Abstract

We experimentally demonstrate that hybrid ordered–disordered photonic lattices can generate faster than the ballistic growth of the second moment of a spreading wave packet for parametrically large time intervals.

© 2013 Optical Society of America

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  1. E. Abrahams, 50 Years of Anderson Localization (World Scientific, 2010).
  2. A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature 404, 850 (2000).
    [CrossRef]
  3. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
    [CrossRef]
  4. Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
    [CrossRef]
  5. J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
    [CrossRef]
  6. G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Nature 453, 895 (2008).
    [CrossRef]
  7. I. Guarneri and H. Schulz-Baldes, Rev. Math. Phys. 11, 1249 (1999).
    [CrossRef]
  8. I. Guarneri, Europhys. Lett. 10, 95 (1989).
    [CrossRef]
  9. R. Ketzmerick, K. Kruse, S. Kraut, and T. Geisel, Phys. Rev. Lett. 79, 1959 (1997).
    [CrossRef]
  10. L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, Science 332, 1541 (2011).
    [CrossRef]
  11. L. Hufnagel, R. Ketzmerick, T. Kottos, and T. Geisel, Phys. Rev. E 64, 012301 (2001).
    [CrossRef]
  12. Z. Zhang, P. Tong, J. Gong, and B. Li, Phys. Rev. Lett. 108, 070603 (2012).
    [CrossRef]
  13. R. Klages, G. Radons, and I. M. Sokolov, Anomalous Transport: Foundations and Applications, 1st ed. (Wiley-VCH, 2012).
  14. D. Dunlap, H.-L. Wu, and P. Phillips, Phys. Rev. Lett. 65, 88 (1990).
    [CrossRef]
  15. P. Barthelemy, J. Bertolotti, and D. S. Wiersma, Nature 453, 495 (2008).
    [CrossRef]
  16. U. Naether, S. Stützer, R. A. Vicencio, M. I. Molina, A. Tünnermann, S. Nolte, T. Kottos, D. N. Christodoulides, and A. Szameit, New J. Phys. 15, 013045 (2013).
    [CrossRef]
  17. A. Schreiber, K. N. Cassemiro, V. Potoček, A. Gábris, I. Jex, and C. Silberhorn, Phys. Rev. Lett. 106, 180403 (2011).
    [CrossRef]
  18. L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, Nat. Phys. 8, 912 (2012).
    [CrossRef]
  19. A. Szameit and S. Nolte, J. Phys. B 43, 163001 (2010).
    [CrossRef]
  20. A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tünnermann, and F. Lederer, Appl. Phys. Lett. 90, 241113 (2007).
    [CrossRef]
  21. J. Fitzsimons and J. Twamley, Phys. Rev. A 72, 050301(R) (2005).
    [CrossRef]

2013

U. Naether, S. Stützer, R. A. Vicencio, M. I. Molina, A. Tünnermann, S. Nolte, T. Kottos, D. N. Christodoulides, and A. Szameit, New J. Phys. 15, 013045 (2013).
[CrossRef]

2012

Z. Zhang, P. Tong, J. Gong, and B. Li, Phys. Rev. Lett. 108, 070603 (2012).
[CrossRef]

L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, Nat. Phys. 8, 912 (2012).
[CrossRef]

2011

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, Science 332, 1541 (2011).
[CrossRef]

A. Schreiber, K. N. Cassemiro, V. Potoček, A. Gábris, I. Jex, and C. Silberhorn, Phys. Rev. Lett. 106, 180403 (2011).
[CrossRef]

2010

A. Szameit and S. Nolte, J. Phys. B 43, 163001 (2010).
[CrossRef]

2008

P. Barthelemy, J. Bertolotti, and D. S. Wiersma, Nature 453, 495 (2008).
[CrossRef]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef]

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Nature 453, 895 (2008).
[CrossRef]

2007

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[CrossRef]

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tünnermann, and F. Lederer, Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

2005

J. Fitzsimons and J. Twamley, Phys. Rev. A 72, 050301(R) (2005).
[CrossRef]

2001

L. Hufnagel, R. Ketzmerick, T. Kottos, and T. Geisel, Phys. Rev. E 64, 012301 (2001).
[CrossRef]

2000

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature 404, 850 (2000).
[CrossRef]

1999

I. Guarneri and H. Schulz-Baldes, Rev. Math. Phys. 11, 1249 (1999).
[CrossRef]

1997

R. Ketzmerick, K. Kruse, S. Kraut, and T. Geisel, Phys. Rev. Lett. 79, 1959 (1997).
[CrossRef]

1990

D. Dunlap, H.-L. Wu, and P. Phillips, Phys. Rev. Lett. 65, 88 (1990).
[CrossRef]

1989

I. Guarneri, Europhys. Lett. 10, 95 (1989).
[CrossRef]

Abrahams, E.

