Quantized Angular Momentum in Topological Optical Systems

The Chern index characterizes the topological phases of nonreciprocal photonic systems. Unlike in electronic systems, the photonic Chern number has no clear physical meaning, except that it determines the net number of unidirectional edge states supported by an interface with a trivial mirror. Here, we fill in this gap by demonstrating that the photonic Chern number can be understood as a quantum of the light-angular momentum in a photonic insulator cavity. It is proven that for a large cavity, when the discrete spectrum can be approximated by a continuum, the spectral density of the thermal fluctuation-induced angular momentum is precisely quantized in the band-gaps of the bulk states. The nontrivial expectation of the light angular momentum is due to a circulation of thermal energy in closed orbits. Remarkably, this result can be extended to systems without a topological classification, and in such a case the "quantum" of the angular momentum density is determined by the net number of unidirectional edge states supported by the cavity walls.