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arXiv · 2503.22792

Detection of anyon braiding through pump-probe spectroscopy

Xu Yang·Ryan Buechele·Nandini Trivedi
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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 which hosts mobile electric $e$ and magnetic $m$ anyonic excitations. While the linear response signal oscillates and decays with time like $\sim t^{-1.3}$, the amplitude of the nonlinear signal for $χ^{(3)}_{XZZ}$ features a linear-in-time enhancement at early times. The comparison between $χ^{(3)}_{XZZ}$, which involves the non-trivial braiding of $e$ and $m$ 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. 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.

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Xu Yang, Ryan Buechele, Nandini Trivedi. 2025-04-21. Detection of anyon braiding through pump-probe spectroscopy. https://doi.org/10.1073/pnas.2511917122

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