorana modes induce characteristic features in the spectral response.
- The developed models aid interpretation of experimental data.

## Abstract

We study nanowire-based Josephson junctions shunted by a capacitor and take into account the presence of low-energy quasiparticle excitations. These are treated by extending conventional models used to describe superconducting qubits to include the coherent coupling between fermionic quasiparticles, in particular the Majorana zero modes that emerge in topological superconductors, and the plasma mode of the junction. Using accurate, unbiased matrix-product state techniques, we compute the energy spectrum and response function of the system across the topological phase transition. Furthermore, we develop a perturbative approach, valid in the harmonic limit with small charging energy, illustrating how the presence of low-energy quasiparticles affects the spectrum and response of the junction. Our results are of direct interest to on-going experimental investigations of nanowire-based superconducting qubits.