Ultracold fermions in a graphene-type optical lattice

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 80, Issue 4, 2009, Pages

  Lee, Kean Loon ^a,b,c   Grémaud, Benoît ^a,b,d   Han, Rui ^a   Englert, Berthold Georg ^a,d   Miniatura, Christian ^a,d,e  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b CNRS   (France)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^d NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^e INSTITUT NON LINÉAIRE DE NICE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ACTUAL EXPERIMENTS; BRILLOUIN ZONES; COHERENT SUPERPOSITIONS; CRITICAL INTENSITY; DIAGONALIZATIONS; DIRAC FERMIONS; FERMIONIC ATOMS; FINE TUNING; GRAPHENES; HALF-FILLING; HAMILTONS; HOPPING PARAMETERS; INCOHERENT SUPERPOSITION; INSTANTONS; LASER CONFIGURATION; LASER WAVES; NEAREST-NEIGHBORS; OPTICAL LATTICES; OPTICAL POTENTIAL; SQUARE ROOTS; STANDING WAVE; TEMPERATURE RANGE; TIGHT BINDING; TWO-DIMENSIONAL OPTICAL LATTICES; ULTRA-COLD; ULTRACOLD FERMIONS;

CRYSTAL LATTICES; FERMIONS; GRAPHITE; LASERS; OPTICAL MATERIALS; SOUND REPRODUCTION;

OPTICAL PROPERTIES;

EID: 70350214942     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.80.043411     Document Type: Article

References (67)

