Anderson localization of a weakly interacting one-dimensional Bose gas

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 80, Issue 3, 2009, Pages

  Paul, T ^a,b   Albert, M ^a   Schlagheck, P ^c,d   Leboeuf, P ^a   Pavloff, N ^a  

^a UNIVERSITÉ PARIS SUD   (France)

^b INSTITUT FÜR THEORETISCHE PHYSIK   (Germany)

^c UNIVERSITY OF REGENSBURG   (Germany)

^d LUND INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

ANDERSON LOCALIZATION; BOSE GAS; CONDENSED PARTICLES; DISORDERED REGIONS; INTERACTION EFFECT; LENGTH SCALE; LOCALIZATION LENGTH; PHASE-COHERENT TRANSPORT; PROBABILITY DENSITIES; QUASI-ONE-DIMENSIONAL; RANDOM POTENTIALS; STATIONARY REGIME; THEORETICAL PREDICTION; TIME-DEPENDENT FLOW; TRANSMISSION COEFFICIENTS;

FOKKER PLANCK EQUATION; FORECASTING; PROBABILITY DENSITY FUNCTION;

SEMICONDUCTOR QUANTUM DOTS;

EID: 70349296898     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.80.033615     Document Type: Article

References (81)

1. P. W. Anderson, Phys. Rev. 109, 1492 (1958). 10.1103/PhysRev.109.1492
2. J. Billy, Nature (London) 453, 891 (2008). 10.1038/nature07000
3. G. Roati, Nature (London) 453, 895 (2008). 10.1038/nature07071
4. K. Huang and H. F. Meng, Phys. Rev. Lett. 69, 644 (1992). 10.1103/PhysRevLett.69.644
5. S. Giorgini, L. Pitaevskii, and S. Stringari, Phys. Rev. B 49, 12938 (1994). 10.1103/PhysRevB.49.12938
6. G. E. Astrakharchik, J. Boronat, J. Casulleras, and S. Giorgini, Phys. Rev. A 66, 023603 (2002). 10.1103/PhysRevA.66.023603
7. D. Clément, P. Bouyer, A. Aspect, and L. Sanchez-Palencia, Phys. Rev. A 77, 033631 (2008). 10.1103/PhysRevA.77.033631
8. Y. P. Chen, J. Hitchcock, D. Dries, M. Junker, C. Welford, and R. G. Hulet, Phys. Rev. A 77, 033632 (2008). 10.1103/PhysRevA.77.033632
9. T. Giamarchi and H. J. Schulz, Phys. Rev. B 37, 325 (1988). 10.1103/PhysRevB.37.325
10. M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B 40, 546 (1989). 10.1103/PhysRevB.40.546
11. S. A. Gredeskul and Y. S. Kivshar, Phys. Rep. 216, 1 (1992). 10.1016/0370-1573(92)90023-S
12. N. Bilas and N. Pavloff, Phys. Rev. Lett. 95, 130403 (2005). 10.1103/PhysRevLett.95.130403
13. T. Paul, P. Leboeuf, N. Pavloff, K. Richter, and P. Schlagheck, Phys. Rev. A 72, 063621 (2005). 10.1103/PhysRevA.72.063621
14. T. Paul, P. Schlagheck, P. Leboeuf, and N. Pavloff, Phys. Rev. Lett. 98, 210602 (2007). 10.1103/PhysRevLett.98.210602
15. C. Menotti and S. Stringari, Phys. Rev. A 66, 043610 (2002). 10.1103/PhysRevA.66.043610
16. D. S. Petrov, G. V. Shlyapnikov, and J. T. M. Walraven, Phys. Rev. Lett. 85, 3745 (2000). 10.1103/PhysRevLett.85.3745
17. C. Raman, M. Kohl, R. Onofrio, D. S. Durfee, C. E. Kuklewicz, Z. Hadzibabic, and W. Ketterle, Phys. Rev. Lett. 83, 2502 (1999). 10.1103/PhysRevLett.83.2502
18. R. Onofrio, C. Raman, J. M. Vogels, J. R. Abo-Shaeer, A. P. Chikkatur, and W. Ketterle, Phys. Rev. Lett. 85, 2228 (2000). 10.1103/PhysRevLett.85.2228
19. P. Engels and C. Atherton, Phys. Rev. Lett. 99, 160405 (2007). 10.1103/PhysRevLett.99.160405
20. M. Olshanii, Phys. Rev. Lett. 81, 938 (1998). 10.1103/PhysRevLett.81.938
