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The density-density correlations of ultracold Bosons released from a two-dimensional square optical lattice are investigated based on the quantum phase field U (1) rotor field. With the effects of the particle number fluctuations and the phase degrees of freedom taken into consideration, the theory can be used to describe the cold atom system with strong interaction. Using this theory, the characteristics of ultracold atom gas in the process in which the superfluid state of optical lattice transits to insulating state, are well described. The results show that in the patterns of the density-density correlations, the continuous diagonal lines gradually transit to scattered peaks. The results match the experimental ones. In addition, the effects of the quantum depletion on the density-density correlation are also included in the result, and the relevant conclusions are also consistent with the existing theoretical and experimental results.
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Keywords:
- ultracold Bosonic gas /
- optical lattice /
- density-density correlations
[1] Greiner M, Mandel O, Esslinger T Hansch T W, Bloch I 2002 Nature 415 39
[2] Bloch I 2005 Nat. Phys. 1 23
[3] Hen I, Rigol M 2010 Phys. Rev. A 82 043634
[4] Xu Z J, Wang D M, Li Z 2007 Acta Phys. Sin. 56 3076 (in Chinese) [徐志君, 王冬梅, 李珍 2007 物理学报 56 3076]
[5] Xu Z J, Chen C, Yang H S, Wu Q, Xiong H W 2004 Acta Phys. Sin. 53 2835 (in Chinese) [徐志君, 程成, 杨欢耸, 武强, 熊宏伟 2004 物理学报 53 2835]
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[7] Kampf A P, Zimanyi G T 1993 Phys. Rev. B 47 279
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[9] Elstner N, Monien H 1999 Phys. Rev. B 59 12184
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[11] Sengupta K, Dupuis N 2005 Phys. Rev. A 71 033629
[12] Spielman I B, Phillips W D, Porto J V 2007 Phys. Rev. Lett. 98 080404
[13] Polak T P, Kopeć T K 2007 Phys. Rev. B 76 094503
[14] Polak T P, Kopeć T K 2009 Annalen der Physik 17 947
[15] Polak T P, Kopeć T K 2009 J. Phys. B 42 095302
[16] Kopeć T K 2004 Phys. Rev. B 70 054518
[17] Polak T P, Kopeć T K 2010 Phys. Rev. A 81 043612
[18] Polak T P, Kopeć T K 2011 Phys. Rev. A 84 053613
[19] Zaleski T A 2012 Phys. Rev. A 85 043611
[20] Polak T P, Zaleski T A 2012 Acta Phys. Pol. A 121 1312
[21] Zaleski T A, Polak T P 2011 Phys. Rev. A 83 023607
[22] Capogrosso-Sansone B, Söyler S G, Prokof’ev N, Svistunov B 2008 Phys. Rev. A 77 015602
[23] Teichmann N, Hinrichs D, Holthaus M, Eckardt A 2009 Phys. Rev. B 79 100503
[24] Li Y Y, Cheng M T, Zhou H J, Liu S D, Wang Q Q 2005 Chin. Phys. Lett. 22 2960
[25] Chen L M, Cao L, Wu D J 2005 Chin. Phys. Lett. 22 2500
[26] Schellekens M, Hoppeler R, Perrin A, Gomes J V, Boiron D, Aspect A, Westbrook C I 2005 Science 310 648
[27] Fölling S, Gerbier F, Widera A, Mandel O, Gericke T, Bloch I 2005 Nature 434 481
[28] Spielman I B, Phillips W D, Porto J V 2007 Phys. Rev. Lett. 98 080404
[29] Rom T, Best T, Oosten D, Schneider U, Fölling S, Paredes B, Bloch I 2006 Nature 444 733
[30] Wang M Y, Liang J Q 2012 Chin. Phys. B 21 060305
[31] Xu Z J, Liu X Y 2011 Acta Phys. Sin. 60 120305 (in Chinese) [徐志君, 刘夏吟 2011 物理学报 60 120305]
[32] Xu Z J, Li P H 2007 Acta Phys. Sin. 56 5607 (in Chinese) [徐志君, 李鹏华 2007 物理学报 56 5607]
[33] Huang J S, Chen H F, Xie Z W 2008 Acta Phys. Sin. 57 3435 (in Chinese) [黄劲松, 陈海峰, 谢征微 2008 物理学报 57 3435]
[34] Teng F, XIe Z W 2013 Acta Phys. Sin. 62 026701 (in Chinese) [藤斐, 谢征微 2013 物理学报 62 026701]
