The Bose-Hubbard model: From Josephson junction arrays to optical lattices

Annalen der Physik (Leipzig)

Volumn 14, Issue 9-10, 2005, Pages 566-577

  Bruder, Christoph ^a   Fazio, Rosario ^b   Schön, Gerd ^c  

^a UNIVERSITY OF BASEL   (Switzerland)

^b INFM   (Italy)

^c UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Bose Hubbard model; Josephson junction arrays; Optical lattices

Indexed keywords

CRYSTAL LATTICES; GAS CONDENSATES; MATHEMATICAL MODELS; PHASE TRANSITIONS; QUANTUM THEORY; TOPOLOGY;

JOSEPHSON JUNCTION ARRAYS; OPTICAL LATTICES; QUANTUM DYNAMICS; TOPOLOGICAL EXCITATIONS;

JOSEPHSON JUNCTION DEVICES;

EID: 25844526625     PISSN: 00033804     EISSN: None     Source Type: Journal    
DOI: 10.1002/andp.200510157     Document Type: Article

References (70)

1. For a number of articles see: Coherence in Superconducting Networks, edited by J. E. Mooij and G. Schön, Physica B 152 (1988).
2. K. B. Efetov, Sov. Phys. JETP 51, 1015 (1980);
3. R. M. Bradley and S. Doniach, Phys. Rev. B 30, 1138 (1984);
4. S. Chakravarty, G.-L. Ingold, S. Kivelson, and A. Luther, Phys. Rev. Lett. 56, 2303 (1986);
5. M.P.A. Fisher, Phys. Rev. B 36, 1917 (1987);
6. W. Zwerger, J. Low Temp. Phys. 72, 291 (1988).
7. A. Kampf and G. Schön, Phys. Rev. B 36, 3651 (1987);
8. Phys. Rev. B 37, 5954 (1988).
9. P. Fazekas, B. Mühlschlegel, and M. Schröter, Z. Phys. B 57, 193 (1984);
10. B. Mühlschlegel and D. L. Mills, Phys. Rev. B 29, 159 (1984).
11. M.P.A. Fisher, G. Grinstein, and S.M. Girvin, Phys. Rev. Lett. 64, 587 (1990).
12. R. Fazio and G. Schön, Phys. Rev. B 43, 5307 (1991).
13. R. Fazio and H. vander Zant, Phys. Rep. 355, 235 (2001).
14. U. Eckern and A. Schmid, Phys. Rev. B 39, 6441 (1989).
15. A. Minguzzi, S. Succi, F. Toschi, M. P. Tosi, and P. Vignolo, Phys. Rep. 395, 223 (2004).
16. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 81, 3108 (1998).
17. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature (London) 415, 39 (2002).
18. M. P. A. Fisher, B. P. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B 40, 546 (1989).
19. R. F. Voss and R.A. Webb, Phys. Rev. B 25, 3446 (1982);
20. R. A. Webb, R. F. Voss, G. Grinstein, and P. M. Hörn, Phys. Rev. Lett. 51, 690 (1983).
21. Percolation, Localization, and Superconductivity, edited by A. M. Goldmann and S. A. Wolf (Plenum, New York, 1984), NATO ASI Series B, vol. 109.
22. Josephson Junction Arrays, edited by H. A. Cerdeira and S. R. Shenoy, Physica B 222 (1996).
23. L. J. Geerligs et al., Phys. Rev. Lett. 63, 326 (1989).
24. R. Fazio and G. Schön, Phys. Rev. B 43, 5307 (1991).
25. R. Fazio, A. van Otterlo, G. Schön, H. S. J. van der Zant, and J. E. Mooij, Helv. Phys. Acta 65, 228 (1992).
26. Ya. M. Blanter, and G. Schön, Phys. Rev. B 53, 14534 (1996).
27. Ya. M. Blanter, R. Fazio, and G. Schön, Nucl. Phys. B S58, 79 (1997).
28. J.E. Mooij, B. J. van Wees, L. J. Geerligs, M. Peters, R. Fazio, and G. Schön, Phys. Rev. Lett. 65, 645 (1990).
29. R. Fazio, A. van Otterlo, and G. Schön, Europhys. Lett. 25, 453 (1994).
30. U. Geigenmüller, C. J. Lobb, and C. B. Whan, Phys. Rev. B 47, 348 (1993).
31. H. S. J. van der Zant, F. C. Fritschy, T. P. Orlando, and J. E. Mooij, Phys. Rev. Lett. 66, 2531 (1991).
32. T. S. Tighe, A. T. Jonson, and M. Tinkham, Phys. Rev. B 44, 10286 (1991).
33. A. Matsuda and T. Kawakami, Phys. Rev. Lett. 51, 694 (1983).
34. A. Fujimaki, K. Nakajima, and Y. Sawada, Phys. Rev. Lett. 59, 2985 (1987).
