Abstract
A hallmark feature of topological physics is the presence of one-way propagating chiral modes at the system boundary1,2. The chirality of edge modes is a consequence of the topological character of the bulk. For example, in a non-interacting quantum Hall model, edge modes manifest as mid-gap states between two topologically distinct bulk bands. The bulk–boundary correspondence dictates that the number of chiral edge modes, a topological invariant called the winding number, is completely determined by the bulk topological invariant, the Chern number3. Here, for the first time, we measure the winding number in a 2D photonic system. By inserting a unit flux quantum at the edge, we show that the edge spectrum resonances shift by the winding number. This experiment provides a new approach for unambiguous measurement of topological invariants, independent of the microscopic details, and could possibly be extended to probe strongly correlated topological orders.
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Acknowledgements
This research was supported by the Air Force Office of Scientific Research grant no. FA9550-14-1-0267, Army Research Office, Office of Naval Research, Bethe postdoctoral fellowship, National Science Foundation Career grant, Laboratory for Physical Sciences—Condensed Matter Theory Center, Microsoft and the Physics Frontier Center at the Joint Quantum Institute. We thank M. Levin, A. G. Abanov, A. Lobos, A. Migdall and J. Taylor for fruitful discussions and E. Barnes, M. Davanco and E. Goldschmidt for useful comments on the manuscript.
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S.M. and M.H. conceived and designed the experiment. S.M. and J.F. performed the experiment. All authors contributed significantly in analysing the data and editing the manuscript.
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Mittal, S., Ganeshan, S., Fan, J. et al. Measurement of topological invariants in a 2D photonic system. Nature Photon 10, 180–183 (2016). https://doi.org/10.1038/nphoton.2016.10
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DOI: https://doi.org/10.1038/nphoton.2016.10
