Detection of anyon braiding through pump–probe spectroscopy

We show that the braiding of anyons in a quantum spin liquid leaves a distinct dynamical signature in the nonlinear pump-probe response. Using a combination of exact diagonalization and matrix product state techniques, we study the nonlinear pump-probe response of the toric code in a magnetic field, a model with mobile electric <i>e</i> and magnetic <i>m</i> anyonic excitations. While the linear response signal oscillates and decays with time like [Formula: see text], the amplitude of the nonlinear signal for [Formula: see text] features a linear-in-time enhancement at early times and a stronger enhancement [Formula: see text] with [Formula: see text] at later times. The comparison between [Formula: see text], which involves nontrivial braiding of <i>e</i> and <i>m</i> anyons, and [Formula: see text] that involves trivial braiding of the same types of anyons, distinguishes the braiding statistics of anyons. We support our analysis with a hard-core anyon model with statistical gauge fields to develop further insights into the time dependence of the pump-probe response. Pump-probe spectroscopy provides a distinctive new probe of quantum spin liquid states, beyond the inconclusive broad features observed in single spin-flip inelastic neutron scattering.