Photonic two-particle quantum walks in Su–Schrieffer–Heeger lattices

Friederike Klauck; Matthias Heinrich; Alexander Szameit

doi:10.1364/PRJ.409005

[1] L. Lu, J. D. Joannopoulos, M. Soljačić. Topological photonics. Nat. Photonics, 8, 821-829(2014).

[2] T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, I. Carusotto. Topological photonics. Rev. Mod. Phys., 91, 015006(2019).

[3] C. L. Kane, E. J. Mele. Z2 topological order and the quantum spin Hall effect. Phys. Rev. Lett., 95, 146802(2005).

[4] B. A. Bernevig, S. C. Zhang. Quantum spin Hall effect. Phys. Rev. Lett., 96, 106802(2006).

[5] M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X. L. Qi, S. C. Zhang. Quantum spin hall insulator state in HgTe quantum wells. Science, 318, 766-770(2007).

[6] D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, M. Z. Hasan. A topological Dirac insulator in a quantum spin Hall phase. Nature, 452, 970-974(2008).

[7] S. Raghu, F. D. M. Haldane. Analogs of quantum-Hall-effect edge states in photonic crystals. Phys. Rev. A, 78, 033834(2008).

[8] F. D. M. Haldane, S. Raghu. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett., 100, 013904(2008).

[9] Z. Wang, Y. D. Chong, J. D. Joannopoulos, M. Soljačić. Reflection-free one-way edge modes in a gyromagnetic photonic crystal. Phys. Rev. Lett., 100, 013905(2008).

[10] Z. Wang, Y. Chong, J. D. Joannopoulos, M. Soljačić. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature, 461, 772-775(2009).

[11] M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit. Photonic Floquet topological insulators. Nature, 496, 196-200(2013).

[12] M. Hafezi, S. Mittal, J. Fan, A. Migdall, J. M. Taylor. Imaging topological edge states in silicon photonics. Nat. Photonics, 7, 1001-1005(2013).

[13] L. J. Maczewsky, J. M. Zeuner, S. Nolte, A. Szameit. Observation of photonic anomalous Floquet topological insulators. Nat. Commun., 8, 13756(2017).

[14] S. Mukherjee, A. Spracklen, M. Valiente, E. Andersson, P. Öhberg, N. Goldman, R. R. Thomson. Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice. Nat. Commun., 8, 13918(2017).

[15] O. Zilberberg, S. Huang, J. Guglielmon, M. Wang, K. P. Chen, Y. E. Kraus, M. C. Rechtsman. Photonic topological boundary pumping as a probe of 4D quantum Hall physics. Nature, 553, 59-62(2018).

[16] J. Noh, S. Huang, D. Leykam, Y. D. Chong, K. P. Chen, M. C. Rechtsman. Experimental observation of optical Weyl points and Fermi arc-like surface states. Nat. Phys., 13, 611-617(2017).

[17] S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, A. Szameit. Photonic topological Anderson insulators. Nature, 560, 461-465(2018).

[18] E. Lustig, S. Weimann, Y. Plotnik, Y. Lumer, M. A. Bandres, A. Szameit, M. Segev. Photonic topological insulator in synthetic dimensions. Nature, 567, 356-360(2019).

[19] S. Weimann, M. Kremer, Y. Plotnik, Y. Lumer, S. Nolte, K. G. Makris, M. Segev, M. C. Rechtsman, A. Szameit. Topologically protected bound states in photonic parity–time-symmetric crystals. Nat. Mater., 16, 433-438(2017).

[20] J. M. Zeuner, M. C. Rechtsman, Y. Plotnik, Y. Lumer, S. Nolte, M. S. Rudner, M. Segev, A. Szameit. Observation of a topological transition in the bulk of a non-Hermitian system. Phys. Rev. Lett., 115, 040402(2015).

[21] S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, E. Waks. A topological quantum optics interface. Science, 359, 666-668(2018).

[22] A. Blanco-Redondo, B. Bell, D. Oren, B. J. Eggleton, M. Segev. Topological protection of biphoton states. Science, 362, 568-571(2018).

[23] W. P. Su, J. R. Schrieffer, A. J. Heeger. Solitons in polyacetylene. Phys. Rev. Lett., 42, 1698-1701(1979).

[24] A. P. Schnyder, S. Ryu, A. Furusaki, A. W. W. Ludwig. “Classification of topological insulators and superconductors in three spatial dimensions. Phys. Rev. B, 78, 195125(2008).

[25] N. Malkova, I. Hromada, X. Wang, G. Bryant, Z. Chen. Observation of optical Shockley-like surface states in photonic superlattices. Opt. Lett., 34, 1633-1635(2009).

[26] C. Jürß, D. Bauer. High-harmonic generation in Su-Schrieffer-Heeger chains. Phys. Rev. B, 99, 195428(2019).

[27] V. Dal Lago, M. Atala, L. E. F. Foa Torres. Floquet topological transitions in a driven one-dimensional topological insulator. Phys. Rev. A, 92, 023624(2015).

