Emulating Non-Abelian Topological Matter in Cold Atom Optical Lattices

TL;DR

This paper explores the possibility of simulating non-Abelian topological states using cold atom optical lattices, highlighting the challenges in achieving the required anisotropic interactions and low temperatures.

Contribution

It analyzes the feasibility of realizing non-Abelian topological order in optical lattices and discusses specific experimental difficulties.

Findings

Current optical lattice setups cannot easily realize the necessary anisotropic hopping.

Achieving the low temperatures needed remains a significant challenge.

Implementation of non-Abelian topological states in cold atoms requires overcoming key technical hurdles.

Abstract

Certain proposed extended Bose-Hubbard models may exhibit topologically ordered ground states with excitations obeying non-Abelian braid statistics. A sufficient tuning of Hubbard parameters could yield excitation braiding rules allowing implementation of a universal set of topologically protected quantum gates. We discuss potential difficulties in realizing a model with a proposed non-Abelian topologically ordered ground state using optical lattices containing bosonic dipoles. Our direct implementation scheme does not realize the necessary anisotropic hopping, anisotropic interactions, and low temperatures.