# Differentiating Majorana from Andreev Bound States in a Superconducting Circuit

## TL;DR

This paper explores how charge fluctuations in a topological Josephson junction can be used to distinguish Majorana bound states from Andreev bound states through unique spectroscopic signatures.

## Contribution

It introduces a low-energy theoretical framework linking microscopic bound states to macroscopic phase dynamics for state identification.

## Key findings

- Distinct spectroscopic patterns differentiate Majorana from Andreev bound states.
- Charge fluctuations provide a viable probe for microscopic excitations.
- The approach enhances the ability to detect Majorana fermions in superconducting circuits.

## Abstract

We investigate the low-energy theory of a one-dimensional finite capacitance topological Josephson junction. Charge fluctuations across the junction couple to resonant microwave fields and can be used to probe microscopic excitations such as Majorana and Andreev bound states. This marriage between localized microscopic degrees of freedom and macroscopic dynamics of the superconducting phase, leads to unique spectroscopic patterns which allow us to reveal the presence of Majorana fermions among the low-lying excitations.