Light propagation in locally symmetric arrays of waveguides

• Applicants: Professor Dr. Peter Schmelcher; Professor Alexander Szameit, Ph.D.
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2016 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 314425454

• Final Report Year: 2022

Final Report Abstract

This project in the framework of the Deutsche Forschungsgemeinschaft has pushed forward the frontiers of our understanding and design of local symmetries both from the theoretical as well as experimental side. On the one hand side the theory of local symmetries including operator representations and continuity equations has been developed for discrete systems, which is quite different from the continuous case. Systematically introducing local symmetries in disordered systems it has been shown how extended states emerge and contribute to the transfer efficiency in an array. Strikingly, local symmetries can be identified and processed via graph theory thereby yielding a deep understanding of their appearance and impact on the spectral properties. Compact localized states and resultingly flat bands emerge due to local symmetries and can be systematically designed. As an extension, again motivated by recent developments in graph theory, so-called latent symmetries have been shown to provide another important pathway for the system design and their properties. On the experimental side, we were able to push our abilities significantly beyond the former technological state-of-the-art. during the course of the project we were not only able to implement local symmetries, but also to explore novel experimental techniques to realize mapping from higher-dimensions, system optimization procedures using quantum metric, and the engineering of (the joint) phase transition of complex intrinsic symmetries. This achievements are now the basis for our ongoing efforts to implement hidden (latent) symmetries for the first time in physics, using an optical platform.

Publications

• Non-Local Currents and the Structure of Eigenstates in Planar Discrete Systems with Local Symmetries, Annals of Physics 380, 135 (2017)
  M. Röntgen, C.V. Morfonios, F.K. Diakonos and P. Schmelcher
  
• Nonlocal Discrete Continuity and Invariant Currents in Locally Symmetric Effective Schrödinger Arrays, Annals of Physics 385, 623 (2017)
  C.V. Morfonios, P.A. Kalozoumis, F.K. Diakonos and P. Schmelcher
  
• Compact Localized States and Flat Bands from Local Symmetry Partitioning, Physical Review B 97, 035161 (2018)
  M. Röntgen, C.V. Morfonios and P. Schmelcher
  
• Optimal design strategy for non-Abelian geometric phases using Abelian gauge fields based on quantum metric, Phys. Rev. Research 1, 033117 (2019)
  M. Kremer, L. Teuber, A. Szameit, and S. Scheel
  
• Experimental study of the interplay between dynamic localization and Anderson localization, Opt. Lett. 45, 415 (2020)
  D. Guzman-Silva, M. Heinrich, T. Biesenthal, Y. V. Kartashov, and A. Szameit
  
• Non-adiabatic dynamicphase-free geometric phase in multiport photonic lattices, J. Opt. 22, 035801(2020)
  K. Wang, A. Perez-Leija, S. Weimann, and A. Szameit
  
• Observation of Local Symmetry in Photonic Systems, Laser and Photonics Reviews 14, 1900222 (2020)
  N. Schmitt, S. Weimann, C.V. Morfonios, M. Röntgen, M. Heinrich, P. Schmelcher and A. Szameit
  
• Synthesizing multi-dimensional excitation dynamics and localization transition in one-dimensional lattices, Nature Photon. 14, 76 (2020)
  L. J. Maczewsky, K. Wang, A. A. Dovgiy, A. E. Miroshnichenko, A. Moroz, M. Ehrhardt, M. Heinrich, D. N. Christodoulides, A. Szameit, and A. A. Sukhorukov
  
• Topological state engineering via supersymmetric transformations, Commun. Phys. 3, 49 (2020)
  G. Queralto, M. Kremer, L. J. Maczewsky, M. Heinrich, J. Mompart, V. Ahufinger, and A. Szameit
  
• Transfer Efficiency Enhancement and Eigenstate Properties in Locally Symmetric Disordered Finite Chains, Annals of Physics 418, 168163 (2020)
  C.V. Morfonios, M. Röntgen, F.K. Diakonos and P. Schmelcher
  
• Flat Bands by Latent Symmetry, Physical Review B 104, 035105 (2021)
  C.V. Morfonios, M. Röntgen, M. Pyzh and P. Schmelcher
  
• Observation of photonic constant-intensity waves and induced transparency in tailored non-Hermitian lattices, subm. f. publ. Sci. Adv. (2022)
  A. Steinfurth, I. Kresic, S. Weidemann, M. Kremer, K. G. Makris, M. Heinrich, S. Rotter, and A. Szameit
  
• Topological triple phase transition in non-Hermitian Floquet quasicrystals, Nature 601, 354 (2022)
  S. Weidemann, M. Kremer, S. Longhi und A. Szameit