Raman spectroscopy of anyons in generic Kitaev spin liquids

Optical probes have emerged as versatile tools for detecting exotic fractionalized phases in quantum materials. We calculate the low-energy Raman response arising from mobile, interacting Ising anyons (or visons) in the chiral Kitaev spin liquid perturbed by symmetry allowed interactions - a phase relevant to \rucl. under a magnetic field. At zero temperature, the two-anyon continuum response shows a leading power-law scaling of the intensity near the onset of the signal: $I(\omega) \sim (\omega-E^0_{2\sigma})^{\frac{1}{8}}$ for linear and parallel-circular polarization channels, where $E^0_{2\sigma}$ is the two-particle gap. Strong corrections due to short-range interactions arise at order $\frac{1}{4}$. For cross-circularly polarized channels, the scaling is given by $I(\omega) \sim (\omega-E^0_{2\sigma})^{|l\pm 1/8|}$, where the value of $l=0,1,2$ is determined by the number of minima in the single anyon dispersion. The exponents are directly related to the topological spin of Ising anyons $\theta_\sigma =\frac{\pi}{8}$, describing their exchange statistics. Our theory generalizes to spectral probes of anyonic quasiparticles with multiple band minima in other quantum liquids. Interaction between anyons may also induce bound-states, resulting in sharp peaks that show strong polarization dependence.