Parafermionic zero modes in ultracold bosonic systems

TL;DR

This paper proposes a method to realize parafermionic zero modes in ultracold bosonic systems, specifically within Bose-Einstein condensate trenches in a fractional quantum Hall state, enabling topologically protected degeneracy.

Contribution

It introduces a novel setup for creating parafermions in bosonic ultracold atom systems, advancing the potential for topological quantum computation.

Findings

Parafermionic zero modes are predicted at trench endpoints.

The system exhibits topologically protected degeneracy.

Methods for preparing and detecting these modes are discussed.

Abstract

Exotic topologically protected zero modes with parafermionic statistics (also called fractionalized Majorana modes) have been proposed to emerge in devices fabricated from a fractional quantum Hall system and a superconductor. The fractionalized statistics of these modes takes them an important step beyond the simplest non-Abelian anyons, Majorana fermions. Building on recent advances towards the realization of fractional quantum Hall states of bosonic ultracold atoms, we propose a realization of parafermions in a system consisting of Bose-Einstein-condensate trenches within a bosonic fractional quantum Hall state. We show that parafermionic zero modes emerge at the endpoints of the trenches and give rise to a topologically protected degeneracy. We also discuss methods for preparing and detecting these modes.