Rostock 2019 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 36: Photonics II

Q 36.3: Talk

Wednesday, March 13, 2019, 14:30–14:45, S Gr. HS Maschb.

Non-Abelian geometric phases in photonics and their optimal design strategy based on quantum metric — •Lucas Teuber, Mark Kremer, Alexander Szameit, and Stefan Scheel — Institut für Physik, Universität Rostock, Albert-Einstein-Str. 23, 18059 Rostock, Germany.

We showed in a proof-of-principle experiment how to synthesize a non-Abelian geometric phase in a system of photonic waveguides that possesses a degenerate dark subspace. A cyclic adiabatic evolution in this subspace then results in a matrix-valued and thus non-Abelian geometric phase. The crucial condition of adiabaticity is fulfilled by optimization of the waveguide structure utilizing the so-called quantum metric. Based on this metric we established a distance measure on the underlying control parameter manifold, i.e. the manifold of waveguide couplings. Minimizing this measure along the cyclic evolution under additional experimental constraints yields the optimally adiabatic process. Our results prove the possibility to implement a non-Abelian geometric phase in a photonic system and showcase the quantum-metric-based optimization of an adiabatic process.