Photonic Floquet topological insulators with fluctuations and disorders

We study how the feature of chiral edge transport changes in photonic Floquet topological insulators when the driving is not perfectly periodic and the system is under the effect of disorders. Assuming that the aperiodicity is caused by fluctuations in the driving, we find that the fluctuations with finite correlation time can cause leakage of chiral edge excitations into the bulk of the system. For fluctuations with short correlation time, an effective master equation that captures the leakage of edge excitations is derived. When the correlation time of the fluctuations is longer than the typical time of the system, the lifetime of chiral edge excitations increases as a power of the correlation time. The lifetime of chiral edge excitations is insensitive to disorders with short correlation time, though when the disorder is strong enough, the lifetime of pointlike edge excitations can be several orders of magnitude longer than the lifetime of chiral edge excitations. The loss of photons into environment cannot stop the leakage of photons into the bulk of the system, but it eventually determines the lifetime of the excitation in the system. On the contrary, the chiral edge transport is robust against the quasirandom fluctuations.