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Part of the book series: Springer Theses ((Springer Theses))

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Abstract

Waves may fail to propagate in random media. First predicted for quantum particles in the presence of a disordered potential, Anderson localization has been observed also in classical acoustics, electromagnetism and optics. Here, I report the observation of Anderson localization of pairs of entangled photons in a two-particle discrete quantum walk affected by position dependent disorder. The quantum walk on a disordered lattice is realized by starting from an integrated array of interferometersfabricated in glass by femtosecond laser writing and using a novel technique to introduce a controlled phase shift into each unit mesh of the network. Polarization entanglement is exploited to simulate the different symmetries of the two-walker system.

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Notes

  1. 1.

    The pattern of phases of each QW circuit, has been selected between many randomly chosen patterns in such a way that the strength of localization was the maximum achievable.

  2. 2.

    The set {\(\phi _n\)} has been selected a posteriori: between some randomly chosen sets we choose the pattern of phases which mostly manifested the expected behavior. This choice does not represent a loss of generality, because we are not demonstrating that each pattern of phases gives rise to a classical distribution (in the case of space-correlated dynamic disorder) or to a speckle distribution (when uncorrelated dynamic disorder is implemented), but that it is possible to observe these phenomena on our chip.

References

  1. P. Anderson, Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492 (1958)

    Article  ADS  Google Scholar 

  2. N.F. Mott, Electrons in disordered structures. Adv. Phys. 16, 49 (1967)

    Article  ADS  Google Scholar 

  3. P.A. Lee, T.V. Ramakrishnan, Disordered electron systems. Rev. Mod. Phys. 57, 287 (1985)

    Article  ADS  Google Scholar 

  4. E. Abrahams, 50 Years of Anderson Localization (World Scientific, Singapore, 2010)

    Book  MATH  Google Scholar 

  5. G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, M. Inguscio, Anderson localization of a non-interacting Bose-Einstein condensate. Nature 453, 895 (2008)

    Article  ADS  Google Scholar 

  6. J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. ClÈment, L. Sanchez-Palencia, P. Bouyer, A. Aspect, Direct observation of Anderson localization of matter waves in a controlled disorder. Nature 453, 891 (2008)

    Article  ADS  Google Scholar 

  7. D.S. Wiersma, P. Bartolini, A. Lagendijk, R. Righini, Localization of light in a disordered medium. Nature 390, 671 (1997)

    Article  ADS  Google Scholar 

  8. C. Conti, A. Fratalocchi, Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals. Nat. Phys. 4, 794 (2008)

    Article  Google Scholar 

  9. T. Pertsch, J.K.U. Peschel, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, F. Lederer, Nonlinearity and disorder in fiber arrays. Phys. Rev. Lett. 93, 053901 (2004)

    Article  ADS  Google Scholar 

  10. T. Schwartz, G. Bartal, S. Fishman, M. Segev, Transport and Anderson localization in disordered two-dimensional photonic lattices. Nature 466, 52 (2007)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  12. M.A. Broome, A. Fedrizzi, B.P. Lanyon, I. Kassal, A. Aspuru-Guzik, A.G. White, Discrete single-photon quantum walks with tunable decoherence. Phys. Rev. Lett. 104, 153602 (2010)

    Article  ADS  Google Scholar 

  13. A. Schreiber, K.N. Cassemiro, V. Potocek, A. Gabris, P.J. Mosley, I. Jex, C. Silberhorn, Decoherence and disorder in quantum walks: from ballistic spread to localization. Phys. Rev. Lett. 106, 180403 (2011)

    Article  ADS  Google Scholar 

  14. M. Störzer, P. Gross, C.M. Aegerter, G. Maret, Observation of the critical regime near Anderson localization of light. Phys. Rev. Lett. 96, 063904 (2006)

    Article  ADS  Google Scholar 

  15. H. Hu, A. Strybulevych, J.H. Page, S.E. Skipetrov, B.A. van Tiggelen, Localization of ultrasound in a three-dimensional elastic network. Nat. Phys. 4, 945 (2008)

    Article  Google Scholar 

  16. Y. Omar, N. Paunković, L.S.S. Bose, Quantum walk on a line with two entangled particles. Phys. Rev. A 74, 042304 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  17. C. Beenakker, J. Venderbos, M. van Exter, Two-photon speckle as a probe of multi-dimensional entanglement. Phys. Rev. Lett. 102, 193601 (2009)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. D. Shepelyansky, Coherent propagation of two interacting particles in a random potential. Phys. Revi. Lett. 73, 2607 (1994)

    Article  ADS  Google Scholar 

  21. L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, R. Osellame, Two-particle bosonic-fermionic quantum walk via integrated photonics. Phys. Rev. Lett. 108, 010502 (2012)

