Nonlinear Spectroscopy for Anyon Braiding

Anyons are fractionalized quasiparticles with nontrivial braiding statistics that emerge in topologically ordered phases such as fractional quantum Hall states and quantum spin liquids. While anyon braiding has been inferred through interference of chiral edge modes in quantum Hall systems, direct detection of bulk anyons remains a major experimental challenge. We propose and analyze a spectroscopic approach based on pump–probe nonlinear response which can reveal bulk signatures of anyon braiding. Using the Toric Code as a prototypical model, we employ exact diagonalization and infinite density matrix renormalization group techniques to compute the pump-probe response; by analyzing the time scaling of signals for different anyon trajectories, we demonstrate a clear distinction between contributions arising from braiding and those from local scattering of excitations. These findings are corroborated by an effective anyon-hopping model, which allows us to isolate and precisely control the dynamics of anyons on a lattice. Beyond the Toric Code, we extend this framework to study nonlinear anyon dynamics in systems with other Abelian and non-Abelian topological orders, uncovering distinctive signatures associated with different braiding statistics. Our results establish pump–probe spectroscopy as a useful tool for probing bulk anyon dynamics and provide concrete guidance for identifying topological order in candidate materials.