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

Aspect, A.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef]

Avidan, A.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[CrossRef]

Barthelemy, P.

P. Barthelemy, J. Bertolotti, and D. S. Wiersma, Nature 453, 495 (2008).
[CrossRef]

Bernard, A.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef]

Bertolotti, J.

P. Barthelemy, J. Bertolotti, and D. S. Wiersma, Nature 453, 495 (2008).
[CrossRef]

Billy, J.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef]

Bouyer, P.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef]

Cassemiro, K. N.

A. Schreiber, K. N. Cassemiro, V. Potoček, A. Gábris, I. Jex, and C. Silberhorn, Phys. Rev. Lett. 106, 180403 (2011).
[CrossRef]

Chabanov, A. A.

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature 404, 850 (2000).
[CrossRef]

Christodoulides, D. N.

U. Naether, S. Stützer, R. A. Vicencio, M. I. Molina, A. Tünnermann, S. Nolte, T. Kottos, D. N. Christodoulides, and A. Szameit, New J. Phys. 15, 013045 (2013).
[CrossRef]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

Clément, D.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef]

D’Errico, C.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Nature 453, 895 (2008).
[CrossRef]

Dreisow, F.

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tünnermann, and F. Lederer, Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

Dunlap, D.

D. Dunlap, H.-L. Wu, and P. Phillips, Phys. Rev. Lett. 65, 88 (1990).
[CrossRef]

Fallani, L.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Nature 453, 895 (2008).
[CrossRef]

Fattori, M.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Nature 453, 895 (2008).
[CrossRef]

Fishman, S.

L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, Nat. Phys. 8, 912 (2012).
[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[CrossRef]

Fitzsimons, J.

J. Fitzsimons and J. Twamley, Phys. Rev. A 72, 050301(R) (2005).
[CrossRef]

Fort, C.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Nature 453, 895 (2008).
[CrossRef]

Freedman, B.

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, Science 332, 1541 (2011).
[CrossRef]

Gábris, A.

A. Schreiber, K. N. Cassemiro, V. Potoček, A. Gábris, I. Jex, and C. Silberhorn, Phys. Rev. Lett. 106, 180403 (2011).
[CrossRef]

Geisel, T.

L. Hufnagel, R. Ketzmerick, T. Kottos, and T. Geisel, Phys. Rev. E 64, 012301 (2001).
[CrossRef]

R. Ketzmerick, K. Kruse, S. Kraut, and T. Geisel, Phys. Rev. Lett. 79, 1959 (1997).
[CrossRef]

Genack, A. Z.

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature 404, 850 (2000).
[CrossRef]

Gong, J.

Z. Zhang, P. Tong, J. Gong, and B. Li, Phys. Rev. Lett. 108, 070603 (2012).
[CrossRef]

Guarneri, I.

I. Guarneri and H. Schulz-Baldes, Rev. Math. Phys. 11, 1249 (1999).
[CrossRef]

I. Guarneri, Europhys. Lett. 10, 95 (1989).
[CrossRef]

Hambrecht, B.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef]

Hartung, H.

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tünnermann, and F. Lederer, Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

Hufnagel, L.

L. Hufnagel, R. Ketzmerick, T. Kottos, and T. Geisel, Phys. Rev. E 64, 012301 (2001).
[CrossRef]

Inguscio, M.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Nature 453, 895 (2008).
[CrossRef]

Jex, I.

A. Schreiber, K. N. Cassemiro, V. Potoček, A. Gábris, I. Jex, and C. Silberhorn, Phys. Rev. Lett. 106, 180403 (2011).
[CrossRef]

Josse, V.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef]

Ketzmerick, R.

L. Hufnagel, R. Ketzmerick, T. Kottos, and T. Geisel, Phys. Rev. E 64, 012301 (2001).
[CrossRef]

R. Ketzmerick, K. Kruse, S. Kraut, and T. Geisel, Phys. Rev. Lett. 79, 1959 (1997).
[CrossRef]

Klages, R.

R. Klages, G. Radons, and I. M. Sokolov, Anomalous Transport: Foundations and Applications, 1st ed. (Wiley-VCH, 2012).

Kottos, T.

