Creating and manipulating non-Abelian anyons in cold atom systems using auxiliary bosons

TL;DR

This paper proposes a method to create and manipulate non-Abelian anyons in cold atom systems by using auxiliary bosons to capture quasiholes, enabling the generation of non-Abelian quasiholes of the Moore-Read Pfaffian state with potential experimental applications.

Contribution

It introduces a novel approach using auxiliary bosons and three-body interactions to produce and verify non-Abelian quasiholes in cold atom systems, advancing quantum simulation capabilities.

Findings

Two-quasihole states with non-Abelian fusion channels demonstrated

Measurement of auxiliary bosons' relative angular momentum reveals non-Abelian properties

Feasibility analysis for experimental realization in cold atom systems

Abstract

The possibility of realizing bosonic fractional quantum Hall effect in ultra-cold atomic systems suggests a new route to producing and manipulating anyons, by introducing auxiliary bosons of a different species that capture quasiholes and thus inherit their non-trivial braiding properties. States with localized quasiholes at any desired locations can be obtained by annihilating the auxiliary bosons at those locations. We explore how this method can be used to generate non-Abelian quasiholes of the Moore-Read Pfaffian state for bosons at filling factor $\nu=1$. We show that a Hamiltonian with an appropriate three-body interaction can produce two-quasihole states in two distinct fusion channels of the topological "qubit." Characteristics of these states that are related to the non-Abelian nature can be probed and verified by a measurement of the effective relative angular momentum of the auxiliary bosons, which is directly related to their pair distribution function. Moore-Read states of more than two quasiholes can also be produced in a similar fashion. We investigate some issues related to the experimental feasibility of this approach, in particular, how large the systems should be for a realization of this physics and to what extent this physics carries over to systems with the more standard two-body contact interaction.