Photonic Topological Insulators Y. Plotnik1, J.M. Zeuner2, M.C. Rechtsman1, Y. Lumer1, S. Nolte2, M. Segev1, A. Szameit2 1Department of Physics, Technion – Israel Institute of Technology, Haifa, Israel 2Institute of Applied Physics, Friedrich-Schiller-Universität, Jena, Germany

Outline What are Topological Insulators? Topological protection of photons? How can we get unidirectional edge states in photonics? Floquet! Description of our experimental system: photonic lattices First observation of topological insulators -This is also the first observation of optical unidirectional edge states in optics! -Future directions

What are Topological insulators? Spin Orbit Interaction: Topological Insulator Scattering protected Edge states Kane and Mele, PRL (2005) Magnetic field: Quantum Hall Effect Unidirectional edge state Von Klitzing et al. PRL (1980) Valance band Conduction band Ef Regular insulator Main characteristics: Edge conductance only Immune to scattering/defects: No back-scattering No scattering into the bulk Only for Topological insulators: No need for external fields

Motivation: No back scattering       No back scattering → Robust Photon transport!

Topological?   Ef   Robust to small changes

For optical frequencies, magnetic response is weak Background: photonic topological protection by magnetic field Wang et. al. Nature (2009) For optical frequencies, magnetic response is weak Raghu, Haldane PRL (2008) Unidirectional edge state: Quantum hall Credit to marin Wang et. al., PRL (2008)

Challenge of scaling down: weak magnetic response

We need a solution without a magnetic field Quantum hall No magnetic field Topological Insulator Kane and Mele, PRL (2005) von Klitzing et. al., PRL (1980) We need a type of Kane-Mele transition, but how, without Kramers’ degeneracy ? (1) Hafezi, Demler, Lukin, Taylor, Nature Phys. (2011): aperiodic coupled resonator system (2) Umucalilar and Carusotto, PRA (2011): using polarization as spin in PCs (3) Fang, Yu, Fan, Nature Photon. (2012): electrical modulation of refractive index in PCs (4) Khanikev et. al. Nature Mat. (2012): birefringent metamaterials

Enter Floquet Topological Insulators We can explicitly break TR by modulating! Gu, Fertig, Arovas, Auerbach, PRL (2011). New Floquet eigenvalue equation: + Kitagawa, Berg, Rudner, Demler, PRB (2010). Lindner, Refael, Galitski, Nature Phys. (2011).

= Experimental system: photonic lattices Array of coupled waveguides Peleg et. al., PRL (2007) Paraxial approximation + + Maxwell Field envelope = Paraxial Schrödinger equation:

+ Helical rotation induces a gauge field Paraxial Schrödinger equation Coordinate Transformation + Tight Binding Model (Peierls substitution)

Graphene opens a Floquet gap for helical waveguides Band gap ky kx Edge states Top edge Bottom edge kxa kxa

Experimental results: rectangular arrays Microscope image No scattering from the corner Armchair edge confinement

“Time”-domain simulations

Experimental results: group velocity vs. helix radius, R R = 2µm (c) R = 4µm (d) R = 6µm (e) (b) R = 0µm R = 0µm R = 8µm (f) R =10µm (g) R = 12µm (h) R = 14µm (i) R = 16µm (j) R, b c d e f g h i j R =0 R =10µm

Experimental results: triangular arrays with defects missing waveguide R = 8 µm z = 10cm

Y. Lumer et. al., (in preparation) Interactions: focusing nonlinearity gives solitons Band gap ky kx Bulk! Y. Lumer et. al., (in preparation)

Conclusion and Future work First Optical Topological Insulator First robust one way optical edge states (without any magnetic field!) Future Work: - Non-scattering in optoelectronics - Topological cloak? - Disorder: Topological Anderson insulator? - What effect do interactions have on edge states? - many modes on-site.

Acknowledgments Discussions: Daniel Podolsky

Challenge of scaling down: Faraday effect is weak Largest Verdet constant (e.g. in TGG) is ~100 Optical wavelengths are the key to all nanophotonics applications The effect is too weak. We need another way!

(2) Modulation to break TR Theoretical proposals (1) Two copies of the QHE (2) Modulation to break TR Hafezi, Demler, Lukin, Taylor, Nature Phys. (2005). Fang, Yu, Fan, Nature Photon. (2012). Other theoretical papers in different systems: (3) Koch, Houck, Le Hur, Girvin, PRA (2010): cavity QED system (4) Umucalilar and Carusotto, PRA (2011): using spin as polarization in PCs (5) Khanikev et. al. Nature Mat. (2012): birefringent metamaterials