I will discuss how pump-probe non-linear spectroscopy provides a distinctive new probe of quantum spin liquid states, beyond the inconclusive broad features observed in single spin flip inelastic neutron scattering. While the linear response signal oscillates and decays with time, the amplitude of the nonlinear signal for χ(3)XZZ signal features a linear-in-time enhancement at early times. Here XZZ are the directions of pump, probe, and measurement magnetic fields. The comparison between χ(3)XZZ, which involves the non-trivial braiding of electric e and magnetic m anyons, and χ(3)XXX that involves the trivial braiding of the same types of anyons, serves to distinguish the braiding statistics of anyons. We support our analysis by constructing a hard-core anyon model with statistical gauge fields to develop further insights into the time dependence of the pump-probe response.