Comptes Rendus
Photonic topological Anderson insulator in a two-dimensional atomic lattice
Comptes Rendus. Physique, Online first (2023), pp. 1-16.

Disorder in atomic positions can induce a topologically nontrivial phase—topological Anderson insulator (TAI)—for transverse electric optical quasimodes of a two-dimensional honeycomb lattice of immobile atoms. TAI requires both time-reversal and inversion symmetries to be broken to similar extents. It is characterized by a nonzero topological invariant, a reduced density of states and spatially localized quasimodes in the bulk, as well as propagating edge states. A transition from TAI to the topological insulator (TI) phase can take place at a constant value of the topological invariant, showing that TAI and TI represent the same topological phase.

Le désordre dans les positions atomiques peut induire une phase topologiquement non triviale – l’isolant topologique d’Anderson (TAI) - pour les quasi-modes optiques électriques transversaux d’un réseau en nid d’abeille bidimensionnel d’atomes immobiles. Le TAI nécessite que les symétries de renversement du temps et d’inversion soient brisées dans des proportions similaires. Il est caractérisé par un invariant topologique non nul, une densité d’états réduite et des quasi-modes spatialement localisés dans le volume, ainsi que des états de bord propagatifs. Une transition du TAI à la phase d’isolant topologique (TI) peut avoir lieu à une valeur constante de l’invariant topologique, montrant que le TAI et le TI représentent la même phase topologique.

Online First:
DOI: 10.5802/crphys.147
Keywords: Topological photonics, Light scattering by atoms, Disorder, Topological Anderson insulator, Bott index
Mot clés : photonique topologique, diffusion de la lumière par les atomes, désordre, isolant topologique d’Anderson, indice de Bott
Sergey E. Skipetrov 1; Pierre Wulles 1

1 Univ. Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
     author = {Sergey E. Skipetrov and Pierre Wulles},
     title = {Photonic topological {Anderson} insulator in a two-dimensional atomic lattice},
     journal = {Comptes Rendus. Physique},
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Sergey E. Skipetrov; Pierre Wulles. Photonic topological Anderson insulator in a two-dimensional atomic lattice. Comptes Rendus. Physique, Online first (2023), pp. 1-16. doi : 10.5802/crphys.147.

[1] Claude Cohen-Tannoudji; Jacques Dupont-Roc; Gilbert Grynberg Atom-Photon Interactions: Basic Processes and Applications, John Wiley & Sons, 1998 | DOI

[2] Claude Cohen-Tannoudji; David Guéry-Odelin Advances in Atomic Physics: An Overview, World Scientific, 2011 | DOI

[3] E. A. Cornell; C. E. Wieman Nobel Lecture: Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments, Rev. Mod. Phys., Volume 74 (2002) no. 3, pp. 875-893 | DOI

[4] Juliette Billy; Vincent Josse; Zhanchun Zuo; Alain Bernard; Ben Hambrecht; Pierre Lugan; David Clément; Laurent Sanchez-Palencia; Philippe Bouyer; Alain Aspect Direct observation of Anderson localization of matter waves in a controlled disorder, Nature, Volume 453 (2008) no. 7197, pp. 891-894 | DOI

[5] F. Jendrzejewski; A. Bernard; K. Müller; P. Cheinet; Vincent Josse; M. Piraud; L. Pezzé; Laurent Sanchez-Palencia; Alain Aspect; Philippe Bouyer Three-dimensional localization of ultracold atoms in an optical disordered potential, Nature Phys., Volume 8 (2012) no. 5, pp. 398-403 | DOI

[6] Immanuel Bloch; Jean Dalibard; Wilhelm Zwerger Many-body physics with ultracold gases, Rev. Mod. Phys., Volume 80 (2008) no. 3, pp. 885-964 | DOI

[7] Nigel R. Cooper; Jean Dalibard; I. B. Spielman Topological bands for ultracold atoms, Rev. Mod. Phys., Volume 91 (2019) no. 1, 015005, 55 pages | DOI | MR

[8] G. Labeyrie; F. de Tomasi; J.-C. Bernard; C. A. Müller; C. Miniatura; R. Kaiser Coherent Backscattering of Light by Cold Atoms, Phys. Rev. Lett., Volume 83 (1999) no. 25, pp. 5266-5269 | DOI

[9] L. Corman; J. L. Ville; R. Saint-Jalm; M. Aidelsburger; T. Bienaimé; S. Nascimbène; Jean Dalibard; J. Beugnon Transmission of near-resonant light through a dense slab of cold atoms, Phys. Rev. A, Volume 96 (2017) no. 5, 053629, 11 pages | DOI

