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Particle loss is the ultimate challenge for preparation of stronglycorrelated many-body states of photons. An established way to overcome the lossis to employ a stabilization setup that autonomously injects new photons inplace of the lost ones. However, as we show, the effectiveness of such astabilization setup is compromised for fractional quantum Hall states. There, ahole formed by a lost photon can separate into several remote quasiholes noneof which can be refilled by injecting a photon locally. By deriving an exactexpression for the steady-state density matrix, we demonstrate that isolatedquasiholes proliferate in the steady state which damages the quality of thestate preparation. The motion of quasiholes leading to their separation isallowed by a repeated process in which a photon is first lost and then quicklyrefilled in the vicinity of the quasihole. We develop the theory of thisdissipative quasihole dynamics and show that it has diffusive character. Ourresults demonstrate that fractionalization might present an obstacle for bothcreation and stabilization of strongly-correlated states with photons.

Stabilizing the Laughlin state of light: dynamics of hole fractionalization