Bogoliubov theory of interacting bosons on a lattice in a synthetic magnetic field

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 83, Issue 1, 2011, Pages

  Powell, Stephen ^a   Barnett, Ryan ^a   Sensarma, Rajdeep ^a   Das Sarma, Sankar ^a  

^a University of Maryland   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC SYSTEM; BOGOLIUBOV THEORY; BOSE HUBBARD MODEL; BRAGG SPECTROSCOPY; GROSS-PITAEVSKII EQUATION; HIGHER ORDER; HOFSTADTER; INTERACTING BOSONS; MAGNETIC SYMMETRY; MOTT INSULATOR PHASE; OPTICAL LATTICES; QUASIPARTICLE EXCITATIONS; SPATIAL ORDERS; SPATIAL STRUCTURE; SUPERFLUID PHASE; SUPERFLUID PHASIS; THERMAL FLUCTUATIONS; TIGHT BINDING; TIME OF FLIGHT;

BOSE-EINSTEIN CONDENSATION; HUBBARD MODEL; THERMAL EXPANSION;

MAGNETIC FIELDS;

EID: 78751489562     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.83.013612     Document Type: Article

References (84)

1. M. Tinkham, Introduction to Superconductivity (McGraw-Hill, New York, 1996).
2. R. J. Donnelly, Quantized Vortices in Helium II (Cambridge University Press, Cambridge, 1991).
3. N. R. Cooper, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730802564122 57, 539 (2008).
4. S. Tung, V. Schweikhard, and E. A. Cornell, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.240402 97, 240402 (2006).
5. J. W. Reijnders and R. A. Duine, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.060401 93, 060401 (2004);
6. J. W. Reijnders and R. A. Duine, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.063607 71, 063607 (2005).
7. R. A. Williams, S. Al-Assam, and C. J. Foot, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.050404 104, 050404 (2010).
8. M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.40.546 40, 546 (1989).
9. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.3108 81, 3108 (1998).
10. I. B. Spielman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.063613 79, 063613 (2009).
11. Y.-J. Lin, R. L. Compton, A. R. Perry, W. D. Phillips, J. V. Porto, and I. B. Spielman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.130401 102, 130401 (2009).
12. Y.-J. Lin, R. L. Compton, K. Jiménez-García, J. V. Porto, and I. B. Spielman, Nature NATUAS 0028-0836 10.1038/nature08609 462, 628 (2009).
13. R. Dum and M. Olshanii, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.1788 76, 1788 (1996).
14. D. Jaksch and P. Zoller, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/5/1/356 5, 56 (2003).
15. E. J. Mueller, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.041603 70, 041603 (R) (2004).
16. A. S. Sørensen, E. Demler, and M. D. Lukin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.086803 94, 086803 (2005).
17. F. Gerbier and J. Dalibard, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/12/3/033007 12, 033007 (2010).
18. M. Hafezi, A. S. Sørensen, E. Demler, and M. D. Lukin, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.023613 76, 023613 (2007).
19. R. N. Palmer, A. Klein, and D. Jaksch, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.013609 78, 013609 (2008).
20. G. Möller and N. R. Cooper, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.105303 103, 105303 (2009).
21. J. M. Luttinger, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.84.814 84, 814 (1951).
22. P. G. Harper, Proc. Phys. Soc. London, Sect. A PPSAAM 0370-1298 10.1088/0370-1298/68/10/304 68, 874 (1955).
23. G. H. Wannier, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.34.645 34, 645 (1962).
24. E. Brown, Bull. Am. Phys. Soc. 8, 257 (1963);
25. E. Brown, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.133.A1038 133, A1038 (1964).
26. J. Zak, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.134.A1602 134, A1602 (1964);
27. J. Zak, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.134.A1607 134, A1607 (1964).
28. D. Hofstadter, Phys. Rev. B PHRVAO 1098-0121 10.1103/PhysRevB.14.2239 14, 2239 (1976).
29. G. M. Obermair and H.-J. Schellnhuber, Phys. Rev. B PHRVAO 1098-0121 10.1103/PhysRevB.23.5185 23, 5185 (1981);
30. H.-J. Schellnhuber, G. M. Obermair, and A. Rauh, Phys. Rev. B PHRVAO 1098-0121 10.1103/PhysRevB.23.5191 23, 5191 (1981).
31. D. S. Goldbaum and E. J. Mueller, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.033629 77, 033629 (2008);
32. D. S. Goldbaum and E. J. Mueller, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.021602 79, 021602 (R) (2009).
33. S. Powell, R. Barnett, R. Sensarma, and S. Das Sarma, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.255303 104, 255303 (2010).
34. A. M. Rey, K. Burnett, R. Roth, M. Edwards, C. J. Williams, and C. W. Clark, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/36/5/304 36, 825 (2003).
35. L.-K. Lim, C. M. Smith, and A. Hemmerich, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.130402 100, 130402 (2008);
36. L.-K. Lim, C. M. Smith, and A. Hemmerich, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.023404 81, 023404 (2010).
37. T. Crossed D signurić and D. K. K. Lee, Phys. Rev. B PLRAAN 1098-0121 10.1103/PhysRevB.81.014520 81, 014520 (2010).
38. H. Zhai, R. O. Umucalilar, and M. ÖOktel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.145301 104, 145301 (2010).
39. S. Alexander, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.27.1541 27, 1541 (1983).
40. B. Pannetier, J. Chaussy, R. Rammal, and J. C. Villegier, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.53.1845 53, 1845 (1984).
41. S. Teitel and C. Jayaprakash, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.51.1999 51, 1999 (1983).
