Stabilization of Fractional Quantum Hall States of Light: Effects of Fractionalization

Recently, the possibility of realizing strongly-correlated states of matter with photons has started to become an experimental reality. In combination with artificial gauge fields this paves the way to simulation of fractional quantum Hall states with light. A major hindrance to such simulations is the inevitable dissipation of photons into the environment which creates holes in the correlated state. The leakage of light can be counteracted by a stabilization scheme in which lost particles are irreversibly refilled. We investigate the efficiency of such a scheme for the preparation of a photonic Laughlin state at half-filling. We explore the limitations imposed by the ability of holes in the Laughlin state to fractionalize into several spatially separated quasiholes. Quasiholes correspond to the absence of a fraction of a particle and thus cannot be refilled efficiently. We find that the fractionalization drastically restricts the steady-state fidelity of the Laughlin state and leads to a long relaxation time in the system.