1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004). 10.1126/science.1102896
2. R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Physical Properties of Carbon Nanotubes (Imperial College Press, London, 1998).
3. G. W. Semenoff, Phys. Rev. Lett. 53, 2449 (1984). 10.1103/PhysRevLett.53. 2449
4. M. Wilson, Phys. Today 59 (1), 21 (2006).
5. A. C. Neto, F. Guinea, and N. M. Peres, Phys. World 19 (11), 33 (2006).
6. S. Y. Zhou, G.-H. Gweon, J. Graf, A. V. Fedorov, C. D. Spataru, R. D. Diehl, Y. Kopelevich, D.-H. Lee, S. G. Louie, and A. Lanzara, Nat. Phys. 2, 595 (2006). 10.1038/nphys393
7. M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, Nat. Phys. 2, 620 (2006). 10.1038/nphys384
8. M. I. Katsnelson and K. S. Novoselov, Solid State Commun. 143, 3 (2007). 10.1016/j.ssc.2007.02.043
9. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009). 10.1103/RevModPhys.81.109
10. K. Novoselov, A. Geim, S. Morozov, D. Jiang, M. Katsnelson, I. Grigorieva, S. Dubonos, and A. Firsov, Nature (London) 438, 197 (2005). 10.1038/nature04233
11. Y. Zhang, Y. Tan, H. Stormer, and P. Kim, Nature (London) 438, 201 (2005). 10.1038/nature04235
12. G. Li and E. Andrei, Nat. Phys. 3, 623 (2007). 10.1038/nphys653
13. I. Bloch, Nat. Phys. 1, 23 (2005). 10.1038/nphys138
14. M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen(de), and U. Sen, Adv. Phys. 56, 243 (2007). 10.1080/00018730701223200
15. E. Timmermans, P. Tommasini, M. Hussein, and A. Kerman, Phys. Rep. 315, 199 (1999). 10.1016/S0370-1573(99)00025-3
16. S.-L. Zhu, B. Wang, and L.-M. Duan, Phys. Rev. Lett. 98, 260402 (2007). 10.1103/PhysRevLett.98.260402
17. P. Dietl, F. Piéchon, and G. Montambaux, Phys. Rev. Lett. 100, 236405 (2008). 10.1103/PhysRevLett.100.236405
18. T. Paiva, R. T. Scalettar, W. Zheng, R. R. P. Singh, and J. Oitmaa, Phys. Rev. B 72, 085123 (2005). 10.1103/PhysRevB.72.085123
19. E. Zhao and A. Paramekanti, Phys. Rev. Lett. 97, 230404 (2006). 10.1103/PhysRevLett.97.230404
20. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley-Interscience, New York, 1998).
21. H. Wallis, Phys. Rep. 255, 203 (1995). 10.1016/0370-1573(94)00090-P
22. R. Grimm, M. Weidemüller, and Y. B. Ovchinnikov, Adv. At., Mol., Opt. Phys. 42, 95 (2000).
23. G. Grynberg and C. Robilliard, Phys. Rep. 355, 335 (2001). 10.1016/S0370-1573(01)00017-5
24. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature (London) 415, 39 (2002). 10.1038/415039a
25. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 81, 3108 (1998). 10.1103/PhysRevLett.81.3108
26. D. Jaksch, H.-J. Briegel, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 82, 1975 (1999). 10.1103/PhysRevLett.82.1975
27. X. Chen, B. Zheng, Z.-C. Gu, B. Yoshida, and I. L. Chuang, Phys. Rev. Lett. 102, 220501 (2009). 10.1103/PhysRevLett.102.220501
28. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Thomson Learning, United Kingdom, 1976).
29. O. Bohigas, Nucl. Phys. A. 751, 343 (2005). 10.1016/j.nuclphysa.2005.02. 013
30. The symmetry aspects of honeycomb potential will be discussed in more details in a follow-up paper.
31. G. Wannier, Phys. Rev. 52, 191 (1937). 10.1103/PhysRev.52.191
32. P. Wallace, Phys. Rev. 71, 622 (1947). 10.1103/PhysRev.71.622
33. G. Mil'nikov and H. Nakamura, J. Chem. Phys. 115, 6881 (2001). 10.1063/1.1406532
34. M. Marder, Condensed Matter Physics (Wiley, New York, 2000).
35. P. B. Blakie and C. W. Clark, J. Phys. B 37, 1391 (2004). 10.1088/0953-4075/37/7/002
36. J. Hubbard, Proc. R. Soc. London, Ser. A 276, 238 (1963). 10.1098/rspa.1963.0204
37. W. Kohn, Phys. Rev. 115, 809 (1959). 10.1103/PhysRev.115.809
38. J. des Cloizeaux, Phys. Rev. 135, A685 (1964). 10.1103/PhysRev.135.A685
39. G. Nenciu, Commun. Math. Phys. 91, 81 (1983). 10.1007/BF01206052
40. C. Brouder, G. Panati, M. Calandra, C. Mourougane, and N. Marzari, Phys. Rev. Lett. 98, 046402 (2007). 10.1103/PhysRevLett.98.046402
41. J. des Cloizeaux, Phys. Rev. 129, 554 (1963). 10.1103/PhysRev.129.554
42. J. des Cloizeaux, Phys. Rev. 135, A698 (1964). 10.1103/PhysRev.135.A698
43. S. Reich, J. Maultzsch, C. Thomsen, and P. Ordejón, Phys. Rev. B 66, 035412 (2002). 10.1103/PhysRevB.66.035412
44. I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80, 885 (2008). 10.1103/RevModPhys.80.885
45. M. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990).
46. L. Schulman, Techniques and Applications of Path Integration (Wiley, New York, 1981).
47. W. Zwerger, J. Opt. B: Quantum Semiclassical Opt. 5, S9 (2003). 10.1088/1464-4266/5/2/352
48. W. M. Lomer, Proc. R. Soc. London, Ser. A 227, 330 (1955). 10.1098/rspa.1955.0014
49. J. Slonczewski and P. Weiss, Phys. Rev. 109, 272 (1958). 10.1103/PhysRev.109.272
50. R. Jördens, N. Strohmaier, K. Günter, H. Moritz, and T. Esslinger, Nature (London) 455, 204 (2008). 10.1038/nature07244
51. U. Schneider, L. Hackermüller, S. Will, T. Best, I. Bloch, T. A. Costi, R. W. Hemes, D. Rasch, and A. Rosch, Science 322, 1520 (2008). 10.1126/science.1165449
52. T. Bourdel, L. Khaykovich, J. Cubizolles, J. Zhang, F. Chevy, M. Teichmann, L. Tarruell, S. J. J. M. F. Kokkelmans, and C. Salomon, Phys. Rev. Lett. 93, 050401 (2004). 10.1103/PhysRevLett.93.050401
53. M. Rigol, A. Muramatsu, G. G. Batrouni, and R. T. Scalettar, Phys. Rev. Lett. 91, 130403 (2003). 10.1103/PhysRevLett.91.130403
54. M. Rigol and A. Muramatsu, Phys. Rev. A 70, 043627 (2004). 10.1103/PhysRevA.70.043627
55. M. Köhl, H. Moritz, T. Stöferle, K. Günter, and T. Esslinger, Phys. Rev. Lett. 94, 080403 (2005). 10.1103/PhysRevLett.94.080403
56. Y. Hasegawa, R. Konno, H. Nakano, and M. Kohmoto, Phys. Rev. B 74, 033413 (2006). 10.1103/PhysRevB.74.033413
57. G. Montambaux, F. Piechon, J.-N. Fuchs, and M. O. Goerbig, e-print arXiv:0904.2117.
58. M. O. Goerbig, J.-N. Fuchs, G. Montambaux, and F. Piéchon, Phys. Rev. B 78, 045415 (2008). 10.1103/PhysRevB.78.045415
59. P. Lee, N. Nagaosa, and X. Wen, Rev. Mod. Phys. 78, 17 (2006). 10.1103/RevModPhys.78.17
60. We thank David Wilkowski for telling us about this way of introducing the phase parameter φ into the optical potential.
61. S. Tung, V. Schweikhard, and E. A. Cornell, Phys. Rev. Lett. 97, 240402 (2006). 10.1103/PhysRevLett.97.240402
62. A. S. Sørensen, E. Demler, and M. D. Lukin, Phys. Rev. Lett. 94, 086803 (2005). 10.1103/PhysRevLett.94.086803
63. E. Demler, W. Hanke, and S. Zhang, Rev. Mod. Phys. 76, 909 (2004). 10.1103/RevModPhys.76.909
64. S.-Q. Su, K.-M. Tam, and H.-Q. Lin, e-print arXiv:0902.3242.
65. C. Wu and S. Das Sarma, Phys. Rev. B 77, 235107 (2008). 10.1103/PhysRevB.77.235107
66. J.-M. Hou, W.-X. Yang, and X.-J. Liu, Phys. Rev. A 79, 043621 (2009). 10.1103/PhysRevA.79.043621
67. N. Goldman, A. Kubasiak, A. Bermudez, P. Gaspard, M. Lewenstein, and M. A. Martin-Delgado, Phys. Rev. Lett. 103, 035301 (2009). 10.1103/PhysRevLett.103. 035301