Abstract

New quasi-periodic arrays of waveguides (AWs) constructed with Fibonacci sequences are proposed to realize localized quantum walks (LQWs). The proposed Fibonacci arrays of waveguides (FAWs) are simple and straightforward to make, but have a rich set of properties that are of potential use for applications in quantum communication. Our simulations show that, in contrast with randomly disordered AWs, LQWs in FAWs are highly controllable due to the deterministic disorder nature of quasi-periodic systems. Furthermore, unique LQWs with symmetrical probability distribution can be conveniently realized in the FAWs.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref] [PubMed]

2018 (2)

H. Tang, X.-F. Lin, Z. Feng, J.-Y. Chen, J. Gao, K. Sun, C.-Y. Wang, P.-C. Lai, X.-Y. Xu, Y. Wang, L.-F. Qiao, A.-L. Yang, and X.-M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4(5), t3174 (2018).
[PubMed]

A. Perez-Leija, D. Guzmán-Silva, R. D. J. León-Montiel, M. Gräfe, M. Heinrich, H. Moya-Cessa, K. Busch, and A. Szameit, “Endurance of quantum coherence due to particle indistinguishability in noisy quantum networks,” Quant. Inf. 4, 45 (2018).

2017 (1)

N. Lo Gullo, C. V. Ambarish, T. Busch, L. Dell’Anna, and C. M. Chandrashekar, “Dynamics and energy spectra of aperiodic discrete-time quantum walks,” Phys. Rev. E 96(1-1), 012111 (2017).
[Crossref] [PubMed]

2016 (4)

M. Gräfe, R. Heilmann, M. Lebugle, D. Guzman-Silva, A. Perez-Leija, and A. Szameit, “Integrated photonic quantum walks,” J. Opt. 18(10), 103002 (2016).
[Crossref]

A. Montanaro, “Quantum algorithms: an overview, ” Quant. Inf. 2, 15023 (2016).

M. Leonetti, S. Karbasi, A. Mafi, E. DelRe, and C. Conti, “Secure information transport by transverse localization of light,” Sci. Rep. 6(1), 29918 (2016).
[Crossref] [PubMed]

M. Boguslawski, N. M. Lucic, F. Diebel, D. V. Timotijevic, C. Denz, and D. J. Savic, “Light localization in optically induced deterministic aperiodic Fibonacci lattices,” Optica 3(7), 711–717 (2016).
[Crossref]

2015 (4)

N. M. Lucic, D. M. J. Savic, A. Piper, D. Ž. Grujic, J. M. Vasiljevic, D. V. Pantelic, B. M. Jelenkovic, and D. V. Timotijevic, “Light propagation in quasi-periodic Fibonacci waveguide arrays,” J. Opt. Soc. Am. B 32(7), 1510–1513 (2015).
[Crossref]

C. M. Chandrashekar and Th. Busch, “Localized quantum walks as secured quantum memory,” Europhys. Lett. 110(1), 10005 (2015).
[Crossref]

Y. Gilead, M. Verbin, and Y. Silberberg, “Ensemble-averaged quantum correlations between path-entangled photons undergoing Anderson localization,” Phys. Rev. Lett. 115(13), 133602 (2015).
[Crossref] [PubMed]

M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of N00N state Bloch oscillations,” Nat. Commun. 6(1), 8273 (2015).
[Crossref] [PubMed]

2013 (6)

G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, and B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and anderson photonic lattices,” Phys. Rev. Lett. 110(15), 150503 (2013).
[Crossref] [PubMed]

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, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339(6121), 798–801 (2013).
[Crossref] [PubMed]

J. C. F. Matthews, K. Poulios, J. D. A. Meinecke, A. Politi, A. Peruzzo, N. Ismail, K. Wörhoff, M. G. Thompson, and J. L. O’Brien, “Observing fermionic statistics with photons in arbitrary processes,” Sci. Rep. 3(1), 1539 (2013), doi:.
[Crossref] [PubMed]

