Observation of the Anderson metal-insulator transition with atomic matter waves: Theory and experiment

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 80, Issue 4, 2009, Pages

  Lemarié, Gabriel ^a   Chabé, Julien ^b,d   Szriftgiser, Pascal ^b   Garreau, Jean Claude ^b   Grémaud, Benoît ^a,c   Delande, Dominique ^a  

^a CNRS   (France)

^b UNIVERSITÉ DES SCIENCES ET TECHNOLOGIES DE LILLE   (France)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^d BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ANDERSON METAL-INSULATOR TRANSITION; ANDERSON MODELS; ATOMIC WAVE FUNCTION; COLD ATOMIC GAS; CRITICAL EXPONENT; FINITE SIZE SCALING; KICKED ROTORS; MATTER WAVES; ONE-PARAMETER SCALING; QUANTUM PHASE TRANSITIONS; QUASI-PERIODIC; SENSITIVE MEASUREMENT; THREE DIMENSIONS;

ATOMS; METAL INSULATOR BOUNDARIES; PARTICLE OPTICS; PULSED LASER APPLICATIONS; SEMICONDUCTOR INSULATOR BOUNDARIES; SEMICONDUCTOR QUANTUM DOTS; WAVE FUNCTIONS;

METAL INSULATOR TRANSITION;

EID: 70350584645     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.80.043626     Document Type: Article

References (79)