[10] Robin Kaiser Quantum multiple scattering, J. Mod. Opt., Volume 56 (2009) no. 18-19, pp. 2082-2088 | DOI | Zbl

[11] S. E. Skipetrov; I. M. Sokolov Absence of Anderson Localization of Light in a Random Ensemble of Point Scatterers, Phys. Rev. Lett., Volume 112 (2014) no. 2, 023905, 5 pages | DOI

[12] B. A. van Tiggelen; S. E. Skipetrov Longitudinal modes in diffusion and localization of light, Phys. Rev. B, Volume 103 (2021) no. 17, 174204, 26 pages | DOI

[13] K. v. Klitzing; G. Dorda; M. Pepper New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance, Phys. Rev. Lett., Volume 45 (1980) no. 6, pp. 494-497 | DOI

[14] Klaus von Klitzing; Tapash Chakraborty; Philip Kim; Vidya Madhavan; Xi Dai; James McIver; Yoshinori Tokura; Lucile Savary; Daria Smirnova; Ana Maria Rey; Claudia Felser; Johannes Gooth; Xiaoliang Qi 40 years of the quantum Hall effect, Nat. Rev. Phys., Volume 2 (2020) no. 8, pp. 397-401 | DOI

[15] D. J. Thouless; M. Kohmoto; M. P. Nightingale; M. den Nijs Quantized Hall Conductance in a Two-Dimensional Periodic Potential, Phys. Rev. Lett., Volume 49 (1982) no. 6, pp. 405-408 | DOI

[16] Barry Simon Holonomy, the Quantum Adiabatic Theorem, and Berry’s Phase, Phys. Rev. Lett., Volume 51 (1983) no. 24, pp. 2167-2170 | DOI | MR

[17] Ling Lu; John D. Joannopoulos; Marin Soljačić Topological photonics, Nature Photon., Volume 8 (2014) no. 11, pp. 821-829 | DOI

[18] Tomoki Ozawa; Hannah M. Price; Alberto Amo; Nathan Goldman; Mohammad Hafezi; Ling Lu; Mikael C. Rechtsman; David Schuster; Jonathan Simon; Oded Zilberberg; Iacopo Carusotto Topological photonics, Rev. Mod. Phys., Volume 91 (2019) no. 1, 015006, 76 pages | DOI | MR

[19] Pierre Delplace; J. B. Marston; Antoine Venaille Topological origin of equatorial waves, Science, Volume 358 (2017) no. 6366, pp. 1075-1077 | DOI | MR | Zbl

[20] Jian Li; Rui-Lin Chu; J. K. Jain; Shun-Qing Shen Topological Anderson Insulator, Phys. Rev. Lett., Volume 102 (2009) no. 13, 136806, 4 pages | DOI

[21] Yanxia Xing; Lei Zhang; Jia Wang Topological Anderson insulator phenomena, Phys. Rev. B, Volume 84 (2011) no. 3, 035110, 9 pages | Zbl

[22] Christoph P. Orth; Tibor Sekera; Christoph Bruder; Thomas L. Schmidt The topological Anderson insulator phase in the Kane-Mele model, Sci. Rep., Volume 6 (2016) no. 1, 24007 | DOI

[23] Adhip Agarwala; Vijay B. Shenoy Topological Insulators in Amorphous Systems, Phys. Rev. Lett., Volume 118 (2017) no. 23, 236402, 6 pages | DOI

[24] B. Andrei Bernevig; Taylor L. Hughes Topological Insulators and Topological Superconductors, Princeton University Press, 2013 | DOI

[25] Changxu Liu; Wenlong Gao; Biao Yang; Shuang Zhang Disorder-Induced Topological State Transition in Photonic Metamaterials, Phys. Rev. Lett., Volume 119 (2017) no. 18, 183901, 5 pages | DOI

[26] Simon Stützer; Yonatan Plotnik; Yaakov Lumer; Paraj Titum; Netanel H. Lindner; Mordechai Segev; Mikael C. Rechtsman; Alexander Szameit Photonic topological Anderson insulators, Nature, Volume 560 (2018) no. 7719, pp. 461-465 | DOI

[27] Gui-Geng Liu; Yihao Yang; Xin Ren; Haoran Xue; Xiao Lin; Yuan-Hang Hu; Hong-xiang Sun; Bo Peng; Peiheng Zhou; Yidong Chong; Baile Zhang Topological Anderson Insulator in Disordered Photonic Crystals, Phys. Rev. Lett., Volume 125 (2020) no. 13, 133603, 6 pages | DOI

