Pump-Probe Spectroscopy for Anyon Braiding

Anyons are fractionalized quasiparticles with nontrivial braiding statistics that emerge in a variety of topologically ordered phases. Understanding and controlling the braiding of anyons in topological materials has been proposed as a route to realize fault tolerant quantum computation. Until now, signatures of anyon braiding have only been seen through interfering chiral edge modes of fractional quantum Hall states. Detection of anyons in quantum spin liquids instead requires a bulk spectroscopic technique. We present results of exact diagonalization and time-evolution block decimation calculations of a pump-probe experiment on the 1-dimensional quantum Ising chain and 2-dimensional Kitaev honeycomb model in a field perpendicular to the honeycomb lattice. We find that the nonlinear response function shows a distinct signature of long-time divergence, suppressed by a beat pattern due to the finite size of the simulated system. This behavior results from nontrivial braiding of quasiparticles induced by the pump pulse with those created by the probe pulse. We will further present results on the differences in the nonlinear response in the Abelian and non-Abelian Kitaev quantum spin liquid phases.