    Google Scholar 

  22. J.L. O’Brien, A. Furusawa, J. Vuckovic, Photonic quantum technologies. Nat. Photonics 3, 687 (2009)

    Article  ADS  Google Scholar 

  23. A. Politi, M.J. Cryan, J.G. Rarity, S. Yu, J.L. O’Brien, Silica-on-silicon waveguide quantum circuits. Science 320, 646 (2008)

    Article  ADS  Google Scholar 

  24. A. Laing, A. Peruzzo, A. Politi, M.R. Verde, M. Halder, T.C. Ralph, M.G. Thompson, J.L. O’Brien, High-fidelity operation of quantum photonic circuits. Appl. Phys. Lett. 97, 211108 (2010)

    Article  ADS  Google Scholar 

  25. L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, R. Osellame, Polarization entangled state measurement on a chip. Phys. Rev. Lett. 105, 200503 (2010)

    Article  ADS  Google Scholar 

  26. A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, P. Mataloni, Integrated photonic quantum gates for polarization qubits. Nat. Commun. 2, 566 (2011)

    Article  ADS  Google Scholar 

  27. A. Politi, J.C.F. Matthews, J.L. O’Brien, Shor’s quantum factoring algorithm on a photonic chip. Science 325, 1221 (2009)

    Article  ADS  MATH  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  29. J.C.F. Matthews, K. Poulios, J.D.A. Meinecke, A. Politi, A. Peruzzo, N. Ismail, K. Worhoff, M.G. Thompson, J.L. O’Brien, Simulating quantum statistics with entangled photons: a continuous transition from bosons to fermions, Scientific Report 3, 1539 (2013)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  31. B.J. Smith, D. Kundys, N. Thomas-Peter, P.G.R. Smith, I.A. Walmsley, Phase-controlled integrated photonic quantum circuits. Opt. Express 17, 13516 (2009)

    Article  ADS  Google Scholar 

  32. J.C.F. Matthews, A. Politi, A. Stefanov, J.L. O’Brien, Manipulation of multiphoton entanglement in waveguide quantum circuits. Nat. Photonics 3, 346 (2009)

    Article  ADS  Google Scholar 

  33. A. Crespi, M. Lobino, J.C.F. Matthews, A. Politi, C.R. Neal, R. Ramponi, R. Osellame, J.L. O’Brien, Measuring protein concentration with entangled photons. Appl. Phys. Lett. 100, 233704 (2012)

    Article  ADS  Google Scholar 

  34. R. Osellame, G. Cerullo, R. Ramponi, Femtosecond Laser Micromachining: Photonic and Microfluidic Devices in Transparent Materials, Topics in Applied Physics, vol. 123. (Springer, Berlin, 2012)

    Google Scholar 

  35. R.R. Gattass, E. Mazur, Femtosecond laser micromachining in transparent materials. Nat. Photonics 2, 219 (2008)

    Article  ADS  Google Scholar 

  36. G. Della Valle, R. Osellame, P. Laporta, Micromachining of photonic devices by femtosecond laser pulses. J. Opt. A Pure Appl. Opt. 11, 049801 (2009)

    Google Scholar 

  37. A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F.D. Nicola, F. Sciarrino, P. Mataloni, Anderson localization of entangled photons in an integrated quantum walk. Nat. Photonics 7, 322-328 (2013)

    Google Scholar 

  38. D. Molinari, A. Fratalocchi, Route to strong localization of light: the role of disorder. Opt. Express 20, 18156 (2012)

    Article  ADS  Google Scholar 

  39. M. Terraneo, D.L. Shepelyansky, Dynamical localization and repeated measurements in a quantum computation process. Phys. Rev. Lett. 92, 037902 (2004)

    Article  ADS  Google Scholar 

  40. Y. Yin, D.E. Katsanos, S.N. Evangelou, Quantum walks on a random environment. Phys. Rev. A 77, 022302 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  41. S. Havlin, D. Ben-Avraham, Diffusion in disordered media. Adv. Phys. 51, 187 (2002)

    Article  ADS  Google Scholar 

  42. B. Aguer, S. de Bièvre, P. Lafitte, P. Parris, Classical motion in force fields with short range correlations. J. Stat. Phys. 138, 780 (2010)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  43. Y. Krivolapov, L. Levi, S. Fishman, M. Segev, M. Wilkinson, Enhanced transport when Anderson localization is destroyed. Arxiv:1110.3024v3 (2012)

    Google Scholar 

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Correspondence to Linda Sansoni .

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Sansoni, L. (2014). Quantum Transport in Presence of Disorder. In: Integrated Devices for Quantum Information with Polarization Encoded Qubits. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-07103-9_10

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