Measuring Anyonic Exchange Phases Using Two-Dimensional Coherent Spectroscopy

TL;DR

This paper proposes using two-dimensional coherent spectroscopy to detect fractional exchange statistics of anyons, including non-Abelian types, by analyzing nonlinear response functions and their threshold behaviors.

Contribution

It extends previous linear response methods to nonlinear spectroscopy, providing a new approach to identify and distinguish non-Abelian anyons through correlation function analysis.

Findings

Nonlinear response functions encode fractional exchange statistics.

Threshold behavior reveals topological charge combinations.

Numerical simulations confirm detection of Abelian and non-Abelian anyons.

Abstract

Identifying experimental signatures of anyons, which exhibit fractional exchange statistics, remains a central challenge in the study of two-dimensional topologically ordered systems. Previous theoretical work has shown that the threshold behavior in linear response spectroscopy can reveal the fractional exchange statistics between an anyon and its antiparticle. In this work, we extend this framework to nonlinear, two-dimensional coherent spectroscopy. We demonstrate by analyzing time-ordered four-point correlation functions that the threshold behavior of nonlinear response functions encodes the fractional statistics between general pairs of anyons that can combine to any composite topological charge. This feature in particular provides a powerful probe for unambiguously distinguishing non-Abelian anyons, which can form multiple composite charges with distinct nontrivial braid statistics. Our approach is validated using numerical simulations that are consistent with the correct fractional exchange statistics for both the Abelian anyons in the toric code and non-Abelian Ising anyons.