Dynamically encircling an exceptional point (EP) in parity-time (PT) symmetric waveguide systems exhibits interesting chiral dynamics that can be applied to asymmetric mode switching for symmetric and anti-symmetric modes. The counterpart symmetry-broken modes (i.e., each eigenmode is localized in one waveguide only), which are more useful for applications such as on-chip optical signal processing, exhibit only non-chiral dynamics and therefore cannot be used for asymmetric mode switching. Here, we solve this problem by resorting to anti-parity-time (anti-PT) symmetric systems and utilizing their unique topological structure, which is very different from that of PT-symmetric systems. We find that the dynamical encircling of an EP in anti-PT-symmetric systems with the starting point in the PT-broken phase results in chiral dynamics. As a result, symmetry-broken modes can be used for asymmetric mode switching, which is a phenomenon and application unique to anti-PT-symmetric systems. We perform experiments to demonstrate the new wave-manipulation scheme, which may pave the way towards designing on-chip optical systems with novel functionalities.

In the past decades, topological concepts have emerged to classify matter states beyond the Ginzburg-Landau symmetry breaking paradigm. The underlying global invariants are usually characterized by integers, such as Chern or winding numbers. Very recently, band topology characterized by non-Abelian topological charges has been proposed, which possess noncommutative and fruitful braiding structures with multiple (>1) bandgaps entangled together. Despite many potential exquisite applications including quantum computations, no experimental observation of non-Abelian topological charges has been reported. Here, we experimentally observe the non-Abelian topological charges in a PT (parity and time-reversal) symmetric system. More importantly, we propose non-Abelian bulk-edge correspondence, where edge states are found to be described by non-Abelian charges. Our work opens the door towards non-Abelian topological phase characterization and manipulation.Topological band theory describes the global topological structure underlying various physical systems, where the interplay between intrinsic spin and external symmetries collectively determines distinct symmetry protected topological phases [1][2][3][4][5][6][7] . Different topological phases are characterized by bulk topological invariants, such as Chern and winding numbers [8][9][10][11] . Until now, most of these are classified into ℤ or ℤ " classes, which are the Abelian groups. The topological charges are commutative and exhibit additive properties. The induced bulk-edge correspondence 1,12,13 also inherits the Abelian nature, with the number of edge states being the difference between the two topological invariants across the domain boundary. This simple yet elegant topological relation serves as an important signature for the prediction and characterization of various topological phases [14][15][16] .Very recently, it is found that symmetry protected topological phases can go beyond the Abelian classifications [17][18][19] . With multiple bandgaps entangled together, the underlying topological invariants are represented by non-Abelian groups, which reveal the underlying braiding topological structures. This leads to interesting observables such as trajectorydependent Dirac node collisions in two-dimensional systems, and admissible nodal line configurations in three-dimension 17,19,20 . Moreover, non-Abelian systems are believed to exhibit many potential applications, such as implementation of fault-tolerant quantum computations 21 . However, the experimental observation of non-Abelian topological charges describing band braiding still remains elusive. And bulk-edge correspondence as the guide principle in topological matters has not yet been discussed in the non-Abelian topological systems. Here, we experimentally demonstrate a three-band PT (parity and time-reversal) symmetric system