1. F. Bloch, Z. Phys. 52, 555 (1928).
2. C. Zener, Proc. R. Soc. London, Ser. A 145, 523 (1934). 10.1098/rspa.1934.0116
3. P. W. Anderson, Phys. Rev. 109, 1492 (1958). 10.1103/PhysRev.109.1492
4. D. J. Thouless, Phys. Rep. 13, 93 (1974). 10.1016/0370-1573(74)90029-5
5. J. T. Edwards and D. J. Thouless, J. Phys. C 5, 807 (1972). 10.1088/0022-3719/5/8/007
6. F. Wegner, Z. Phys. B25, 327 (1976).
7. R. Landauer, Philos. Mag. 21, 863 (1970). 10.1080/14786437008238472
8. E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979). 10.1103/PhysRevLett.42.673
9. A. MacKinnon and B. Kramer, Phys. Rev. Lett. 47, 1546 (1981). 10.1103/PhysRevLett.47.1546
10. J. L. Pichard and G. Sarma, J. Phys. C 14, L127 (1981). 10.1088/0022-3719/14/6/003
11. A. Mackinnon, J. Phys. C: Condens. Matter 6, 2511 (1994). 10.1088/0953-8984/6/13/012
12. K. Slevin and T. Ohtsuki, Phys. Rev. Lett. 82, 382 (1999). 10.1103/PhysRevLett.82.382
13. D. Vollhardt and P. Wölfle, Phys. Rev. Lett. 48, 699 (1982). 10.1103/PhysRevLett.48.699
14. P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985). 10.1103/RevModPhys.57.287
15. D. M. Basko, I. L. Aleiner, and B. L. Altshuler, Ann. Phys. 321, 1126 (2006). 10.1016/j.aop.2005.11.014
16. B. Kramer and A. Mackinnon, Rep. Prog. Phys. 56, 1469 (1993). 10.1088/0034-4885/56/12/001
17. M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, Phys. Rev. Lett. 96, 063904 (2006). 10.1103/PhysRevLett.96.063904
18. T. Schwartz, G. Bartal, S. Fishman, and B. Segev, Nature (London) 446, 52 (2007). 10.1038/nature05623
19. C. A. Condat and T. R. Kirkpatrick, Phys. Rev. B 36, 6782 (1987). 10.1103/PhysRevB.36.6782
20. I. S. Graham, L. Piché, and M. Grant, Phys. Rev. Lett. 64, 3135 (1990). 10.1103/PhysRevLett.64.3135
21. H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. van Tiggelen, Nature Phys. 4, 945 (2008). 10.1038/nphys1101
22. J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature (London) 453, 891 (2008). 10.1038/nature07000
23. B. V. Chirikov, Phys. Rep. 52, 263 (1979). 10.1016/0370-1573(79)90023-1
24. G. Casati, B. V. Chirikov, J. Ford, and F. M. Izrailev, Stochastic Behavior of a Quantum Pendulum Under Periodic Perturbation (Springer-Verlag, Berlin, 1979), Vol. 93, pp. 334-352.
25. D. R. Grempel, R. E. Prange, and S. Fishman, Phys. Rev. A 29, 1639 (1984). 10.1103/PhysRevA.29.1639
26. G. Casati, I. Guarneri, and D. L. Shepelyansky, Phys. Rev. Lett. 62, 345 (1989). 10.1103/PhysRevLett.62.345
27. F. L. Moore, J. C. Robinson, C. F. Bharucha, B. Sundaram, and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995). 10.1103/PhysRevLett.75.4598
28. J. Chabé, G. Lemarié, B. Grémaud, D. Delande, P. Szriftgiser, and J. C. Garreau, Phys. Rev. Lett. 101, 255702 (2008). 10.1103/PhysRevLett.101.255702
29. F. M. Izrailev, Phys. Rep. 196, 299 (1990). 10.1016/0370-1573(90)90067-C
30. D. L. Shepelyansky, Phys. Rev. Lett. 56, 677 (1986). 10.1103/PhysRevLett. 56.677
31. When the quasimomentum is taken into account, m should simply be replaced by m+β, leaving the conclusions unaffected.
32. W (θ) is singular for K/ k- >π and the behavior of Wr is complicated. However, this nonphysical singularity can be avoided by a mapping on a different tight-binding model.
33. H. Lignier, J. C. Garreau, P. Szriftgiser, and D. Delande, Europhys. Lett. 69, 327 (2005). 10.1209/epl/i2004-10353-8
34. Y. V. Fyodorov and A. D. Mirlin, Phys. Rev. Lett. 67, 2405 (1991). 10.1103/PhysRevLett.67.2405
35. K. Efetov, Supersymmetry in Disorder and Chaos (Cambridge University Press, Cambridge, UK, 1997).
36. A. Altland and M. R. Zirnbauer, Phys. Rev. Lett. 77, 4536 (1996). 10.1103/PhysRevLett.77.4536
37. D. Vollhardt and P. Wölfle, Phys. Rev. B 22, 4666 (1980). 10.1103/PhysRevB.22.4666
38. A. Altland, Phys. Rev. Lett. 71, 69 (1993). 10.1103/PhysRevLett.71.69
39. E. Doron and S. Fishman, Phys. Rev. Lett. 60, 867 (1988). 10.1103/PhysRevLett.60.867
