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

Mark Kremer,Tobias Biesenthal,Matthias Heinrich,Lukas J Maczewsky,Ronny Thomale,Alexander Szameit

doi:10.1038/s41467-018-08104-x

Mark Kremer, Tobias Biesenthal + Show 4 more

Open Access

https://doi.org/10.1038/s41467-018-08104-x

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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.

Highlights

With the discovery of PT -symmetric quantum mechanics, it was shown that even nonHermitian systems may exhibit entirely real eigenvalue spectra
We report on the experimental realization and characterization of a two-dimensional PT -symmetric system by means of photonic waveguide lattices with judiciously designed refractive index landscape and alternating loss
PT -symmetric systems are described by a Hamiltonian that is invariant under parity-time symmetry transformations[1]

Summary

Introduction

With the discovery of PT -symmetric quantum mechanics, it was shown that even nonHermitian systems may exhibit entirely real eigenvalue spectra. They showed that Hamiltonians that are invariant under combined parity-time (PT ) symmetry transformations likewise can exhibit entirely real eigenvalue spectra[2] This insight had a profound impact in the field of photonics, where PT -symmetric potential landscapes can be implemented by appropriately distributing gain and loss for electromagnetic waves[3,4,5]. PT -symmetry has enriched other research fields ranging from PT -symmetric atomic diffusion[16], superconducting wires[17,18], and PT -symmetric electronic circuits[19] To this date, all experimental implementations of PT -symmetric systems have been restricted to one effective spatial dimension, which is mostly due to technological limitations involved in realizing appropriate non-Hermitian potential landscapes. Our approach may even hold the key for realizing two-dimensional PT -symmetry beyond photonics, e.g., in matter waves and electronics

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