Coherent generation of photonic fractional quantum Hall states in a cavity and the search for anyonic quasiparticles

TL;DR

This paper proposes a protocol for creating and detecting fractional quantum Hall states and anyons in a polariton cavity system, advancing experimental techniques for topological quantum states.

Contribution

It introduces a coherent, adiabatic protocol for generating Laughlin states and braiding anyons in a cavity polariton system, with detailed measurement schemes.

Findings

Protocol enables creation of fractional quantum Hall states in polariton systems.

Braiding of anyons is demonstrated through local pinning potentials.

Experimental feasibility is discussed with specific interaction-to-decay ratio requirements.

Abstract

We present and analyze a protocol in which polaritons in a noncoplanar optical cavity form fractional quantum Hall states. We model the formation of these states and present techniques for subsequently creating anyons and measuring their fractional exchange statistics. In this protocol, we use a rapid adiabatic passage scheme to sequentially add polaritons to the system, such that the system is coherently driven from $n$- to $(n+1)$-particle Laughlin states. Quasiholes are created by slowly moving local pinning potentials in from outside the cloud. They are braided by dragging the pinning centers around one another, and the resulting phases are measured interferometrically. The most technically challenging issue with implementing our procedure is that maintaining adiabaticity and coherence requires that the two-particle interaction energy $V_0$ be sufficiently large compared to the single-polariton decay rate $\gamma$, $V_0 /\gamma \gg 10 N^2 \ln N$, where $N$ is the number of particles in the target state. While this condition is very demanding for present-day experiments where $V_0 /\gamma\sim 50$, our protocol presents a significant advance over the existing protocols in the literature.