# Detecting fractional Josephson effect through $4\pi$ phase slip

## TL;DR

This paper proposes a novel method to detect the fractional Josephson effect in topological superconductors via 4π phase slip, overcoming experimental challenges and enabling potential quantum information applications.

## Contribution

It introduces a scheme using a topological RF SQUID to observe 4π phase slips, providing a practical way to detect Majorana Fermions in nanowire-based systems.

## Key findings

- The detection time for phase slip is much shorter than quasiparticle poisoning time.
- The 4π phase slip can dominate over trivial 2π slips with appropriate nanowire length.
- The method offers a new approach for exploring quantum fluctuations in topological systems.

## Abstract

Fractional Josephson effect is a unique character of Majorana Fermions in topological superconductor system. This effect is very difficult to detect experimentally because of the disturbance of quasiparticle poisoning and unwanted couplings in the superconductor. Here, we propose a scheme to probe fractional DC Josephson effect of semiconductor nanowire-based topological Josephson junction through 4{\pi} phase slip. By exploiting a topological RF SQUID system we find that the dominant contribution for Josephson coupling comes from the interaction of Majorana Fermions, resulting the resonant tunneling with 4{\pi} phase slip. Our calculations with experimentally reachable parameters show that the time scale for detecting the phase slip is two orders of magnitude shorter than the poisoning time of nonequilibrium quasiparticles. Additionally, with a reasonable nanowire length the 4{\pi} phase slip could overwhelm the topological trivial 2{\pi} phase slip. Our work is meaningful for exploring the effect of modest quantum fluctuations of the phase of the superconductor on the topological system, and provide a new method for quantum information processing.