Measuring Anyonic Exchange Phases Using Two-Dimensional Coherent Spectroscopy

• URL: http://arxiv.org/abs/2511.17420v1
• Date: Fri, 21 Nov 2025 17:18:20 GMT
• Title: Measuring Anyonic Exchange Phases Using Two-Dimensional Coherent Spectroscopy
• Authors: Nico Kirchner, Wonjune Choi, Frank Pollmann,
• Abstract summary: We show that threshold behavior of nonlinear response functions encodes the fractional statistics between general pairs of anyons that can combine to any composite topological charge.<n>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.
• Score: 0.003748389192021574
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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