[28] Z. Fedorova, C. Jörg, C. Dauer, F. Letscher, M. Fleischhauer, S. Eggert, S. Linden, G. von Freymann. Limits of topological protection under local periodic driving. Light Sci. Appl., 8, 1(2019).

[29] E. J. Meier, F. A. An, B. Gadway. Observation of the topological soliton state in the Su-Schrieffer-Heeger model. Nat. Commun., 7, 13986(2016).

[30] M. A. Miri, M. Heinrich, R. El-Ganainy, D. N. Christodoulides. Supersymmetric optical structures. Phys. Rev. Lett., 110, 233902(2013).

[31] G. Queraltó, M. Kremer, L. J. Maczewsky, M. Heinrich, J. Mompart, V. Ahufinger, A. Szameit. Topological state engineering via supersymmetric transformations. Commun. Phys., 3, 49(2020).

[32] M. C. Rechtsman, Y. Lumer, Y. Plotnik, A. Perez-Leija, A. Szameit, M. Segev. Topological protection of photonic path entanglement. Optica, 3, 925-930(2016).

[33] S. Mittal, V. V. Orre, M. Hafezi. Topologically robust transport of entangled photons in a 2D photonic system. Opt. Express, 24, 15631-15641(2016).

[34] S. Mittal, E. A. Goldschmidt, M. Hafezi. A topological source of quantum light. Nature, 561, 502-506(2018).

[35] M. Wang, C. Doyle, B. Bell, M. J. Collins, E. Magi, B. J. Eggleton, M. Segev, A. Blanco-Redondo. Topologically protected entangled photonic states. Nanophotonics, 8, 1327-1335(2019).

[36] J. L. Tambasco, G. Corrielli, R. J. Chapman, A. Crespi, O. Zilberberg, R. Osellame, A. Peruzzo. Quantum interference of topological states of light. Sci. Adv., 4, eaat3187(2018).

[37] Y. Aharonov, L. Davidovich, N. Zagury. Quantum random walks. Phys. Rev. A, 48, 1687-1690(1993).

[38] H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, Y. Silberberg. Realization of quantum walks with negligible decoherence in waveguide lattices. Phys. Rev. Lett., 100, 170506(2008).

[39] Y. Bromberg, Y. Lahini, R. Morandotti, Y. Silberberg. Quantum and classical correlations in waveguide lattices. Phys. Rev. Lett., 102, 253904(2009).

[40] A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. O’Brien. Quantum walks of correlated photons. Science, 329, 1500-1503(2010).

[41] K. Poulios, R. Keil, D. Fry, J. D. A. Meinecke, J. C. F. Matthews, A. Politi, M. Lobino, M. Gräfe, M. Heinrich, S. Nolte, A. Szameit, J. L. O’Brien. Quantum walks of correlated photon pairs in two-dimensional waveguide arrays. Phys. Rev. Lett., 112, 143604(2014).

[42] M. A. Broome, A. Fedrizzi, S. Rahimi-Keshari, J. Dove, S. Aaronson, T. C. Ralph, A. G. White. Photonic boson sampling in a tunable circuit. Science, 339, 794-798(2013).

[43] J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X. M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, I. A. Walmsley. Boson sampling on a photonic chip. Science, 339, 798-801(2013).

[44] A. Crespi, R. Osellame, R. Ramponi, D. J. Brod, E. F. Galvão, N. Spagnolo, C. Vitelli, E. Maiorino, P. Mataloni, F. Sciarrino. Integrated multimode interferometers with arbitrary designs for photonic boson sampling. Nat. Photonics, 7, 545-549(2013).

[45] M. Tillmann, B. Dakić, R. Heilmann, S. Nolte, A. Szameit, P. Walther. Experimental boson sampling. Nat. Photonics, 7, 540-544(2013).

[46] N. Malkova, I. Hromada, X. Wang, G. Bryant, Z. Chen. Transition between Tamm-like and Shockley-like surface states in optically induced photonic superlattices. Phys. Rev. A, 80, 043806(2009).

[47] F. L. J. Vos, D. P. Aalberts, W. van Saarloos. Su-Schrieffer-Heeger model applied to chains of finite length. Phys. Rev. B, 53, 14922-14928(1996).

[48] M. Gräfe, R. Heilmann, R. Keil, T. Eichelkraut, M. Heinrich, S. Nolte, A. Szameit. Correlations of indistinguishable particles in non-Hermitian lattices. New J. Phys., 15, 033008(2013).

[49] K. M. Davis, K. Miura, N. Sugimoto, K. Hirao. Writing waveguides in glass with a femtosecond laser. Opt. Lett., 21, 1729-1731(1996).

[50] A. Szameit, S. Nolte. Discrete optics in femtosecond-laser-written photonic structures. J. Phys. B, 43, 163001(2010).

[51] Y. Lahini, Y. Bromberg, D. N. Christodoulides, Y. Silberberg. Quantum correlations in two-particle Anderson localization. Phys. Rev. Lett., 105, 163905(2010).

[52] M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, A. Szameit. Experimental observation of N00N state Bloch oscillations. Nat. Commun., 6, 8273(2015).

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