# Demonstration of a two-dimensional ${\cal P}{\cal T}$-symmetric crystal

M. Kremer, T. Biesenthal, L. J. Maczewsky, M. Heinrich, R. Thomale, and A. Szameit

## Abstract

With the discovery of ${\cal P}{\cal T}$-symmetric quantum mechanics, it was shown that even non-Hermitian systems may exhibit entirely real eigenvalue spectra. This finding did not only change the perception of quantum mechanics itself, it also significantly influenced the field of photonics. By appropriately designing one-dimensional distributions of gain and loss, it was possible to experimentally verify some of the hallmark features of ${\cal P}{\cal T}$-symmetry using electromagnetic waves. Nevertheless, an experimental platform to study the impact of ${\cal P}{\cal T}$-symmetry in two spatial dimensions has so far remained elusive. We break new grounds by devising a two-dimensional ${\cal P}{\cal T}$-symmetric system based on photonic waveguide lattices with judiciously designed refractive index landscape and alternating loss. With this system at hand, we demonstrate a non-Hermitian two-dimensional topological phase transition that is closely linked to the emergence of topological mid-gap edge states.