Nonlinear Photonic Topological Insulators

• Applicant: Professor Alexander Szameit, Ph.D.
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2017 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 388976608

• Final Report Year: 2024

Final Report Abstract

With the discovery of topological insulators (TIs), materials science ushered in a new era of physics. Solid state TIs prohibit electrons from traversing the bulk while simultaneously supporting chiral surface currents that are topologically protected from scattering at defects and disorder. Soon after their first realizations in condensed matter systems, topological concepts were implemented across other fields of physics, resulting in the experimental demonstrations of topological dynamics in various platforms, in particular photonics. While the original proposals of TIs in the context of condensed matter were purely linear effects, recently ongoing efforts have been directed towards connecting topology and nonlinearity. Such physics may enable topological Mott insulators, interaction-induced TIs such as the Kondo insulator, and non-Abelian TIs. However, before this project started work on nonlinear TIs and their corresponding robust edge transport has thus far had to cope with various limitations of the respective implementations that only allowed for experiments with purely linear edge state dynamics. With this project, we entered uncharted territory and explored theoretically and experimentally the physics of nonlinear (photonic) TIs. Our results opened a new frontier in TI research by demonstrating, among other things, the first nonlinear-induced TI, the first nonlinear higherorder TI, and the first observation of nonlinear dynamics in non-Hermitian topological systems.

Publications

• Demonstration of a two-dimensional PT-symmetric crystal. Nature Communications, 10(1).
  Kremer, Mark; Biesenthal, Tobias; Maczewsky, Lukas J.; Heinrich, Matthias; Thomale, Ronny & Szameit, Alexander
  
• Experimental Realization of PT-Symmetric Flat Bands. Physical Review Letters, 123(18).
  Biesenthal, Tobias; Kremer, Mark; Heinrich, Matthias & Szameit, Alexander
  
• A square-root topological insulator with non-quantized indices realized with photonic Aharonov-Bohm cages. Nature Communications, 11(1).
  Kremer, Mark; Petrides, Ioannis; Meyer, Eric; Heinrich, Matthias; Zilberberg, Oded & Szameit, Alexander
  
• Bragg solitons in topological Floquet insulators. Optics Letters, 45(8), 2271.
  Ivanov, S. K.; Kartashov, Y. V.; Maczewsky, L. J.; Szameit, A. & Konotop, V. V.
  
• Edge solitons in Lieb topological Floquet insulator. Optics Letters, 45(6), 1459.
  Ivanov, Sergey K.; Kartashov, Yaroslav V.; Maczewsky, Lukas J.; Szameit, Alexander & Konotop, Vladimir V.
  
• Fermionic time-reversal symmetry in a photonic topological insulator. Nature Materials, 19(8), 855-860.
  Maczewsky, Lukas J.; Höckendorf, Bastian; Kremer, Mark; Biesenthal, Tobias; Heinrich, Matthias; Alvermann, Andreas; Fehske, Holger & Szameit, Alexander
  
• Nonlinearity-induced photonic topological insulator. Science, 370(6517), 701-704.
  Maczewsky, Lukas J.; Heinrich, Matthias; Kremer, Mark; Ivanov, Sergey K.; Ehrhardt, Max; Martinez, Franklin; Kartashov, Yaroslav V.; Konotop, Vladimir V.; Torner, Lluis; Bauer, Dieter & Szameit, Alexander
  
• Vector Topological Edge Solitons in Floquet Insulators. ACS Photonics, 7(3), 735-745.
  Ivanov, Sergey K.; Kartashov, Yaroslav V.; Szameit, Alexander; Torner, Lluis & Konotop, Vladimir V.
  
• Floquet Edge Multicolor Solitons. Laser & Photonics Reviews, 16(3).
  Ivanov, Sergey K.; Kartashov, Yaroslav V.; Szameit, Alexander; Torner, Lluis & Konotop, Vladimir V.
  
• Nonlinear second-order photonic topological insulators. Nature Physics, 17(9), 995-1000.
  Kirsch, Marco S.; Zhang, Yiqi; Kremer, Mark; Maczewsky, Lukas J.; Ivanov, Sergey K.; Kartashov, Yaroslav V.; Torner, Lluis; Bauer, Dieter; Szameit, Alexander & Heinrich, Matthias
  
• Nonlinear tuning of PT symmetry and non-Hermitian topological states. Science, 372(6537), 72-76.
  Xia, Shiqi; Kaltsas, Dimitrios; Song, Daohong; Komis, Ioannis; Xu, Jingjun; Szameit, Alexander; Buljan, Hrvoje; Makris, Konstantinos G. & Chen, Zhigang
  
• Topological dipole Floquet solitons. Physical Review A, 103(5).
  Ivanov, Sergey K.; Kartashov, Yaroslav V.; Heinrich, Matthias; Szameit, Alexander; Torner, Lluis & Konotop, Vladimir V.