A. M. Childs, D. Gosset, and Z. Webb, “Universal computation by multiparticle quantum walk,” Science 339(6121), 791–794 (2013).
[Crossref] [PubMed]

A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F. De Nicola, F. Sciarrino, and P. Mataloni, “Anderson localization of entangled photons in an integrated quantum walk,” Nat. Photonics 7(4), 322–328 (2013).
[Crossref]

M. Segev, Y. Silberberg, and D. N. Christodoulides, “Anderson localization of light,” Nat. Photonics 7(3), 197–204 (2013).
[Crossref]

2012 (2)

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Two-particle bosonic-fermionic quantum walk via integrated photonics,” Phys. Rev. Lett. 108(1), 010502 (2012).
[Crossref] [PubMed]

S. E. Venegas-Andraca, “Quantum walks: a comprehensive review,” Quantum Inform. Process. 11(5), 1015–1106 (2012).
[Crossref]

2011 (3)

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science 332(6037), 1541–1544 (2011).
[Crossref] [PubMed]

J. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13(7), 075003 (2011).
[Crossref]

L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, and B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19(14), 13636–13646 (2011).
[Crossref] [PubMed]

2010 (3)

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, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
[Crossref] [PubMed]

D. T. Nguyen, R. Norwood, and N. Peyghambarian, “Multiple spectral window mirrors based on Fibonacci chains of dielectric layers,” Opt. Commun. 283(21), 4199–4202 (2010).
[Crossref]

N. B. Lovett, S. Cooper, M. Everitt, M. Trevers, and V. Kendon, “Universal quantum computation using the discrete-time quantum walk,” Phys. Rev. A 81(4), 042330 (2010).
[Crossref]

2009 (1)

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide lattices,” Phys. Rev. Lett. 102(25), 253904 (2009).
[Crossref] [PubMed]

2008 (3)

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett. 100(17), 170506 (2008).
[Crossref] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100(1), 013906 (2008).
[Crossref] [PubMed]

J. Hendrickson, B. C. Richards, J. Sweet, G. Khitrova, A. N. Poddubny, E. L. Ivchenko, M. Wegener, and H. M. Gibbs, “Excitonic polaritons in Fibonacci quasicrystals,” Opt. Express 16(20), 15382–15387 (2008).
[Crossref] [PubMed]

2007 (2)

D. T. Nguyen, A. Chavez-Pirson, S. Jiang, and N. Peyghambarian, “A Novel approach of modeling cladding-pumped highly Er–Yb co-doped fiber amplifiers,” IEEE J. Quantum Electron. 43(11), 1018–1027 (2007).
[Crossref]

P. K. Pathak and G. S. Agrawal, “Quantum random walk of two photons in separable and entangled states,” Phys. Rev. A 75(3), 032351 (2007).
[Crossref]

2006 (1)

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
[Crossref] [PubMed]

2005 (1)

2003 (1)

A. Ambainis, “Quantum walks and their algorithmic applications,” Int. J. Quant. Inf. 1(4), 507–518 (2003).
[Crossref]

1997 (1)

N. Liu, “Propagation of light waves in Thue–Morse dielectric multilayers,” Phys. Rev. B Condens. Matter 55(6), 3543–3547 (1997).
[Crossref]

1994 (1)

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72(5), 633–636 (1994).
[Crossref] [PubMed]

1992 (1)

M. Dulea, M. Johansson, and R. Riklund, “Localization of electrons and electromagnetic waves in a deterministic aperiodic system,” Phys. Rev. B Condens. Matter 45(1), 105–114 (1992).
[Crossref] [PubMed]

1987 (1)

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987).
[Crossref] [PubMed]

1984 (1)

D. Levine and P. J. Steinhardt, “Quasicrystals: A new class of ordered structures,” Phys. Rev. Lett. 53(26), 2477–2480 (1984).
[Crossref]

1958 (1)

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[Crossref]

Abouraddy, A. F.