[28] Peiheng Zhou; Gui-Geng Liu; Xin Ren; Yihao Yang; Haoran Xue; Lei Bi; Longjiang Deng; Yidong Chong; Baile Zhang Photonic amorphous topological insulator, Light. Sci. Appl., Volume 9 (2020) no. 1, 133 | DOI

[29] Xiaohan Cui; Ruo-Yang Zhang; Zhao-Qing Zhang; C. T. Chan Photonic 2 Topological Anderson Insulators, Phys. Rev. Lett., Volume 129 (2022) no. 4, 043902, 7 pages | DOI | MR

[30] J. Perczel; J. Borregaard; D. E. Chang; H. Pichler; S. F. Yelin; P. Zoller; M. D. Lukin Topological Quantum Optics in Two-Dimensional Atomic Arrays, Phys. Rev. Lett., Volume 119 (2017) no. 2, 023603, 6 pages | DOI

[31] S. E. Skipetrov; P. Wulles Topological transitions and Anderson localization of light in disordered atomic arrays, Phys. Rev. A, Volume 105 (2022) no. 4, 043514, 11 pages | DOI

[32] Mauro Antezza; Yvan Castin Photonic band gap in an imperfect atomic diamond lattice: Penetration depth and effects of finite size and vacancies, Phys. Rev. A, Volume 88 (2013) no. 3, 033844, 14 pages | DOI

[33] S. E. Skipetrov Localization of light in a three-dimensional disordered crystal of atoms, Phys. Rev. B, Volume 102 (2020) no. 13, 134206, 6 pages | DOI

[34] Kohei Kawabata; Ken Shiozaki; Masahito Ueda; Masatosh Sato Symmetry and Topology in Non-Hermitian Physics, Phys. Rev. X, Volume 9 (2019) no. 4, 041015, 52 pages | DOI

[35] L. Lepori; L. Dell’Anna Long-range topological insulators and weakened bulk-boundary correspondence, New J. Phys., Volume 19 (2017) no. 10, 103030 | DOI

[36] P. Wulles; S. E. Skipetrov (in preparation)

[37] Takahiro Fukui; Yasuhiro Hatsugai; Hiroshi Suzuki Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances, J. Phys. Soc. Japan, Volume 74 (2005) no. 6, pp. 1674-1677 | DOI

[38] Robert J. Bettles; Jiří Minář; Charles S. Adams; Igor Lesanovsky; Beatriz Olmos Topological properties of a dense atomic lattice gas, Phys. Rev. A, Volume 96 (2017) no. 4, 041603, 6 pages | DOI

[39] Q. Niu; D. J. Thouless Quantised adiabatic charge transport in the presence of substrate disorder and many-body interaction, J. Phys. A, Math. Gen., Volume 17 (1984) no. 12, 2453 | MR | Zbl

[40] Andrew M. Essin; J. E. Moore Topological insulators beyond the Brillouin zone via Chern parity, Phys. Rev. B, Volume 76 (2007) no. 16, 165307, 11 pages | DOI

[41] Emil Prodan; Taylor L. Hughes; B. Andrei Bernevig Entanglement Spectrum of a Disordered Topological Chern Insulator, Phys. Rev. Lett., Volume 105 (2010) no. 11, 115501, 4 pages | DOI

[42] Emil Prodan Disordered topological insulators: a non-commutative geometry perspective, J. Phys. A, Math. Theor., Volume 44 (2011), 113001 | DOI | MR | Zbl

[43] Raffaello Bianco; Raffaele Resta Mapping topological order in coordinate space, Phys. Rev. B, Volume 84 (2011) no. 24, 241106, 4 pages | DOI

[44] Alexander Cerjan; Terry A. Loring Local invariants identify topology in metals and gapless systems, Phys. Rev. B, Volume 106 (2022) no. 6, 064109, 10 pages | DOI

[45] T. A. Loring; M. B. Hastings Disordered topological insulators via C*-algebras, Eur. Phys. Lett., Volume 92 (2010) no. 6, 67004 | DOI

[46] Miguel A. Bandres; Mikael C. Rechtsman; Mordechai Segev Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport, Phys. Rev. X, Volume 6 (2016) no. 1, 011016, 12 pages | Zbl

[47] Eran Lustig; Steffen Weimann; Yonatan Plotnik; Yaakov Lumer; Miguel A. Bandres; Alexander Szameit; Mordechai Segev Photonic topological insulator in synthetic dimensions, Nature, Volume 567 (2019) no. 7748, pp. 356-360 | DOI

[48] Fei Song; Shunyu Yao; Zhong Wang Non-Hermitian Topological Invariants in Real Space, Phys. Rev. Lett., Volume 123 (2019) no. 24, 246801, 8 pages | DOI | MR

