Detection of anyon braiding through pump–probe spectroscopy

Abstract

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 e and magnetic m anyonic excitations. While the linear response signal oscillates and decays with time like ∼ t − 1.3 , the amplitude of the nonlinear signal for χ XZZ ( 3 ) features a linear-in-time enhancement at early times and a stronger enhancement t α with α > 1 at later times. The comparison between χ XZZ ( 3 ) , which involves nontrivial braiding of e and m anyons, and χ XXX ( 3 ) 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.