G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, and B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and anderson photonic lattices,” Phys. Rev. Lett. 110(15), 150503 (2013).
[Crossref] [PubMed]

L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, and B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19(14), 13636–13646 (2011).
[Crossref] [PubMed]

Agrawal, G. S.

P. K. Pathak and G. S. Agrawal, “Quantum random walk of two photons in separable and entangled states,” Phys. Rev. A 75(3), 032351 (2007).
[Crossref]

Akbulut, M.

V. Demir, M. Akbulut, D. T. Nguyen, Y. Kaneda, M. Neifeld, and N. Peyghambarian, “Injection-locked, single frequency, multi-core Yb-doped phosphate fiber laser,” Sci. Rep. (to be published).

Ambainis, A.

A. Ambainis, “Quantum walks and their algorithmic applications,” Int. J. Quant. Inf. 1(4), 507–518 (2003).
[Crossref]

Ambarish, C. V.

N. Lo Gullo, C. V. Ambarish, T. Busch, L. Dell’Anna, and C. M. Chandrashekar, “Dynamics and energy spectra of aperiodic discrete-time quantum walks,” Phys. Rev. E 96(1-1), 012111 (2017).
[Crossref] [PubMed]

Ams, M.

J. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13(7), 075003 (2011).
[Crossref]

Anderson, P. W.

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[Crossref]

Avidan, A.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100(1), 013906 (2008).
[Crossref] [PubMed]

Balasubramanian, S.

Barbieri, M.

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, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339(6121), 798–801 (2013).
[Crossref] [PubMed]

Biggerstaff, D. N.

J. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13(7), 075003 (2011).
[Crossref]

Boguslawski, M.

Bromberg, Y.

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, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
[Crossref] [PubMed]

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide lattices,” Phys. Rev. Lett. 102(25), 253904 (2009).
[Crossref] [PubMed]

Broome, M. A.

J. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13(7), 075003 (2011).
[Crossref]

Busch, K.

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N. Lo Gullo, C. V. Ambarish, T. Busch, L. Dell’Anna, and C. M. Chandrashekar, “Dynamics and energy spectra of aperiodic discrete-time quantum walks,” Phys. Rev. E 96(1-1), 012111 (2017).
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G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, and B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and anderson photonic lattices,” Phys. Rev. Lett. 110(15), 150503 (2013).
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M. Leonetti, S. Karbasi, A. Mafi, E. DelRe, and C. Conti, “Secure information transport by transverse localization of light,” Sci. Rep. 6(1), 29918 (2016).
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N. Lo Gullo, C. V. Ambarish, T. Busch, L. Dell’Anna, and C. M. Chandrashekar, “Dynamics and energy spectra of aperiodic discrete-time quantum walks,” Phys. Rev. E 96(1-1), 012111 (2017).
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M. Leonetti, S. Karbasi, A. Mafi, E. DelRe, and C. Conti, “Secure information transport by transverse localization of light,” Sci. Rep. 6(1), 29918 (2016).
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V. Demir, M. Akbulut, D. T. Nguyen, Y. Kaneda, M. Neifeld, and N. Peyghambarian, “Injection-locked, single frequency, multi-core Yb-doped phosphate fiber laser,” Sci. Rep. (to be published).

Denz, C.

Di Giuseppe, G.

G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, and B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and anderson photonic lattices,” Phys. Rev. Lett. 110(15), 150503 (2013).
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L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, and B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19(14), 13636–13646 (2011).
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Do, B.

Dreisow, F.

G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, and B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and anderson photonic lattices,” Phys. Rev. Lett. 110(15), 150503 (2013).
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L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, and B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19(14), 13636–13646 (2011).
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M. Dulea, M. Johansson, and R. Riklund, “Localization of electrons and electromagnetic waves in a deterministic aperiodic system,” Phys. Rev. B Condens. Matter 45(1), 105–114 (1992).
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Elliott, D. S.

