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The effective Lagrangian density function and the quantum fluctuation of the wave function in the form of quantized operators are presented for a quasi two-dimensional Bose-Einstein condensate by means of Madelung transformation. This paper calculates the two-point density-density correlation function of the condensate during its free expansion after its confinement potential is removed. Results show that the two-point density-density correlation function in the long-wave limit is proportional to the wave number k and it tends to be a constant in the short-wave limit.
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Keywords:
- Bose-Einstein condensates /
- quantum fluctuation /
- density correlation
[1] Yasunaga M, Tsubota M 2010 Phys. Rev. A 81 023624 Yasunaga M, Tsubota M 2011 Phys. Rev. A 83 013618
[2] Levy S, Lahoud E, Shoroni I, Steinhauer J 2007 Nature 449 579
[3] Liu B, Fu L B, Yang S P, Liu J 2007 Phys. Rev. A 75 033601
[4] Zhang J N, Sun C P, Yi S, Nori F 2011 Phys. Rev. A 83 033614
[5] Wang W Y, Meng H J, Yang Y, Qi P T, Ma Y Y, Ma Y, Wang S J, Duan W S 2012 Acta Phys. Sin. 61 087302 (in Chinese) [王文元, 蒙红娟, 杨阳, 祁鹏堂, 马云云, 马莹, 王善进, 段文山 2012 61 087302]
[6] Meng H J, Yang Y, Wang W Y, Qi P T, Ma Y Y, Ma Y, Wang S J, Duan W S 2012 Acta Phys. Sin. 61 060303 (in Chinese) [蒙红娟, 杨阳, 王文元, 祁鹏堂, 马云云, 马莹, 王善进, 段文山 2012 61 060303]
[7] Wang J Z, Cao H, Dou F Q 2012 Acta Phys. Sin. 61 220305 (in Chinese) [王建忠, 曹辉, 豆福全 2012 61 220305]
[8] Liu J, Zhang C W, Raizen M G, Niu Q 2006 Phys. Rev. A 73 013601
[9] Teng F, Xie Z W 2013 Acta Phys. Sin. 62 026701 (in Chinese) [藤斐, 谢征微 2013 62 026701]
[10] Cui B, Wang L C, Yi X X 2010 Phys. Rev. A 82 062105
[11] Wuster S, Dabrowska-Wuster B J, Davis M J 2012 Phys. Rev. Lett. 109 080401
[12] Wang G F, Fu L B, Zhao H, Liu J 2005 Acta Phys. Sin. 54 5003 (in Chinese) [王冠芳, 傅立斌, 赵鸿, 刘杰 2005 54 5003]
[13] Tozzo C, Dalfovo F 2004 Phys. Rev. A 69 05360 Liu S J, Xiong H W 2009 Physica B-Condensed Matter 404 3510 Wu M Z, Zhou XJ, Liu W M, Chen X Z 2010 Phys. Rev. A 81 033625
[14] Xu Y, Xiong Z Z, Li Z X, Chen B, Tan L 2009 Chin. Phys. B 18 4734
[15] Imambekov A, Mazets I E, Petrov D S, Gritsev V, Manz S, Hofferberth S, Schumm T, Demler E, Schmiedmayer J 2009 Phys. Rev. A 80 033604
[16] Salasnich L, Manini N, Bonelli F, Korbman M, Parola A 2007 Phys. Rev. A 75 043616
[17] Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198
[18] Castin Y, Dum R, 1996 Phys. Rev. Lett. 77 5315 Ohberg P, Santos L 2002 Phys. Rev. Lett. 89 240402
[19] Kagan Yu, Surkov E L, Shlyapnikov G V 1996 Phys. Rev. A 54 R1753 Kagan Yu, Surkov E L, Shlyapnikov G V 1997 Phys. Rev. A 55 R18
[20] Salasnich L, Parola A, Reatto L, 2005 Phys. Rev. A 72 025602 Diana G, Manini N, Salasnich L 2006 Phys. Rev. A 73 065601
[21] Prain A, Fagnocchi S, Liberati S 2010 Phys. Rev. D 82 105018
[22] Carusotto I, Fagnocchi S, Recati A, Balbinot R, Fabbri A, 2008 New J. Phys. 10 103001
[23] Balbinot R, Fabbri A, Fagnocchi S, Recati A, Carusotto I 2008 Phys. Rev. A 78 021603
[24] Recati A, Pavloff N, Carusotto I 2009 Phys. Rev. A 80 043603
[25] Zapata I, Albert M, Parentani R, Sols F 2011 New J. Phys. 13 063048
