Hall viscosity from metric-sensitive dichroic probes

Abstract

Hall viscosity characterizes the geometric response of a quantum Hall droplet to deformations of the underlying metric, yet it has remained difficult to measure directly. We propose a spectroscopic probe based on circular dichroism, using chiral metric-sensitive drives -- implemented as rotating quadrupolar ("saddle") perturbations -- that effectively modulate the metric and couple to the generators of area-preserving deformations. The resulting dichroic signal directly measures the Hall viscosity, while frequency-resolved spectroscopy disentangles it from other excitations. A local formulation further enables spatially resolved markers of Hall viscosity applicable to both continuum and lattice systems. Our results open a direct route to measuring Hall viscosity in quantum-engineered platforms such as cold atoms in optical lattices.