Everitt, M.

N. B. Lovett, S. Cooper, M. Everitt, M. Trevers, and V. Kendon, “Universal quantum computation using the discrete-time quantum walk,” Phys. Rev. A 81(4), 042330 (2010).
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A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F. De Nicola, F. Sciarrino, and P. Mataloni, “Anderson localization of entangled photons in an integrated quantum walk,” Nat. Photonics 7(4), 322–328 (2013).
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Fischbach, M. A.

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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, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339(6121), 798–801 (2013).
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W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72(5), 633–636 (1994).
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J. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13(7), 075003 (2011).
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A. M. Childs, D. Gosset, and Z. Webb, “Universal computation by multiparticle quantum walk,” Science 339(6121), 791–794 (2013).
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A. Perez-Leija, D. Guzmán-Silva, R. D. J. León-Montiel, M. Gräfe, M. Heinrich, H. Moya-Cessa, K. Busch, and A. Szameit, “Endurance of quantum coherence due to particle indistinguishability in noisy quantum networks,” Quant. Inf. 4, 45 (2018).

M. Gräfe, R. Heilmann, M. Lebugle, D. Guzman-Silva, A. Perez-Leija, and A. Szameit, “Integrated photonic quantum walks,” J. Opt. 18(10), 103002 (2016).
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M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of N00N state Bloch oscillations,” Nat. Commun. 6(1), 8273 (2015).
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M. Gräfe, R. Heilmann, M. Lebugle, D. Guzman-Silva, A. Perez-Leija, and A. Szameit, “Integrated photonic quantum walks,” J. Opt. 18(10), 103002 (2016).
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Heilmann, R.

M. Gräfe, R. Heilmann, M. Lebugle, D. Guzman-Silva, A. Perez-Leija, and A. Szameit, “Integrated photonic quantum walks,” J. Opt. 18(10), 103002 (2016).
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M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of N00N state Bloch oscillations,” Nat. Commun. 6(1), 8273 (2015).
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A. Perez-Leija, D. Guzmán-Silva, R. D. J. León-Montiel, M. Gräfe, M. Heinrich, H. Moya-Cessa, K. Busch, and A. Szameit, “Endurance of quantum coherence due to particle indistinguishability in noisy quantum networks,” Quant. Inf. 4, 45 (2018).

L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, and B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19(14), 13636–13646 (2011).
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Hermatschweiler, M.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
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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, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339(6121), 798–801 (2013).
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Jelenkovic, B. M.

Jiang, S.

D. T. Nguyen, A. Chavez-Pirson, S. Jiang, and N. Peyghambarian, “A Novel approach of modeling cladding-pumped highly Er–Yb co-doped fiber amplifiers,” IEEE J. Quantum Electron. 43(11), 1018–1027 (2007).
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H. Tang, X.-F. Lin, Z. Feng, J.-Y. Chen, J. Gao, K. Sun, C.-Y. Wang, P.-C. Lai, X.-Y. Xu, Y. Wang, L.-F. Qiao, A.-L. Yang, and X.-M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4(5), t3174 (2018).
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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, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339(6121), 798–801 (2013).
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M. Dulea, M. Johansson, and R. Riklund, “Localization of electrons and electromagnetic waves in a deterministic aperiodic system,” Phys. Rev. B Condens. Matter 45(1), 105–114 (1992).
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V. Demir, M. Akbulut, D. T. Nguyen, Y. Kaneda, M. Neifeld, and N. Peyghambarian, “Injection-locked, single frequency, multi-core Yb-doped phosphate fiber laser,” Sci. Rep. (to be published).

Karbasi, S.

M. Leonetti, S. Karbasi, A. Mafi, E. DelRe, and C. Conti, “Secure information transport by transverse localization of light,” Sci. Rep. 6(1), 29918 (2016).
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G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, and B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and anderson photonic lattices,” Phys. Rev. Lett. 110(15), 150503 (2013).
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L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, and B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19(14), 13636–13646 (2011).
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Kendon, V.