U. Naether, S. Stützer, R. A. Vicencio, M. I. Molina, A. Tünnermann, S. Nolte, T. Kottos, D. N. Christodoulides, and A. Szameit, New J. Phys. 15, 013045 (2013).
[CrossRef]

L. Hufnagel, R. Ketzmerick, T. Kottos, and T. Geisel, Phys. Rev. E 64, 012301 (2001).
[CrossRef]

Kraut, S.

R. Ketzmerick, K. Kruse, S. Kraut, and T. Geisel, Phys. Rev. Lett. 79, 1959 (1997).
[CrossRef]

Krivolapov, Y.

L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, Nat. Phys. 8, 912 (2012).
[CrossRef]

Kruse, K.

R. Ketzmerick, K. Kruse, S. Kraut, and T. Geisel, Phys. Rev. Lett. 79, 1959 (1997).
[CrossRef]

Lahini, Y.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

Lederer, F.

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tünnermann, and F. Lederer, Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

Levi, L.

L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, Nat. Phys. 8, 912 (2012).
[CrossRef]

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, Science 332, 1541 (2011).
[CrossRef]

Li, B.

Z. Zhang, P. Tong, J. Gong, and B. Li, Phys. Rev. Lett. 108, 070603 (2012).
[CrossRef]

Lugan, P.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef]

Manela, O.

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, Science 332, 1541 (2011).
[CrossRef]

Modugno, G.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Nature 453, 895 (2008).
[CrossRef]

Modugno, M.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Nature 453, 895 (2008).
[CrossRef]

Molina, M. I.

U. Naether, S. Stützer, R. A. Vicencio, M. I. Molina, A. Tünnermann, S. Nolte, T. Kottos, D. N. Christodoulides, and A. Szameit, New J. Phys. 15, 013045 (2013).
[CrossRef]

Morandotti, R.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

Naether, U.

U. Naether, S. Stützer, R. A. Vicencio, M. I. Molina, A. Tünnermann, S. Nolte, T. Kottos, D. N. Christodoulides, and A. Szameit, New J. Phys. 15, 013045 (2013).
[CrossRef]

Nolte, S.

U. Naether, S. Stützer, R. A. Vicencio, M. I. Molina, A. Tünnermann, S. Nolte, T. Kottos, D. N. Christodoulides, and A. Szameit, New J. Phys. 15, 013045 (2013).
[CrossRef]

A. Szameit and S. Nolte, J. Phys. B 43, 163001 (2010).
[CrossRef]

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tünnermann, and F. Lederer, Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

Phillips, P.

D. Dunlap, H.-L. Wu, and P. Phillips, Phys. Rev. Lett. 65, 88 (1990).
[CrossRef]

Potocek, V.

A. Schreiber, K. N. Cassemiro, V. Potoček, A. Gábris, I. Jex, and C. Silberhorn, Phys. Rev. Lett. 106, 180403 (2011).
[CrossRef]

Pozzi, F.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

Radons, G.

R. Klages, G. Radons, and I. M. Sokolov, Anomalous Transport: Foundations and Applications, 1st ed. (Wiley-VCH, 2012).

Rechtsman, M.

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, Science 332, 1541 (2011).
[CrossRef]

Roati, G.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Nature 453, 895 (2008).
[CrossRef]

Sanchez-Palencia, L.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef]

Schreiber, A.

A. Schreiber, K. N. Cassemiro, V. Potoček, A. Gábris, I. Jex, and C. Silberhorn, Phys. Rev. Lett. 106, 180403 (2011).
[CrossRef]

Schulz-Baldes, H.

I. Guarneri and H. Schulz-Baldes, Rev. Math. Phys. 11, 1249 (1999).
[CrossRef]

Schwartz, T.

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, Science 332, 1541 (2011).
[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[CrossRef]

Segev, M.

L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, Nat. Phys. 8, 912 (2012).
[CrossRef]

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, Science 332, 1541 (2011).
[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[CrossRef]

Silberberg, Y.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

Silberhorn, C.

A. Schreiber, K. N. Cassemiro, V. Potoček, A. Gábris, I. Jex, and C. Silberhorn, Phys. Rev. Lett. 106, 180403 (2011).
[CrossRef]

Sokolov, I. M.

R. Klages, G. Radons, and I. M. Sokolov, Anomalous Transport: Foundations and Applications, 1st ed. (Wiley-VCH, 2012).

Sorel, M.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

Stoytchev, M.

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature 404, 850 (2000).
[CrossRef]

Stützer, S.

U. Naether, S. Stützer, R. A. Vicencio, M. I. Molina, A. Tünnermann, S. Nolte, T. Kottos, D. N. Christodoulides, and A. Szameit, New J. Phys. 15, 013045 (2013).
[CrossRef]

Szameit, A.