21. A. D. Jackson, G. M. Kavoulakis, and C. J. Pethick, Phys. Rev. A 58, 2417 (1998). 10.1103/PhysRevA.58.2417
22. P. Leboeuf and N. Pavloff, Phys. Rev. A 64, 033602 (2001). 10.1103/PhysRevA.64.033602
23. L. P. Pitaevskii and S. Stringari, J. Low Temp. Phys. 85, 377 (1991). 10.1007/BF00682193
24. M. Schwartz, Phys. Rev. B 15, 1399 (1977). 10.1103/PhysRevB.15.1399
25. D. S. Petrov, Ph.D. thesis, University of Amsterdam, 2003
26. available online at http://www-old.amolf.nl/publications/theses/petrow
27. A. V. Lopatin and V. M. Vinokur, Phys. Rev. Lett. 88, 235503 (2002). 10.1103/PhysRevLett.88.235503
28. G. E. Astrakharchik and L. P. Pitaevskii, Phys. Rev. A 70, 013608 (2004). 10.1103/PhysRevA.70.013608
29. T. Ernst, T. Paul, and P. Schlagheck, e-print arXiv:0905.4750.
30. V. Hakim, Phys. Rev. E 55, 2835 (1997). 10.1103/PhysRevE.55.2835
31. H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, England, 1997).
32. P. Leboeuf, N. Pavloff, and S. Sinha, Phys. Rev. A 68, 063608 (2003). 10.1103/PhysRevA.68.063608
33. T. Paul, M. Hartung, K. Richter, and P. Schlagheck, Phys. Rev. A 76, 063605 (2007). 10.1103/PhysRevA.76.063605
34. B. I. Ivlev and N. B. Kopnin, Adv. Phys. 33, 47 (1984). 10.1080/00018738400101641
35. J. S. Langer and V. Ambegaokar, Phys. Rev. 164, 498 (1967). 10.1103/PhysRev.164.498
36. Note in particular that condition 11 is always fulfilled in the absence of interaction since in this case the speed of sound is c≡0.
37. B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped Semiconductors (Springer-Verlag, Berlin, 1984).
38. J. Fortágh and C. Zimmermann, Rev. Mod. Phys. 79, 235 (2007). 10.1103/RevModPhys.79.235
39. S. Kraft, A. Gúnther, H. Ott, D. Wharam, C. Zimmermann, and J. Fortágh, J. Phys. B 35, L469 (2002). 10.1088/0953-4075/35/21/102
40. J. Estève, C. Aussibal, T. Schumm, C. Figl, D. Mailly, I. Bouchoule, C. I. Westbrook, and A. Aspect, Phys. Rev. A 70, 043629 (2004) 10.1103/PhysRevA.70.043629
41. T. Schumm, Eur. Phys. J. D 32, 171 (2005). 10.1140/epjd/e2005-00016-x
42. D.-W. Wang, M. D. Lukin, and E. Demler, Phys. Rev. Lett. 92, 076802 (2004). 10.1103/PhysRevLett.92.076802
43. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications, (Roberts and Company Publishers, Greenwood Village, 2007).
44. D. Clément, A. F. Varón, J. A. Retter, L. Sanchez-Palencia, A. Aspect and P. Bouyer, New J. Phys. 8, 165 (2006). 10.1088/1367-2630/8/8/165
45. L. Fallani, C. Fort, and M. Inguscio, Adv. At., Mol., Opt. Phys. 56, 119 (2008).
46. Equation 36 corresponds to a typical physical situation where the potential seen by the particles is proportional to the intensity of an electric field whose components are random Gaussian variables.
47. In Ref. this region has been improperly called "Ohmic."
48. T. N. Antsygina, L. A. Pastur, and V. A. Slyusarev, Fiz. Nizk. Temp. 7, 5 (1981)
49. [T. N. Antsygina, L. A. Pastur, and V. A. Slyusarev, Sov. J. Low Temp. Phys. 7, 1 (1981)].
50. I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (John Wiley, New York, 1988).
51. O. N. Dorokhov, Pis'ma Zh. Eksp. Teor. Fiz. 36, 259 (1982)
52. [O. N. Dorokhov, JETP Lett. 36, 318 (1982)]