N. B. Lovett, S. Cooper, M. Everitt, M. Trevers, and V. Kendon, “Universal quantum computation using the discrete-time quantum walk,” Phys. Rev. A 81(4), 042330 (2010).
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Kohmoto, M.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72(5), 633–636 (1994).
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M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987).
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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, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339(6121), 798–801 (2013).
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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, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339(6121), 798–801 (2013).
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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, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
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H. Tang, X.-F. Lin, Z. Feng, J.-Y. Chen, J. Gao, K. Sun, C.-Y. Wang, P.-C. Lai, X.-Y. Xu, Y. Wang, L.-F. Qiao, A.-L. Yang, and X.-M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4(5), t3174 (2018).
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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, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339(6121), 798–801 (2013).
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Lebugle, M.

M. Gräfe, R. Heilmann, M. Lebugle, D. Guzman-Silva, A. Perez-Leija, and A. Szameit, “Integrated photonic quantum walks,” J. Opt. 18(10), 103002 (2016).
[Crossref]

M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of N00N state Bloch oscillations,” Nat. Commun. 6(1), 8273 (2015).
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A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
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M. Leonetti, S. Karbasi, A. Mafi, E. DelRe, and C. Conti, “Secure information transport by transverse localization of light,” Sci. Rep. 6(1), 29918 (2016).
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A. Perez-Leija, D. Guzmán-Silva, R. D. J. León-Montiel, M. Gräfe, M. Heinrich, H. Moya-Cessa, K. Busch, and A. Szameit, “Endurance of quantum coherence due to particle indistinguishability in noisy quantum networks,” Quant. Inf. 4, 45 (2018).

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L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science 332(6037), 1541–1544 (2011).
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J. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13(7), 075003 (2011).
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N. Lo Gullo, C. V. Ambarish, T. Busch, L. Dell’Anna, and C. M. Chandrashekar, “Dynamics and energy spectra of aperiodic discrete-time quantum walks,” Phys. Rev. E 96(1-1), 012111 (2017).
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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, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329(5998), 1500–1503 (2010).
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N. B. Lovett, S. Cooper, M. Everitt, M. Trevers, and V. Kendon, “Universal quantum computation using the discrete-time quantum walk,” Phys. Rev. A 81(4), 042330 (2010).
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M. Gräfe, R. Heilmann, M. Lebugle, D. Guzman-Silva, A. Perez-Leija, and A. Szameit, “Integrated photonic quantum walks,” J. Opt. 18(10), 103002 (2016).
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M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of N00N state Bloch oscillations,” Nat. Commun. 6(1), 8273 (2015).
[Crossref] [PubMed]

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D. T. Nguyen, R. Norwood, and N. Peyghambarian, “Multiple spectral window mirrors based on Fibonacci chains of dielectric layers,” Opt. Commun. 283(21), 4199–4202 (2010).
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V. Demir, M. Akbulut, D. T. Nguyen, Y. Kaneda, M. Neifeld, and N. Peyghambarian, “Injection-locked, single frequency, multi-core Yb-doped phosphate fiber laser,” Sci. Rep. (to be published).

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H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett. 100(17), 170506 (2008).
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M. Gräfe, R. Heilmann, M. Lebugle, D. Guzman-Silva, A. Perez-Leija, and A. Szameit, “Integrated photonic quantum walks,” J. Opt. 18(10), 103002 (2016).
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J. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13(7), 075003 (2011).
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A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
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Supplementary Material (6)

