Suppression of 2\pi\ phase-slip due to hidden zero modes in one dimensional topological superconductors

TL;DR

This paper investigates phase slips in one-dimensional topological superconductors, revealing their suppression due to hidden zero modes, which enhances qubit stability and suggests experimental verification methods.

Contribution

It uncovers the role of hidden zero modes in suppressing 2π phase slips in topological superconductors, providing new insights into their decoherence resistance.

Findings

Phase slips occur in multiples of 4π in topological superconductors.

Hidden zero modes explain the suppression of 2π phase slips.

Proposed experimental setup to test phase-slip suppression.

Abstract

We study phase slips in one-dimensional topological superconducting wires. These wires have been proposed as building blocks for topologically protected qubits in which the quantum information is distributed over the length of the device and thus is immune to local sources of decoherence. However, phase-slips are non-local events that can result in decoherence. Phase slips in topological superconductors are peculiar for the reason that they occur in multiples of 4\pi\ (instead of 2\pi\ in conventional superconductors). We re-establish this fact via a beautiful analogy to the particle physics concept of dynamic symmetry breaking by explicitly finding a "hidden" zero mode in the fermion spectrum computed in the background of a 2\pi\ phase-slip. Armed with the understanding of phase-slips in topological superconductors, we propose a simple experimental setup with which the predictions can be tested by monitoring tunneling rate of a superconducting flux quantum through a topological superconducting wire.