Photonic Floquet topological insulators

Abstract

Topological insulators are a new phase of matter1, with the striking property that conduction of electrons occurs only on their surfaces1,2,3. In two dimensions, electrons on the surface of a topological insulator are not scattered despite defects and disorder, providing robustness akin to that of superconductors. Topological insulators are predicted to have wide-ranging applications in fault-tolerant quantum computing and spintronics. Substantial effort has been directed towards realizing topological insulators for electromagnetic waves4,5,6,7,8,9,10,11,12,13. One-dimensional systems with topological edge states have been demonstrated, but these states are zero-dimensional and therefore exhibit no transport properties11,12,14. Topological protection of microwaves has been observed using a mechanism similar to the quantum Hall effect15, by placing a gyromagnetic photonic crystal in an external magnetic field5. But because magnetic effects are very weak at optical frequencies, realizing photonic topological insulators with scatter-free edge states requires a fundamentally different mechanism—one that is free of magnetic fields. A number of proposals for photonic topological transport have been put forward recently6,7,8,9,10. One suggested temporal modulation of a photonic crystal, thus breaking time-reversal symmetry and inducing one-way edge states10. This is in the spirit of the proposed Floquet topological insulators16,17,18,19, in which temporal variations in solid-state systems induce topological edge states. Here we propose and experimentally demonstrate a photonic topological insulator free of external fields and with scatter-free edge transport—a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges. Our system is composed of an array of evanescently coupled helical waveguides20 arranged in a graphene-like honeycomb lattice21,22,23,24,25,26. Paraxial diffraction of light is described by a Schrödinger equation where the propagation coordinate (z) acts as ‘time’27. Thus the helicity of the waveguides breaks z-reversal symmetry as proposed for Floquet topological insulators. This structure results in one-way edge states that are topologically protected from scattering.