Physical Society Colloquium

Tying knots with energy bands: Non-Hermitian topological photonics in synthetic dimensions

Kai Wang

Department of Physics
McGill University

The nontrivial topological features in the energy bands of non-Hermitian systems provide promising pathways to achieve robust physical behaviors in classical or quantum open systems. Recent advances in synthesizing dimensions beyond the spatial degree of freedom, especially in photonics, have provided great flexibility in realizing lattice Hamiltonians. A synthetic-dimension approach to non-Hermitian topology can enable new opportunities for observing non-Hermitian topological effects that are difficult to achieve by other means.

In this colloquium, I will summarize some of our results in the experimental and theoretical exploration of non-Hermitian eigenvalue topology enabled by the concept of synthetic dimensions. I will show our experimental demonstrations of the topological winding of non-Hermitian band energies, achieved by implementing non-Hermitian lattice Hamiltonians along a frequency synthetic dimension formed in a ring resonator undergoing simultaneous phase and amplitude modulations. With two or more non-Hermitian bands, the system can be topologically classified by nontrivial braid groups. By generalizing the experiment to two modulated ring resonators, we demonstrated such braid-group topology with two energy bands braiding around each other, forming nontrivial knots or links.  Furthermore, I will show how such braid-group topology can be generalized to two and three dimensions.