35. H. S. J. van der Zant, T. P. Orlando, S. Watanabe, and S. H. Strogatz, Phys. Rev. Lett. 74, 174 (1995).
36. S. Watanabe, S. H. Strogatz, H. S. J. van der Zant, and T. P. Orlando, Phys. Rev. Lett. 74, 379 (1995).
37. H. S. J. van der Zant, F. C. Fritschy, T. P. Orlando, and J. E. Mooij, Europhys. Lett. 18, 343 (1992).
38. E. B. Sonin, Phys. Rev. B 55, 485 (1997).
39. M. P.A. Fisher, Physica A 177, 553 (1991).
40. Yu. G. Makhlin and G. E. Volovik, Pis'ma Zh. Eksp. Teor. Fiz. 62, 923 (1985)
41. [JETP Lett. 62, 941 (1995)].
42. G. E. Volovik, cond-mat/9707136.
43. There was some controversy in the literature on this point. It has been suggested that the offset charge in the equation of motion should be replaced with the electron number (F. Gaitan and S. R. Shenoy, Phys. Rev. Lett. 76, 4404 (1996)). We do not share this point of view since only the offset charges responsible for deviations from local charge neutrality in the array lead to the Magnus force.
44. B. J. van Wees, H.S.J. van der Zant, and J. E. Mooij, Phys. Rev. B 35, 7291 (1987).
45. P. Delsing, C. D. Chen, D. B. Haviland, T. Bergsten, and T. Claeson, in: Superconductivity in Networks and Mesoscopic Structures, edited by C. Giovannella and C. J. Lambert (AIP, Woodbury, NY, 1998).
46. W. Zwerger, J. Opt. B: Quantum Semiclass. Opt. 5, S9 (2003).
47. L. Pitaevskii and S. Stringari, Phys. Rev. Lett. 87, 180402 (2001).
48. A. Cuccoli, A. Fubini, R. Vaia, and V. Tognetti, Phys. Rev. A 64, 061601 (2001).
49. R. Roth and K. Burnett, Phys. Rev. A 67, 031602(R) (2003).
50. C. Schroll, F. Marquardt, and C. Bruder, Phys. Rev. A 70, 053609 (2004).
51. J. K. Freericks and H. Monien, Phys. Rev. B 53, 2691 (1996);
52. N. Elstner and H. Monien, cond-mat/9905367.
53. i - 1) in order not to include the interaction if there is only one boson on a given site [12].
54. H. P. Büchler and G. Blatter, Phys. Rev. Lett. 91, 130404 (2003).
55. C. Bruder, R. Fazio, and G. Schön, Phys. Rev. B 47, 342 (1993);
56. A. van Otterlo, K.-H. Wagenblast, R. Baltin, C. Bruder, R. Fazio, and G. Schön, Phys. Rev. B 52, 16176 (1995).
57. B. Damski, J. Zakrzewski, L. Santos, P. Zoller, and M. Lewenstein, Phys. Rev. Lett. 91, 080403 (2003).
58. D. Jaksch, H.-J. Briegel, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 82, 1975 (1999).
59. O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, Nature (London) 425, 937 (2003).
60. H.-J. Briegel and R. Raussendorf, Phys. Rev. Lett. 86, 910 (2001).
61. W. Hofstetter, J. I. Cirac, P. Zoller, E. Demier, and M. D. Lukin, Phys. Rev. Lett. 89, 220407 (2002).
62. M. Lewenstein, L. Santos, M. A. Baranov, and H. Fehrmann, Phys. Rev. Lett. 92, 050401 (2004).
63. A. S. Sorensen, E. Demler, and M. D. Lukin, Phys. Rev. Lett. 94, 086803 (2005).
64. D. Jaksch and P. Zoller, New J. Phys. 5, 56 (2003).
65. M. Polini, R. Fazio, A. H. MacDonald, and M. P. Tosi, Phys. Rev. Lett. 95, 010401 (2005).
66. E. Demler and F. Zhou, Phys. Rev. Lett. 88, 163001 (2002).
67. O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, Nature 425, 937 (2003).
68. B. Paredes, A. Widera, V. Murg, O. Mandel, S. Fölling, I. Cirac, G. V. Shlyapnikov, T. Rom, T. W. Hänsch, and I. Bloch, Nature 429, 277 (2004).
69. T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, Phys. Rev. Lett. 92, 130403 (2004).
70. M. Köhl, H. Moritz, T. Stöferle, K. Günter, and T. Esslinger, Phys. Rev. Lett. 94, 080403 (2005).