NameDescription
» Visualization 1       Visualization 1 is animation simulation of quatum walks in regular array of waveguides RAW39 corresponding to the top view image shown in Fig. 5a
» Visualization 2       Visualization 2 is animation simulation of quatum walks in regular array of waveguides RAW39 corresponding to the front view image shown in Fig. 5b
» Visualization 3       Visualization 3 is animation simulation of quatum walks in Fibonacci array of waveguides FAW6A-I2 corresponding to the top view image shown in Fig. 5h
» Visualization 4       Visualization 4 is animation simulation of quatum walks in Fibonacci array of waveguides FAW6A-I2 corresponding to the top view image shown in Fig. 5g
» Visualization 5       Visualization 5 is animation simulation of quatum walks in regular array of waveguides RAW39 corresponding to the 3D photon propability distribution front view image shown in Fig. 6a
» Visualization 6       Visualization 6 is animation simulation of quatum walks in Fibonacci array of waveguides FAW6A-I2 corresponding to the 3D photon propability distribution front view image shown in Fig. 6b

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Figures (8)

Fig. 1
Fig. 1 Elements S1, S2 … S6 of FAWs composed by two waveguides A and B.
Fig. 2
Fig. 2 Diagram of 6th order Fibonacci arrays of waveguides (FAW6) composed by two waveguides A and B (front view). Sj and dotted lines on top of waveguides indicate corresponding Fibonacci elements.
Fig. 3
Fig. 3 Diagrams of two different types of 6th-order symmetrical FAWs F 6A(B) I (or FAW6A(B)-I), and F 6 II (or FAW6-II) with different configurations of inputs.
Fig. 4
Fig. 4 QWs in AW of 23 identical SM waveguides with input is central core. (a) AW without disorder of waveguide positions; (b, c, d, e) AWs with randomly disorder of positions of 10%. From bottom to top: top-view, front-view and probability distribution of photon (in the same scale). Upper: diagram of array of waveguides.
Fig. 5
Fig. 5 Quantum walks in RAW39 (left), FAW6-I1 (center) and FAW6-I2 (right). From bottom to top: top-view, front-view and probability distribution with the same scale. Input signal is in the center waveguide (red arrows). Visualization 1 (a), Visualization 2 (b), Visualization 3 (g) and Visualization 4 (h).
Fig. 6
Fig. 6 Structural difference of QWs in RAW and FAW: Visualization 5 (a), and Visualization 6 (b) shown 3D photon probability distributions in RAW39 and FAW6A-I2, respectively.
Fig. 7
Fig. 7 LQWs in FAW6A-I with input in center waveguide S1 (a), FAW6B-I with input in two S2 waveguides near center (b); and FAW6-II (c) with input in two center waveguides S1. From bottom to top: top-view, front-view and probability distribution. Red arrows indicate the input signal.
Fig. 8
Fig. 8 LQWs in FAW6A-I with input in center waveguide S1 with signal of different wavelengths 1.3μm, 1.5μm and 1.7μm in order from left to right. From bottom to top: top-view, front-view and probability distribution (in different scales).

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

S j = S j2 + S j1 , with S 1 = S 2 =1.
S j = S j2 S j1 , with S 1 =A, S 2 =B,
F j = S 1 S 2 S 3 S j .
F j I = S j S j1 S 2 S 1 S 2 S j1 S j ,
F j II = S j S j1 S 2 S 1 S 1 S 2 S j1 S j .
H= n { β n a n a n + m κ nm a n a m } ,
d a k dz = i [ a k ,H ]=i( β k a k + κ k,k+1 a k+1 + κ k,k1 a k1 ).
a k (z)= j=1 N U j,k a j (0).
U k,j = i (kj) exp(iβz) J kj (2κz),
d dz E(x,y,z)=( D ^ + V ^ )E(x,y,z).
D ^ = i 2k ( 2 x 2 + 2 y 2 ), and V ^ ={ ikΔn(x,y)α(x,y) }.
E(x,y,z+Δz)= e ( D ^ + V ^ )Δz E(x,y,z) e D ^ Δz 2 e V ^ Δz e D ^ Δz 2 E(x,y,z),

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