Circular Dichroism on the Edge of Quantum Hall Systems: From Many-Body Chern Number to Anisotropy Measurements

Quantum Hall states are characterized by a topological invariant, the many-body Chern number, which determines their quantized Hall conductivity. This invariant also emerges in circular dichroic responses, namely, by applying a circular drive and comparing excitation rates for opposite orientations. This work explores the dichroic response of confined, isolated quantum Hall systems, where bulk and edge contributions cancel exactly: When the edge response is properly isolated, the circular dichroic signal becomes quantized, serving as a direct and elegant probe of the many-body Chern number encoded in the edge physics. We demonstrate that this quantized edge response is entirely captured by low-energy chiral edge modes, allowing for a universal description of this effect based on Wen's edge theory. Its low-energy nature implies that the quantized edge response can be distinguished from the bulk response in the frequency domain. The edge response is also shown to be a sensitive diagnostic of geometric features. This opens the possibility of characterizing the shape of quantum Hall droplets through edge spectroscopic measurements, without requiring knowledge of the system's boundary profile. We illustrate our findings using realistic models of integer and fractional Chern insulators, with different edge geometries, and propose detection schemes suitable for ultracold atoms.