42. T. C. Halsey, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.31.5728 31, 5728 (1985).
43. M. Polini, R. Fazio, A. H. MacDonald, and M. P. Tosi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.010401 95, 010401 (2005).
44. K. Kasamatsu, J. Low Temp. Phys. JLTPAC 0022-2291 10.1007/s10909-007- 9601-9 150, 593 (2008);
45. K. Kasamatsu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.021604 79, 021604 (R) (2009).
46. M. ÖOktel, M. Nita, and B. Tanatar, Phys. Rev. B PLRAAN 1098-0121 10.1103/PhysRevB.75.045133 75, 045133 (2007).
47. R. O. Umucalilar and M. ÖOktel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.055601 76, 055601 (2007).
48. R. Sachdeva, S. Johri, and S. Ghosh, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.82.063617 82, 063617 (2010).
49. V. W. Scarola and S. Das Sarma, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.210403 98, 210403 (2007).
50. D. S. Goldbaum and E. J. Mueller, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.063625 79, 063625 (2009).
51. E. Lundh, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/84/10007 84, 10007 (2008).
52. S. Sinha and K. Sengupta, e-print arXiv: 1003.0258v1.
53. R. Moessner, Can. J. Phys. CJPHAD 0008-4204 10.1139/cjp-79-11-12-1283 79, 1283 (2001).
54. T. D. Stanescu, V. Galitski, J. Y. Vaishnav, C. W. Clark, and S. Das Sarma, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.053639 79, 053639 (2009);
55. T. D. Stanescu, V. Galitski, and S. Das Sarma, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.82.013608 82, 013608 (2010).
56. K. Saha, K. Sengupta, and K. Ray, e-print arXiv: 1005.4476v1.
57. N. N. Bogoliubov, J. Phys. (USSR) 11, 23 (1947).
58. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1963).
59. R. Bhat, M. Krämer, J. Cooper, and M. J. Holland, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.043601 76, 043601 (2007).
60. X.-G. Wen, Phys. Rev. B PLRAAN 1098-0121 10.1103/PhysRevB.65.165113 65, 165113 (2002).
61. y act simultaneously each of the N particles. The more familiar expression in which N is replaced by 1 applies for operators defined to act on the single-particle wave function.
62. L. Balents, L. Bartosch, A. Burkov, S. Sachdev, and K. Sengupta, Phys. Rev. B PLRAAN 1098-0121 10.1103/PhysRevB.71.144508 71, 144508 (2005);
63. L. Balents, L. Bartosch, A. Burkov, S. Sachdev, and K. Sengupta, Prog. Theor. Phys. Suppl. PTPSAL 0375-9687 10.1143/PTPS.160.314 160, 314 (2005).
64. M. Kohmoto, Phys. Rev. B PTPSAL 1098-0121 10.1103/PhysRevB.39.11943 39, 11943 (1989).
65. W. S. Bakr, J. I. Gillen, A. Peng, S. Fölling, and M. Greiner, Nature NATUAS 0028-0836 10.1038/nature08482 462, 74 (2009);
66. W. S. Bakr, A. Peng, M. E. Tai, R. Ma, J. Simon, J. I. Gillen, S. Fölling, L. Pollet, and M. Greiner, Science 0036-8075 10.1126/science. 1192368 329, 547 (2010).
67. J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, and S. Kuhr, Nature NATUAS 0028-0836 10.1038/nature09378 467, 68 (2010).
68. J.-P. Blaizot and G. Ripka, Quantum Theory of Finite Systems (MIT Press, Cambridge, MA, 1986).
69. N. D. Mermin and H. Wagner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.17.1133 17, 1133 (1966).
70. P. C. Hohenberg, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.158.383 158, 383 (1966).
71. V. Bagnato and D. Kleppner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.44.7439 44, 7439 (1991).
72. K. Jiménez-García, R. L. Compton, Y.-J. Lin, W. D. Phillips, J. V. Porto, and I. B. Spielman, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.105.110401 105, 110401 (2010).
73. B. Capogrosso-Sansone, S. G. Soyler, N. Prokofev, and B. Svistunov, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.015602 77, 015602 (2008).
74. E. Toth, A. M. Rey, and P. B. Blakie, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.013627 78, 013627 (2008).
75. One can easily check that this gives the correct result for a classical particle that starts at position r with zero kinetic energy. It has zero dynamical momentum, and hence canonical momentum A (r). When the Raman beams are suddenly switched off, its canonical momentum is preserved, so its final momentum (dynamical or canonical) is A (r). This momentum can be viewed as the result of an induced electric field - A • acting during the period that the gauge potential is switched off [10,11].
76. J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.4569 82, 4569 (1999).
77. D. M. Stamper-Kurn, A. P. Chikkatur, A. Görlitz, S. Inouye, S. Gupta, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.2876 83, 2876 (1999).
78. C. Kollath, M. Köhl, and T. Giamarchi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.063602 76, 063602 (2007).
79. J. T. Stewart, J. P. Gaebler, and D. S. Jin, Nature NATUAS 0028-0836 10.1038/nature07172 454, 744 (2008).
80. R. Sensarma, D. Pekker, M. D. Lukin, and E. Demler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.035303 103, 035303 (2009).
81. N. Strohmaier, D. Greif, R. Jördens, L. Tarruell, H. Moritz, T. Esslinger, R. Sensarma, D. Pekker, E. Altman, and E. Demler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.080401 104, 080401 (2010).
82. D. Clément, N. Fabbri, L. Fallani, C. Fort, and M. Inguscio, J. Low Temp. Phys. JLTPAC 0022-2291 10.1007/s10909-009-0040-7 158, 5 (2010).
83. A. M. Rey, P. B. Blakie, G. Pupillo, C. J. Williams, and C. W. Clark, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.023407 72, 023407 (2005).
84. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature NATUAS 0028-0836 10.1038/415039a 415, 39 (2002).