Stabilizing the Laughlin state of light: dynamics of hole fractionalization

TL;DR

This paper investigates how photon loss and the resulting quasihole fractionalization hinder the stabilization of fractional quantum Hall states of light, revealing diffusive quasihole dynamics that challenge state preparation.

Contribution

The authors derive an exact steady-state density matrix and develop a theory describing the diffusive dynamics of quasiholes in photon-based fractional quantum Hall states.

Findings

Isolated quasiholes proliferate in the steady state.

Quasihole motion exhibits diffusive behavior.

Photon loss leads to fractionalization obstacles in state stabilization.

Abstract

Particle loss is the ultimate challenge for preparation of strongly correlated many-body states of photons. An established way to overcome the loss is to employ a stabilization setup that autonomously injects new photons in place of the lost ones. However, as we show, the effectiveness of such a stabilization setup is compromised for fractional quantum Hall states. There, a hole formed by a lost photon can separate into several remote quasiholes none of which can be refilled by injecting a photon locally. By deriving an exact expression for the steady-state density matrix, we demonstrate that isolated quasiholes proliferate in the steady state which damages the quality of the state preparation. The motion of quasiholes leading to their separation is allowed by a repeated process in which a photon is first lost and then quickly refilled in the vicinity of the quasihole. We develop the theory of this dissipative quasihole dynamics and show that it has diffusive character. Our results demonstrate that fractionalization might present an obstacle for both creation and stabilization of strongly-correlated states with photons.