53. P. A. Mello, P. Pereyra, and N. Kumar, Ann. Phys. (N.Y.) 181, 290 (1988). 10.1016/0003-4916(88)90169-8
54. V. I. Mel'nikov, Fiz. Tverd. Tela (Leningrad) 23, 782 (1981)
55. [V. I. Mel'nikov, Sov. Phys. Solid State 23, 444 (1981)].
56. C. W. J. Beenakker, Rev. Mod. Phys. 69, 731 (1997). 10.1103/RevModPhys. 69.731
57. P. A. Mello, J. Math. Phys. 27, 2876 (1986). 10.1063/1.527265
58. C. W. J. Beenakker and J. A. Melsen, Phys. Rev. B 50, 2450 (1994). 10.1103/PhysRevB.50.2450
59. In order to complete the proof of this equivalence one has to show that the mean value λ =t=L/ Lloc (κ) obtained from Eq. 68 for a sample of length X=L is identical to result 45. This amounts to show that for a potential of form 21 one has | U δ (2κ) | 2 = (2 /m) 2 σL, which is easily obtained.
60. A. A. Abrikosov, Solid State Commun. 37, 997 (1981). 10.1016/0038- 1098(81)91203-5
61. B. A. Van Tiggelen, in Diffusive Waves in Complex Media, edited by, J. P. Fouque, (Kluwer Academic Publishers, Dordrecht, 1999), p. 1.
62. Note that in Ref. the theoretical determination of L□ was obtained using a criterion different from Eq. 80 resulting in a less precise estimate at high V/c.
63. F. M. Izrailev and A. A. Krokhin, Phys. Rev. Lett. 82, 4062 (1999). 10.1103/PhysRevLett.82.4062
64. L. Sanchez-Palencia, D. Clement, P. Lugan, P. Bouyer, G. V. Shlyapnikov, and A. Aspect, Phys. Rev. Lett. 98, 210401 (2007). 10.1103/PhysRevLett.98.210401
65. L. Tessieri, J. Phys. A 35, 9585 (2002). 10.1088/0305-4470/35/45/307
66. E. Gurevich and O. Kenneth, Phys. Rev. A 79, 063617 (2009). 10.1103/PhysRevA.79.063617
67. P. Lugan, A. Aspect, L. Sanchez-Palencia, D. Delande, B. Gremaud, C. Muller, and C. Miniatura, Phys. Rev. A 80, 023605 (2009). 10.1103/PhysRevA.80. 023605
68. A. F. Ioffe and A. R. Regel, Prog. Semicond. 4, 237 (1960).
69. Note that the value V□ /c=7.95 does not depend on the type of correlation of the disordered potential considered since it is simply the value of V/c for which Eq. 81 admits the solution t□ =1.
70. W. Guerin, J.-F. Riou, J. P. Gaebler, V. Josse, P. Bouyer, and A. Aspect, Phys. Rev. Lett. 97, 200402 (2006). 10.1103/PhysRevLett.97.200402
71. N. Pavloff, Phys. Rev. A 66, 013610 (2002). 10.1103/PhysRevA.66.013610
72. Note that there is a factor of 2 difference between the present definition 14 of κ and the one used in Ref.
73. Y. Imry, Introduction to Mesoscopic Physics (Oxford University Press, Oxford, 1997).
74. D. L. Shepelyansky, Phys. Rev. Lett. 70, 1787 (1993) 10.1103/PhysRevLett. 70.1787
75. G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, Phys. Rev. Lett. 100, 084103 (2008) 10.1103/PhysRevLett.100.084103
76. A. S. Pikovsky and D. L. Shepelyansky, Phys. Rev. Lett. 100, 094101 (2008) 10.1103/PhysRevLett.100.094101
77. S. Fishman, A. Iomin, and K. Mallick, Phys. Rev. E 78, 066605 (2008). 10.1103/PhysRevE.78.066605
78. S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge University Press, Cambridge, England, 1995).
79. M. V. Berry and S. Klein, Eur. J. Phys. 18, 222 (1997). 10.1088/0143-0807/18/3/017
80. C. Texier, Ph.D. thesis, Université Paris 6, 1999
81. available online at http://www.lptms.u-psud.fr/membres/texier/research. html