A photonic thermalization gap in disordered lattices

The formation of gaps – forbidden ranges in the values of a physical parameter – is a ubiquitous feature of a variety of physical systems: from energy bandgaps of electrons in periodic lattices and their analogs in photonic, phononic, and plasmonic systems to pseudo energy gaps in aperiodic quasicrystals. Here, we report on a thermalization' gap for light propagating in finite disordered structures characterized by disorder-immune chiral symmetry -- the appearance of the eigenvalues and eigenvectors in skew-symmetric pairs. In this class of systems, the span of sub- thermal photon statistics is inaccessible to input coherent light, which -- once the steady state is reached -- always emerges with super-thermal statistics no matter how small the disorder level. We formulate an independent constraint that must be satisfied by the input field for the chiral symmetry to be activated’ and the gap to be observed. This unique feature enables a new form of photon-statistics interferometry: the deterministic tuning of photon statistics – from sub-thermal to super-thermal – in a compact device, without changing the disorder level, via controlled excitation-symmetry-breaking realized by sculpting the amplitude or phase of the input coherent field.