40. J. Wang and A. M. García-García, Phys. Rev. E 79, 036206 (2009). 10.1103/PhysRevE.79.036206
41. D. L. Shepelyansky, Physica D 8, 208 (1983). 10.1016/0167-2789(83)90318-4
42. O. I. Lobkis and R. L. Weaver, Phys. Rev. E 71, 011112 (2005). 10.1103/PhysRevE.71.011112
43. R. Scharf, J. Phys. A 22, 4223 (1989). 10.1088/0305-4470/22/19/016
44. R. Blümel and U. Smilansky, Phys. Rev. Lett. 69, 217 (1992). 10.1103/PhysRevLett.69.217
45. F. Haake, Quantum Signatures of Chaos, 2nd ed. (Springer-Verlag, Berlin, 2001).
46. H. J. Stöckmann, Quantum Chaos: An Introduction (Cambridge University Press, Cambridge, UK, 1999).
47. D. M. Basko, M. A. Skvortsov, and V. E. Kravtsov, Phys. Rev. Lett. 90, 096801 (2003). 10.1103/PhysRevLett.90.096801
48. F. Borgonovi and D. L. Shepelyansky, Physica D 109, 24 (1997). 10.1016/S0167-2789(97)00155-3
49. Q. Li, C. M. Soukoulis, E. N. Economou, and G. S. Grest, Phys. Rev. B 40, 2825 (1989). 10.1103/PhysRevB.40.2825
50. N. A. Panagiotides, S. N. Evangelou, and G. Theodorou, Phys. Rev. B 49, 14122 (1994). 10.1103/PhysRevB.49.14122
51. I. Zambetaki, Q. Li, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 76, 3614 (1996). 10.1103/PhysRevLett.76.3614
52. J. Ringot, Y. Lecoq, J. C. Garreau, and P. Szriftgiser, Eur. Phys. J. D 7, 285 (1999). 10.1007/s100530050571
53. J. Ringot, P. Szriftgiser, and J. C. Garreau, Phys. Rev. A 65, 013403 (2001). 10.1103/PhysRevA.65.013403
54. P. Szriftgiser, H. Lignier, J. Ringot, J. C. Garreau, and D. Delande, Commun. Nonlinear Sci. Numer. Simul. 8, 301 (2003). 10.1016/S1007-5704(03)00031- 5
55. J. Chabé, H. Lignier, P. Szriftgiser, and J. C. Garreau, Opt. Commun. 274, 254 (2007). 10.1016/j.optcom.2007.02.008
56. J. Ringot, P. Szriftgiser, J. C. Garreau, and D. Delande, Phys. Rev. Lett. 85, 2741 (2000). 10.1103/PhysRevLett.85.2741
57. P. Szriftgiser, J. Ringot, D. Delande, and J. C. Garreau, Phys. Rev. Lett. 89, 224101 (2002). 10.1103/PhysRevLett.89.224101
58. H. Lignier, J. Chabé, D. Delande, J. C. Garreau, and P. Szriftgiser, Phys. Rev. Lett. 95, 234101 (2005). 10.1103/PhysRevLett.95.234101
59. J. Chabé, H. Lignier, H. Cavalcante, D. Delande, P. Szriftgiser, and J. C. Garreau, Phys. Rev. Lett. 97, 264101 (2006). 10.1103/PhysRevLett.97. 264101
60. W. H. Zurek, Rev. Mod. Phys. 75, 715 (2003). 10.1103/RevModPhys.75.715
61. M. Janssen, Phys. Rep. 295, 1 (1998). 10.1016/S0370-1573(97)00050-1
62. G. Lemarié (unpublished).
63. M. G. Raizen, F. L. Moore, J. C. Robinson, C. F. Bharucha, and B. Sundaram, J. Eur. Opt. Soc. Rapid Publ. 8, 687 (1996).
64. F. Evers and A. D. Mirlin, Rev. Mod. Phys. 80, 1355 (2008). 10.1103/RevModPhys.80.1355
65. G. Lemarié (unpublished).
66. D. Stauffer and A. Aharony, Introduction to Percolation Theory, 2nd ed. (Taylor and Francis, London, 1994).
67. T. Ohtsuki and T. Kawarabayashi, J. Phys. Soc. Jpn. 66, 314 (1997). 10.1143/JPSJ.66.314
68. A. D. Mirlin and Y. V. Fyodorov, Phys. Rev. Lett. 72, 526 (1994). 10.1103/PhysRevLett.72.526
69. A. MacKinnon and B. Kramer, Z. Phys. B 53, 1 (1983). 10.1007/BF01578242
70. A. M. García-García, Phys. Rev. Lett. 100, 076404 (2008). 10.1103/PhysRevLett.100.076404
71. B. Shapiro and E. Abrahams, Phys. Rev. B 24, 4889 (1981). 10.1103/PhysRevB.24.4889
72. F. Milde, R. Römer, M. Schreiber, and V. Uski, Eur. Phys. J. B 15, 685 (2000). 10.1007/s100510051173
73. G. Lemarié, B. Grémaud, and D. Delande, EPL 87, 37007 (2009). 10.1209/0295-5075/87/37007
74. K. Slevin and T. Ohtsuki, Phys. Rev. Lett. 78, 4083 (1997). 10.1103/PhysRevLett.78.4083
75. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed. (Cambridge University Press, Cambridge, UK, 1992).
76. K. B. Efetov, Adv. Phys. 32, 53 (1983). 10.1080/00018738300101531
77. D. L. Shepelyansky, Physica D 28, 103 (1987). 10.1016/0167-2789(87)90123- 0
78. D. A. Steck, V. Milner, W. H. Oskay, and M. G. Raizen, Phys. Rev. E 62, 3461 (2000). 10.1103/PhysRevE.62.3461
79. J. Wang and J. Gong, Phys. Rev. A 77, 031405 (R) (2008). 10.1103/PhysRevA.77.031405