[49] Qi-Bo Zeng; Yan-Bin Yang; Yong Xu Topological phases in non-Hermitian Aubry-André-Harper models, Phys. Rev. B, Volume 101 (2020) no. 2, 020201, 6 pages | DOI

[50] Ling-Zhi Tang; Ling-Feng Zhang; Guo-Qing Zhang; Dan-Wei Zhang Topological Anderson insulators in two-dimensional non-Hermitian disordered systems, Phys. Rev. A, Volume 101 (2020) no. 6, 063612, 8 pages | DOI | MR

[51] Daniele Toniolo On the Bott index of unitary matrices on a finite torus, Lett. Math. Phys., Volume 112 (2022) no. 6, 126 | DOI | MR | Zbl

[52] Emil Prodan Three-dimensional phase diagram of disordered HgTe/CdTe quantum spin-Hall wells, Phys. Rev. B, Volume 83 (2011) no. 19, 195119, 8 pages | DOI

[53] Ai Yamakage; Kentaro Nomura; Ken-Ichiro Imura; Yoshio Kuramoto Criticality of the metal–topological insulator transition driven by disorder, Phys. Rev. B, Volume 87 (2013) no. 20, 205141, 11 pages | DOI | Zbl

[54] C. W. Groth; M. Wimmer; A. R. Akhmerov; J. Tworzydło; C. W. J. Beenakker Theory of the Topological Anderson Insulator, Phys. Rev. Lett., Volume 103 (2009) no. 19, 196805, 4 pages | DOI

[55] J. Bellissard; A. van Elst; H. Schulz‐ Baldes The noncommutative geometry of the quantum Hall effect, J. Math. Phys., Volume 35 (1994) no. 10, pp. 5373-5451 | DOI | MR | Zbl

[56] C. E. Máximo; N. Piovella; Ph. W. Courteille; R. Kaiser; R. Bachelard Spatial and temporal localization of light in two dimensions, Phys. Rev. A, Volume 92 (2015) no. 6, 062702, 7 pages | DOI

[57] P. Soltan-Panahi; J. Struck; P. Hauke; A. Bick; W. Plenkers; G. Meineke; C. Becker; P. Windpassinger; M. Lewenstein; K. Sengstock Multi-component quantum gases in spin-dependent hexagonal lattices, Nature Phys., Volume 7 (2011) no. 5, pp. 434-440 | DOI

[58] Leticia Tarruell; Daniel Greif; Thomas Uehlinger; Gregor Jotzu; Tilman Esslinger Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice, Nature, Volume 483 (2012) no. 7389, pp. 302-305 | DOI

[59] Sylvain Nascimbene; Nathan Goldman; Nigel R. Cooper; Jean Dalibard Dynamic Optical Lattices of Subwavelength Spacing for Ultracold Atoms, Phys. Rev. Lett., Volume 115 (2015) no. 14, 140401, 5 pages | DOI

[60] R. P. Anderson; D. Trypogeorgos; A. Valdés-Curiel; Q.-Y. Liang; J. Tao; M. Zhao; T. Andrijauskas; G. Juzeliūnas; I. B. Spielman Realization of a deeply subwavelength adiabatic optical lattice, Phys. Rev. Research, Volume 2 (2020) no. 1, 013149, 7 pages | DOI

[61] B. Olmos; Dang Yu; Y. Singh; F. Schreck; K. Bongs; I. Lesanovsky Long-Range Interacting Many-Body Systems with Alkaline-Earth-Metal Atoms, Phys. Rev. Lett., Volume 110 (2013) no. 14, 143602, 5 pages | DOI | Zbl

[62] Zheng Wang; Yidong Chong; John D. Joannopoulos; Marin Soljačić Observation of unidirectional backscattering-immune topological electromagnetic states, Nature, Volume 461 (2009) no. 7265, pp. 772-775 | DOI

[63] Shukai Ma; Bo Xiao; Yang Yu; Kueifu Lai; Gennady Shvets; Steven M. Anlage Topologically protected photonic modes in composite quantum Hall/quantum spin Hall waveguides, Phys. Rev. B, Volume 100 (2019) no. 8, 085118, 7 pages | DOI

[64] Shukai Ma; Steven M. Anlage Microwave applications of photonic topological insulators, Appl. Phys. Lett., Volume 116 (2020) no. 25, 250502 | DOI

[65] Mattis Reisner; Matthieu Bellec; Ulrich Kuhl; Fabrice Mortessagne Microwave resonator lattices for topological photonics (invited), Opt. Mater. Express, Volume 11 (2021) no. 3, pp. 629-653 | DOI

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