Topologically protected bound states in photonic parity-time-symmetric crystals.

Parity-time (PT)-symmetric crystals are a class of non-Hermitian systems that allow, for example, the existence of modes with real propagation constants, for self-orthogonality of propagating modes, and for uni-directional invisibility at defects. Photonic PT-symmetric systems that also support topological states could be useful for shaping and routing light waves. However, it is currently debated whether topological interface states can exist at all in PT-symmetric systems. Here, we show theoretically and demonstrate experimentally the existence of such states: states that are localized at the interface between two topologically distinct PT-symmetric photonic lattices. We find analytical closed form solutions of topological PT-symmetric interface states, and observe them through fluorescence microscopy in a passive PT-symmetric dimerized photonic lattice. Our results are relevant towards approaches to localize light on the interface between non-Hermitian crystals.

[1]  Charles L Fefferman,et al.  Topologically protected states in one-dimensional continuous systems and Dirac points , 2014, Proceedings of the National Academy of Sciences.

[2]  S. Roth,et al.  Solitons in polyacetylene , 1987 .

[3]  M. Segev,et al.  Observation of parity–time symmetry in optics , 2010 .

[4]  Z. Musslimani,et al.  Theory of coupled optical PT-symmetric structures. , 2007, Optics letters.

[5]  M. Hafezi,et al.  Imaging topological edge states in silicon photonics , 2013, Nature Photonics.

[6]  Henning Schomerus,et al.  Topologically protected midgap states in complex photonic lattices. , 2013, Optics letters.

[7]  Gennady Shvets,et al.  Photonic topological insulators. , 2012, Nature materials.

[8]  M. Segev,et al.  Photonic Floquet topological insulators , 2012, Nature.

[9]  Stefano Longhi,et al.  Optical realization of relativistic non-Hermitian quantum mechanics. , 2010, Physical review letters.

[10]  Eisenberg,et al.  Diffraction management , 2000, Physical review letters.

[11]  Tilman Esslinger,et al.  Experimental realization of the topological Haldane model with ultracold fermions , 2014, Nature.

[12]  C. Bender,et al.  Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry , 1997, physics/9712001.

[13]  M. Soljačić,et al.  Topological photonics , 2014, Nature Photonics.

[14]  Z. Musslimani,et al.  Beam dynamics in PT symmetric optical lattices. , 2008, Physical review letters.

[15]  A. Szameit,et al.  Quasi PT ?> -symmetry in passive photonic lattices , 2014, 1401.2299.

[16]  Mohammad Hafezi,et al.  Robust optical delay lines with topological protection , 2011, 1102.3256.

[17]  Alexander Szameit,et al.  Photonic Topological Insulators , 2014, CLEO 2014.

[18]  M. Segev,et al.  Self-localized states in photonic topological insulators. , 2013, Physical review letters.

[19]  Y. Wang,et al.  Single-mode laser by parity-time symmetry breaking , 2014, Science.

[20]  D. Christodoulides,et al.  Parity-time–symmetric microring lasers , 2014, Science.

[21]  C. Kane,et al.  Topological Insulators , 2019, Electromagnetic Anisotropy and Bianisotropy.

[22]  Ulrich Kuhl,et al.  Selective enhancement of topologically induced interface states in a dielectric resonator chain , 2014, Nature Communications.

[23]  A. Szameit,et al.  Impact of loss on the wave dynamics in photonic waveguide lattices. , 2014, Physical review letters.

[24]  U. Peschel,et al.  Parity–time synthetic photonic lattices , 2012, Nature.

[25]  I. Carusotto,et al.  Artificial gauge field for photons in coupled cavity arrays , 2011, 1104.4071.

[26]  M. Soljačić,et al.  Reflection-free one-way edge modes in a gyromagnetic photonic crystal. , 2007, Physical review letters.

[27]  Natalia Malkova,et al.  Observation of optical Shockley-like surface states in photonic superlattices. , 2009, Optics letters.

[28]  G. Montambaux,et al.  Zak phase and the existence of edge states in graphene , 2011, 1109.4608.

[29]  C. Yuce.  PT symmetric Floquet topological phase , 2015, 1507.01415.

[30]  S. Raghu,et al.  Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. , 2008, Physical review letters.

[31]  Zongfu Yu,et al.  Realizing effective magnetic field for photons by controlling the phase of dynamic modulation , 2012, Nature Photonics.

[32]  R. Morandotti,et al.  Observation of PT-symmetry breaking in complex optical potentials. , 2009, Physical review letters.

[33]  R. El-Ganainy,et al.  Optical solitons in PT periodic potentials , 2008, 2008 Conference on Lasers and Electro-Optics and 2008 Conference on Quantum Electronics and Laser Science.

[34]  Yize Jin,et al.  Topological insulators , 2014, Topology in Condensed Matter.

[35]  Z. Musslimani,et al.  Optical Solitons in PT Periodic Potentials , 2008 .

[36]  Zhenghao Gu,et al.  Floquet spectrum and transport through an irradiated graphene ribbon. , 2011, Physical review letters.

[37]  Andreas Tünnermann,et al.  Quasi-incoherent propagation in waveguide arrays , 2007 .

[38]  Stefan Nolte,et al.  Discrete optics in femtosecond-laser-written photonic structures , 2010 .

[39]  Takuya Kitagawa,et al.  Topological Characterization of Periodically-Driven Quantum Systems , 2010, 1010.6126.

[40]  A. Szameit,et al.  Mobility transition from ballistic to diffusive transport in non-Hermitian lattices , 2013, Nature Communications.

[41]  P. Jarillo-Herrero,et al.  Observation of Floquet-Bloch States on the Surface of a Topological Insulator , 2013, Science.

[42]  M. Kohmoto,et al.  Edge states and topological phases in non-Hermitian systems , 2011, 1107.2079.

[43]  A. Szameit,et al.  Radiation-loss management in modulated waveguides. , 2014, Optics letters.

[44]  Gil Refael,et al.  Floquet topological insulator in semiconductor quantum wells , 2010, 1008.1792.

[45]  Tony E. Lee,et al.  PT-breaking threshold in spatially asymmetric Aubry-André and Harper models: Hidden symmetry and topological states , 2016 .

[46]  Stefan Nolte,et al.  Observation of a Topological Transition in the Bulk of a Non-Hermitian System. , 2015, Physical review letters.

[47]  C. Yuce.  Topological phase in a non-Hermitian PT symmetric system , 2015, 1502.07160.

[48]  Zak,et al.  Berry's phase for energy bands in solids. , 1989, Physical review letters.

[49]  T. Hughes,et al.  Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians , 2011, 1107.1064.

[50]  Shachar Klaiman,et al.  Visualization of branch points in PT-symmetric waveguides. , 2008, Physical review letters.

[51]  Liang Feng,et al.  Robust Light State by Quantum Phase Transition in Non-Hermitian Optical Materials , 2015, Scientific Reports.

[52]  M K Moravvej-Farshi,et al.  Optical isolation via 𝒫 𝒯 -symmetric nonlinear Fano resonances. , 2014, Optics express.

[53]  Zheng Wang,et al.  Observation of unidirectional backscattering-immune topological electromagnetic states , 2009, Nature.

[54]  Camille Jouvaud,et al.  Robust reconfigurable electromagnetic pathways within a photonic topological insulator. , 2016, Nature materials.