Pfaffian States in Coupled Atom-Cavity Systems

TL;DR

This paper demonstrates how to generate effective three-body interactions in coupled atom-cavity systems, enabling the realization of Pfaffian-like ground states associated with non-abelian excitations in fractional quantum Hall physics.

Contribution

It introduces a method to produce effective three-body interactions in cavity QED systems, facilitating the simulation of non-abelian fractional quantum Hall states.

Findings

Effective 3-body interactions can be engineered in cavity QED.

A Pfaffian-like ground state exists in these systems.

Potential for emulating non-abelian anyonic states.

Abstract

Coupled atom-cavity arrays, such as those described by the Jaynes-Cummings Hubbard model, have the potential to emulate a wide range of condensed matter phenomena. In particular, the strongly correlated states of the fractional quantum Hall effect can be realised. At some filling fractions, the fraction quantum Hall effect has been shown to possess ground states with non-abelian excitations. The most well studied of these states is the Pfaffian state of Moore and Read, which is the groundstate of a Hall Liquid with a 3-body interaction. In this paper we show how an effective 3-body interaction can be generated within the Cavity QED framework, and that a Pfaffian-like groundstate of these systems exists.