U. Naether, S. Stützer, R. A. Vicencio, M. I. Molina, A. Tünnermann, S. Nolte, T. Kottos, D. N. Christodoulides, and A. Szameit, New J. Phys. 15, 013045 (2013).
[CrossRef]

A. Szameit and S. Nolte, J. Phys. B 43, 163001 (2010).
[CrossRef]

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tünnermann, and F. Lederer, Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

Tong, P.

Z. Zhang, P. Tong, J. Gong, and B. Li, Phys. Rev. Lett. 108, 070603 (2012).
[CrossRef]

Tünnermann, A.

U. Naether, S. Stützer, R. A. Vicencio, M. I. Molina, A. Tünnermann, S. Nolte, T. Kottos, D. N. Christodoulides, and A. Szameit, New J. Phys. 15, 013045 (2013).
[CrossRef]

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tünnermann, and F. Lederer, Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

Twamley, J.

J. Fitzsimons and J. Twamley, Phys. Rev. A 72, 050301(R) (2005).
[CrossRef]

Vicencio, R. A.

U. Naether, S. Stützer, R. A. Vicencio, M. I. Molina, A. Tünnermann, S. Nolte, T. Kottos, D. N. Christodoulides, and A. Szameit, New J. Phys. 15, 013045 (2013).
[CrossRef]

Wiersma, D. S.

P. Barthelemy, J. Bertolotti, and D. S. Wiersma, Nature 453, 495 (2008).
[CrossRef]

Wu, H.-L.

D. Dunlap, H.-L. Wu, and P. Phillips, Phys. Rev. Lett. 65, 88 (1990).
[CrossRef]

Zaccanti, M.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Nature 453, 895 (2008).
[CrossRef]

Zhang, Z.

Z. Zhang, P. Tong, J. Gong, and B. Li, Phys. Rev. Lett. 108, 070603 (2012).
[CrossRef]

Zuo, Z.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef]

Appl. Phys. Lett.

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tünnermann, and F. Lederer, Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

Europhys. Lett.

I. Guarneri, Europhys. Lett. 10, 95 (1989).
[CrossRef]

J. Phys. B

A. Szameit and S. Nolte, J. Phys. B 43, 163001 (2010).
[CrossRef]

Nat. Phys.

L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, Nat. Phys. 8, 912 (2012).
[CrossRef]

Nature

P. Barthelemy, J. Bertolotti, and D. S. Wiersma, Nature 453, 495 (2008).
[CrossRef]

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature 404, 850 (2000).
[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[CrossRef]

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef]

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Nature 453, 895 (2008).
[CrossRef]

New J. Phys.

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Figures (4)

Fig. 1.
Fig. 1.

Microscope image of the front facet of a fabricated waveguide array. Lower row: sketch of the hybrid ordered–disordered optical lattice.

Fig. 2.
Fig. 2.

Upper row: numerical simulation of the averaged light evolution in (a) the ordered array, (b) then disordered, and (c) then the ordered–disordered hybrid lattice with a positioning disorder in the central segment of ±4μm. Lower row: averaged fluorescence images for (d) the ordered system, (e) the disordered system, and (f) an ordered–disordered hybrid system with ±4μm disorder in the position of the waveguides in the central area.

Fig. 3.
Fig. 3.

Theoretical plot of the variance of a propagating wave packet for different disorder strengths W in the couplings of the central waveguides. For W=0 (fully periodic lattice) one finds γ=2; for L=2N+1 (i.e., the position of all waveguides is random) the diffusion exponent is γ=0. Superballistic spreading with γ=2 is observed in the case L2N. As the disorder strength W increases the spreading approaches a cubic growth with γ3.

Fig. 4.
Fig. 4.

(a) Experimental diffusion exponent when calibrating the ballistic spreading to γ=2. Shown are measurements for different disorder levels (solid lines) and respective numerical fits (dashed lines). The superballistic transport of the wave packet boosts up to γ=2.40, which is 20% above ballistic spreading. (b) The logarithmic plot of the ratio between the variance of superballistic wave packets and the ballistic spreading. After an initial drop the logarithmic ratio asymptotically vanishes, that is, the spreading at superballistic transport is faster than ballistic.

Equations (5)

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iψnz+Cn,n1ψn1+Cn,n+1ψn+1=0,
M(z)nn2|ψn(z)|2zγ.
MPS=0dxx20zdz(I˙(z))δ(xv(zz)),
MPS=v2(z22Γz+2Γ22Γ2eΓz)=v2Γ(13z3+O{z4}),
δ(z)=log(M(z)/Mballistic(z))=αlog(z)log(2C0/D),

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