[26] Carusotto I, Balbinot R, Fabbri A, Recati A 2010 Eur. Phys. J. D 56 391
[27] Larre P E, Recati A, Carusotto I, Pavloff N 2012 Phys. Rev. A 85 013621
[28] Gorlitz A, Vogels J M, Leanhardt A E, Raman C, Gustavson T L, Abo-Shaeer J R, Chikkatur A P, Gupta S, Inouye S, Rosenband T, Ketterle W 2001 Phys. Rev. Lett. 87 130402
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[1] Yasunaga M, Tsubota M 2010 Phys. Rev. A 81 023624 Yasunaga M, Tsubota M 2011 Phys. Rev. A 83 013618
[2] Levy S, Lahoud E, Shoroni I, Steinhauer J 2007 Nature 449 579
[3] Liu B, Fu L B, Yang S P, Liu J 2007 Phys. Rev. A 75 033601
[4] Zhang J N, Sun C P, Yi S, Nori F 2011 Phys. Rev. A 83 033614
[5] Wang W Y, Meng H J, Yang Y, Qi P T, Ma Y Y, Ma Y, Wang S J, Duan W S 2012 Acta Phys. Sin. 61 087302 (in Chinese) [王文元, 蒙红娟, 杨阳, 祁鹏堂, 马云云, 马莹, 王善进, 段文山 2012 61 087302]
[6] Meng H J, Yang Y, Wang W Y, Qi P T, Ma Y Y, Ma Y, Wang S J, Duan W S 2012 Acta Phys. Sin. 61 060303 (in Chinese) [蒙红娟, 杨阳, 王文元, 祁鹏堂, 马云云, 马莹, 王善进, 段文山 2012 61 060303]
[7] Wang J Z, Cao H, Dou F Q 2012 Acta Phys. Sin. 61 220305 (in Chinese) [王建忠, 曹辉, 豆福全 2012 61 220305]
[8] Liu J, Zhang C W, Raizen M G, Niu Q 2006 Phys. Rev. A 73 013601
[9] Teng F, Xie Z W 2013 Acta Phys. Sin. 62 026701 (in Chinese) [藤斐, 谢征微 2013 62 026701]
[10] Cui B, Wang L C, Yi X X 2010 Phys. Rev. A 82 062105
[11] Wuster S, Dabrowska-Wuster B J, Davis M J 2012 Phys. Rev. Lett. 109 080401
[12] Wang G F, Fu L B, Zhao H, Liu J 2005 Acta Phys. Sin. 54 5003 (in Chinese) [王冠芳, 傅立斌, 赵鸿, 刘杰 2005 54 5003]
[13] Tozzo C, Dalfovo F 2004 Phys. Rev. A 69 05360 Liu S J, Xiong H W 2009 Physica B-Condensed Matter 404 3510 Wu M Z, Zhou XJ, Liu W M, Chen X Z 2010 Phys. Rev. A 81 033625
[14] Xu Y, Xiong Z Z, Li Z X, Chen B, Tan L 2009 Chin. Phys. B 18 4734
[15] Imambekov A, Mazets I E, Petrov D S, Gritsev V, Manz S, Hofferberth S, Schumm T, Demler E, Schmiedmayer J 2009 Phys. Rev. A 80 033604
[16] Salasnich L, Manini N, Bonelli F, Korbman M, Parola A 2007 Phys. Rev. A 75 043616
[17] Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198
[18] Castin Y, Dum R, 1996 Phys. Rev. Lett. 77 5315 Ohberg P, Santos L 2002 Phys. Rev. Lett. 89 240402
[19] Kagan Yu, Surkov E L, Shlyapnikov G V 1996 Phys. Rev. A 54 R1753 Kagan Yu, Surkov E L, Shlyapnikov G V 1997 Phys. Rev. A 55 R18
[20] Salasnich L, Parola A, Reatto L, 2005 Phys. Rev. A 72 025602 Diana G, Manini N, Salasnich L 2006 Phys. Rev. A 73 065601
[21] Prain A, Fagnocchi S, Liberati S 2010 Phys. Rev. D 82 105018
[22] Carusotto I, Fagnocchi S, Recati A, Balbinot R, Fabbri A, 2008 New J. Phys. 10 103001
[23] Balbinot R, Fabbri A, Fagnocchi S, Recati A, Carusotto I 2008 Phys. Rev. A 78 021603
[24] Recati A, Pavloff N, Carusotto I 2009 Phys. Rev. A 80 043603
[25] Zapata I, Albert M, Parentani R, Sols F 2011 New J. Phys. 13 063048
[26] Carusotto I, Balbinot R, Fabbri A, Recati A 2010 Eur. Phys. J. D 56 391
[27] Larre P E, Recati A, Carusotto I, Pavloff N 2012 Phys. Rev. A 85 013621
[28] Gorlitz A, Vogels J M, Leanhardt A E, Raman C, Gustavson T L, Abo-Shaeer J R, Chikkatur A P, Gupta S, Inouye S, Rosenband T, Ketterle W 2001 Phys. Rev. Lett. 87 130402
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