Observation of dark edge states in parity-time-symmetric quantum dynamics

Abstract

Topological edge states arise in non-Hermitian parity-time ([Formula: see text])-symmetric systems, and manifest themselves as bright or dark edge states, depending on the imaginary components of their eigenenergies. As the spatial probabilities of dark edge states are suppressed during the non-unitary dynamics, it is a challenge to observe them experimentally. Here we report the experimental detection of dark edge states in photonic quantum walks with spontaneously broken [Formula: see text] symmetry, thus providing a complete description of the topological phenomena therein. We experimentally confirm that the global Berry phase in [Formula: see text]-symmetric quantum-walk dynamics unambiguously defines topological invariants of the system in both the [Formula: see text]-symmetry-unbroken and -broken regimes. Our results establish a unified framework for characterizing topology in [Formula: see text]-symmetric quantum-walk dynamics, and provide a useful method to observe topological phenomena in [Formula: see text]-symmetric non-Hermitian systems in general.

Keywords: dark edge states; parity-time symmetry; photonic quantum walks; topological invariants.