摘要We investigate the energy spectrum of ultracold atoms on the two-dimensional Kagomé optical lattice under an effective magnetic field, which can be realized with laser beams. We derive the generalized Harper's equations from the Schrödinger equation. The energy spectrum with a fractal band structure is obtained by numerically solving the generalized Harper's equations. We analyze the properties of the Hofstadter's butterfly spectrum and discuss its observability.
Abstract：We investigate the energy spectrum of ultracold atoms on the two-dimensional Kagomé optical lattice under an effective magnetic field, which can be realized with laser beams. We derive the generalized Harper's equations from the Schrödinger equation. The energy spectrum with a fractal band structure is obtained by numerically solving the generalized Harper's equations. We analyze the properties of the Hofstadter's butterfly spectrum and discuss its observability.
[1] Jaksch D, Bruder C, Cirac J, Gardiner C and Zoller P1998 Phys. Rev. Lett. 81 3108 [2] Greiner M, Mandel O, Esslinger T, H\"ansch T W andBloch I 2002 Nature 415 39 [3] Lewenstein M, Sanpera A, Ahufinger V, Damski B, Sen Aand Sen U 2007 Adv. Phys. 56 243 [4] Rapp \'A, Zar\'and G, Honerkamp C and Hofstetter W 2007 Phys. Rev. Lett. 98 160405 [5] Hofstadter D R 1976 Phys. Rev. B 14 2239 [6] Jaksch D and Zoller P 2003 New J. Phys. 5 56 [7] Juzeli\={unas G, \"Ohberg P, Ruseckas J and Klein A2005 Phys. Rev. A 71 053614 [8] Juzeli\={unas G, Ruseckas J, \"Ohberg P and FleischhauerM 2006 Phys. Rev. A 73 025602 [9] Lin Y J, Compton R L, Perry A R, Phillips W D, Porto J Vand Spielman I B 2009 Phys. Rev. Lett. 102 130401 [10] Li Y, Bruder C and Sun C P 2007 Phys. Rev. Lett. 99 130403 [11] Juzeli\={unas G, Ruseckas J, Jacob A, Santos L and\"Ohberg P 2008 Phys. Rev. Lett. 100 200405 [12] Jacob A, \"Ohberg P, Juzeli\={unas G and Santos L 2008 New J. Phys. 10 045022 [3] Zhu S L, Fu H, Wu C J, Zhang S C and Duan L M 2006 Phys. Rev. Lett. 97 240401 [14] Liu X J, Liu X, Kwek L C and Oh C H 2007 Phys. Rev.Lett. 98 026602 [15] Liu X J, Borunda M F, Liu X and Sinova J 2009 Phys. Rev. Lett. 102 046402 [16] Pietil\"a V and M\"ott\"onen M 2009 Phys. Rev.Lett. 102 080403 [17] Vaishnav J Y, Rusechas J, Clark C W and Juzeli\={unasG 2008 Phys. Rev. Lett. 101 265302 [18] Moessner R and Sondhi S L 2001 Phys. Rev. Lett. 86 1881 [19] Santos L, Baranov M A, Cirac J I, Everts H U,Fehrmann H and Lewenstein M 2004 Phys. Rev. Lett. 93030601 [20] Damski B, Fehrmann H, Everts H U, Baranov M, Santos Land Lewenstein M 2005 Phys. Rev. A 72 053612 [21] Osterloh K, Baig M, Santos L, Zoller P and Lewenstein M2005 Phys. Rev. Lett. 95 010403 [22] Stamper-Kurn D M, Chikkatur A P, G\"orlitz A, Inouye S,Gupta S, Pritchard D E and Ketterle W 1999 Phys. Rev. Lett. 83 2876
2009, Vol. 26 
