Non-Abelian Phenomena and Chern-Euler Duality Transitions in Dissipative Photonic Systems

Free University of Berlin

Topology leads to many robustly quantized physical properties. In solids, topological phenomena appear in Bloch states of nearly free electrons moving in a periodic potential. Recently, periodic media enable photons to carry modulated momenta. These systems have highly tunable band structures and when dissipation is considered, their dynamics are generically described by non-Hermitian matrices. In this presentation, I will demonstrate how the level crossings between such photonic bands, known as exceptional points, are carrying non–Abelian charges. This leads to non-commuting operations of moving them in the reciprocal space and violation of the fermion-doubling theorem, realised in recent experiments. Then I will introduce parity-time symmetric systems, which have two very distinct regimes: symmetry-preserving regime and spontaneous-symmetry-breaking regime. I will show that their transition is described by a rule of topological duality. The Chern numbers of the system in the spontaneous-symmetry-breaking regime must match the Euler numbers in the symmetry-preserving regime. The transition is characterised by qualitative changes in non-Abelian geometric phases and provides new ideas to engineer distinct topological phenomena.