[35] Toth E, Rey A M, Blakie P B 2008 Phys. Rev. A 78 013627
[36] Hu Y H, Wang J Q 2012 Chin. Phys. B 21 014203
[37] Xu Z J, Zhang D M, Liu X Y 2011 Chin. Phys. Lett. 28 010305
[38] Wu Z S, Zhang G 2009 Chin. Phys. Lett. 26 114208
[39] Kheruntsyan K V, Jaskula J C, Deuar P, Bonneau M, Partridge G B, Ruaudel J, Lopes R, Boiron D, Westbrook C I 2012 Phys. Rev. Lett. 108 260401
[40] Bouchoule I, Arzamasov M, Kheruntsyan K V, Gangardt D M 2012 Phys. Rev. A 86 033626
-
[1] Greiner M, Mandel O, Esslinger T Hansch T W, Bloch I 2002 Nature 415 39
[2] Bloch I 2005 Nat. Phys. 1 23
[3] Hen I, Rigol M 2010 Phys. Rev. A 82 043634
[4] Xu Z J, Wang D M, Li Z 2007 Acta Phys. Sin. 56 3076 (in Chinese) [徐志君, 王冬梅, 李珍 2007 物理学报 56 3076]
[5] Xu Z J, Chen C, Yang H S, Wu Q, Xiong H W 2004 Acta Phys. Sin. 53 2835 (in Chinese) [徐志君, 程成, 杨欢耸, 武强, 熊宏伟 2004 物理学报 53 2835]
[6] Jaksh D, Bruder C, Cira J I, Gardiner C W, Zoller P 1998 Phys. Rev. Lett. 81 3108
[7] Kampf A P, Zimanyi G T 1993 Phys. Rev. B 47 279
[8] Freeriks J K, Monien H 1996 Phys. Rev. B 53 2691
[9] Elstner N, Monien H 1999 Phys. Rev. B 59 12184
[10] Sheshadri K, Krishnamurthy H R, Pandit R, Ramakrishnan T V 1993 Europhys. Lett. 22 257
[11] Sengupta K, Dupuis N 2005 Phys. Rev. A 71 033629
[12] Spielman I B, Phillips W D, Porto J V 2007 Phys. Rev. Lett. 98 080404
[13] Polak T P, Kopeć T K 2007 Phys. Rev. B 76 094503
[14] Polak T P, Kopeć T K 2009 Annalen der Physik 17 947
[15] Polak T P, Kopeć T K 2009 J. Phys. B 42 095302
[16] Kopeć T K 2004 Phys. Rev. B 70 054518
[17] Polak T P, Kopeć T K 2010 Phys. Rev. A 81 043612
[18] Polak T P, Kopeć T K 2011 Phys. Rev. A 84 053613
[19] Zaleski T A 2012 Phys. Rev. A 85 043611
[20] Polak T P, Zaleski T A 2012 Acta Phys. Pol. A 121 1312
[21] Zaleski T A, Polak T P 2011 Phys. Rev. A 83 023607
[22] Capogrosso-Sansone B, Söyler S G, Prokof’ev N, Svistunov B 2008 Phys. Rev. A 77 015602
[23] Teichmann N, Hinrichs D, Holthaus M, Eckardt A 2009 Phys. Rev. B 79 100503
[24] Li Y Y, Cheng M T, Zhou H J, Liu S D, Wang Q Q 2005 Chin. Phys. Lett. 22 2960
[25] Chen L M, Cao L, Wu D J 2005 Chin. Phys. Lett. 22 2500
[26] Schellekens M, Hoppeler R, Perrin A, Gomes J V, Boiron D, Aspect A, Westbrook C I 2005 Science 310 648
[27] Fölling S, Gerbier F, Widera A, Mandel O, Gericke T, Bloch I 2005 Nature 434 481
[28] Spielman I B, Phillips W D, Porto J V 2007 Phys. Rev. Lett. 98 080404
[29] Rom T, Best T, Oosten D, Schneider U, Fölling S, Paredes B, Bloch I 2006 Nature 444 733
[30] Wang M Y, Liang J Q 2012 Chin. Phys. B 21 060305
[31] Xu Z J, Liu X Y 2011 Acta Phys. Sin. 60 120305 (in Chinese) [徐志君, 刘夏吟 2011 物理学报 60 120305]
[32] Xu Z J, Li P H 2007 Acta Phys. Sin. 56 5607 (in Chinese) [徐志君, 李鹏华 2007 物理学报 56 5607]
[33] Huang J S, Chen H F, Xie Z W 2008 Acta Phys. Sin. 57 3435 (in Chinese) [黄劲松, 陈海峰, 谢征微 2008 物理学报 57 3435]
[34] Teng F, XIe Z W 2013 Acta Phys. Sin. 62 026701 (in Chinese) [藤斐, 谢征微 2013 物理学报 62 026701]
[35] Toth E, Rey A M, Blakie P B 2008 Phys. Rev. A 78 013627
[36] Hu Y H, Wang J Q 2012 Chin. Phys. B 21 014203
[37] Xu Z J, Zhang D M, Liu X Y 2011 Chin. Phys. Lett. 28 010305
[38] Wu Z S, Zhang G 2009 Chin. Phys. Lett. 26 114208
[39] Kheruntsyan K V, Jaskula J C, Deuar P, Bonneau M, Partridge G B, Ruaudel J, Lopes R, Boiron D, Westbrook C I 2012 Phys. Rev. Lett. 108 260401
[40] Bouchoule I, Arzamasov M, Kheruntsyan K V, Gangardt D M 2012 Phys. Rev. A 86 033626
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