Synthesis and observation of non-Abelian gauge fields in real space

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Science  06 Sep 2019:
Vol. 365, Issue 6457, pp. 1021-1025
DOI: 10.1126/science.aay3183

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An optical contortionist

The development of gauge fields is fundamental to our theoretical understanding of interactions in physical systems. There are two kinds of fields: Abelian, in which the measured effects on an observable parameter are commutative; and non-Abelian (noncommutative), where the sequence in which the field is applied matters. The latter are more difficult to realize in solid-state systems, but recent theoretical work has suggested that these could be synthesized optically. Yang et al. generated non-Abelian gauge fields by cascading multiple nonreciprocal optical elements and verified this accomplishment by the observed interference patterns in a Sagnac interferometer. Having a system that is tunable between Abelian and non-Abelian regimes will be important for studying complex topological states in photonic platforms.

Science, this issue p. 1021


Particles placed inside an Abelian (commutative) gauge field can acquire different phases when traveling along the same path in opposite directions, as is evident from the Aharonov-Bohm effect. Such behaviors can get significantly enriched for a non-Abelian gauge field, where even the ordering of different paths cannot be switched. So far, real-space realizations of gauge fields have been limited to Abelian ones. We report an experimental synthesis of non-Abelian gauge fields in real space and the observation of the non-Abelian Aharonov-Bohm effect with classical waves and classical fluxes. On the basis of optical mode degeneracy, we break time-reversal symmetry in different manners, via temporal modulation and the Faraday effect, to synthesize tunable non-Abelian gauge fields. The Sagnac interference of two final states, obtained by reversely ordered path integrals, demonstrates the noncommutativity of the gauge fields. Our work introduces real-space building blocks for non-Abelian gauge fields, relevant for classical and quantum exotic topological phenomena.

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