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arXiv:2111.01157 · SciPost Physics

Stabilizing the Laughlin state of light: Dynamics of hole fractionalization

Pavel D. Kurilovich, Vladislav D. Kurilovich, José Lebreuilly, S. M. Girvin

Published Nov 14, 2022• 10 citations
arXivHTMLPDF

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.

DOI
10.21468/scipostphys.13.5.107

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We report on the numerically exact simulation of the dissipative dynamics governed by quantum master equations that feature fractional quantum Hall states as unique steady states. In particular, for the paradigmatic Hofstadter model, we show how Laughlin states can be to good approximation prepared in a dissipative fashion from arbitrary initial states by simply pumping strongly interacting bosons into the lowest Chern band of the corresponding single-particle spectrum. While pure (up to topological degeneracy) steady states are only reached in the low-flux limit or for extended hopping range, we observe a certain robustness regarding the overlap of the steady state with fractional quantum Hall states for experimentally well-controlled flux densities. This may be seen as an encouraging step towards addressing the long-standing challenge of preparing strongly correlated topological phases in quantum simulators.
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