雪茄形铷原子玻色-爱因斯坦凝聚中单极子模的朗道阻尼和频移

柴兆亮; 周昱; 马晓栋

doi:10.7498/aps.62.130307

摘要

采用含时哈特里-福克-博戈留波夫近似研究雪茄形铷原子玻色-爱因斯坦凝聚中单极子模的朗道阻尼和频移. 通过考虑元激发的实际弛豫及其各弛豫间的正交关系改进原有方法, 并由此给出计算朗道阻尼和频移的新公式. 此外, 令凝聚体边界处动能密度为零代替令基态能量极小以改进原消除三模耦合矩阵元的方法. 通过这些改进, 同时计算阻尼和频移, 并讨论它们的温度依赖, 所得理论结果都与实验符合.

关键词:

The Landau damping and frequency-shift of monopole mode in an elongated-rubidium Bose-Einstein condensate are investigated by using the time-dependent Hartree-Fock-Bogoliubov approximation. Improving the previous approach, We have taken into account the practical relaxations of elementary excitations and the orthogonal relation among them. With such an approach, we provide a new calculation formula for Landau damping rate and frequency-shift. In addition, our previous method of eliminating the divergence in three-mode coupling matrix elements is also improved by zeroing the kinetic energy at the condensate boundary instead of minimizing the ground-state energy. Based on these improvements, both the Landau damping rate and the frequency-shift of the monopole mode are analytically calculated and their temperature dependences are also discussed. And all the theoretical results are in agree meat with experimental data.

Keywords:

作者及机构信息

1.
新疆师范大学物理与电子工程学院, 乌鲁木齐 830054;

2.
江苏科技大学数理学院, 镇江 212003

基金项目: 国家自然科学基金(批准号: 10864006, 11047101, 11264039, 11205071);新疆高校科研计划重点项目(批准号: XJED2010141);新疆理论物理重点学科(批准号: LLWLY201106, LLWLY201107)和新疆师范大学研究生科技创新项目(批准号: 20111202, 20121214)资助的课题.

Authors and contacts

1.
College of Physics and Electronic Engineering, Xinjiang Normal University, Urumchi 830054, China;

2.
School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang 212003, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 10864006, 11047101, 11264039, 11205071), the Key Research Project of Xinjiang Higher Education, China (Grant No. XJED2010141), the Key Discipline of Theoretical Physics of Xinjiang, China (Grant Nos. LLWLY201106, LLWLY201107), the Postgraduate Scientific and Technological Innovation Project of Xinjiang Normal University, China (Grant Nos. 20111202, 20121214).

参考文献

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[2]	Stringari S 1996 Phys. Rev. Lett. 77 2360
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[4]	Ruprecht P A, Edwards M, Burnett K, Clark C W 1996 Phys. Rev. A 54 4178
[5]	Dalfovo F, Minniti C, Pitaevskii L P 1997 Phys. Rev. A 56 4855
[6]	Morgan S A, Choi S, Burnett K, Edwards M 1998 Phys. Rev. A 57 3818
[7]	Hechenblaikner G, Maragó O M, Hodby E, Arlt J, Hopkins S, Foot C J 2000 Phys. Rev. Lett. 85 692
[8]	Hodby E, Maragó O M, Hechenblaikner G, Foot C J 2001 Phys. Rev. Lett. 86 2196
[9]	Maragó O M, Hopkins S A, Arlt J, Hodby E, Hechenblaikner G, Foot C J 2000 Phys. Rev. Lett. 84 2056
[10]	Khawaja U Al, Stoof H T C 2001 Phys. Rev. A 65 013605
[11]	Hechenblaikner G, Morgan S A, Hodby E, Maragó O M, Foot C J 2002 Phys. Rev. A 65 033612
[12]	Liu W M, Fan W B, Zheng W M, Liang J Q, Chui S T 2002 Phys. Rev. Lett. 88 170408
[13]	Ma Y L, Chui S T 2002 Phys. Rev. A 65 053610
[14]	Hu B, Huang G, Ma Y L 2004 Phys. Rev. A 69 063608
[15]	Huang G, Szeftel J, Zhu S 2002 Phys. Rev. A 65 053605
[16]	Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198
[17]	Jin D S, Matthews M R, Ensher J R, Wieman C E, Cornell E A 1997 Phys. Rev. Lett. 78 764
[18]	Jin D S, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1996 Phys. Rev. Lett. 77 420
[19]	Chevy F, Bretin V, Rosenbusch P, Madison K W, Dalibard J 2002 Phys. Rev. Lett. 88 250402
[20]	Stamper-Kurn D M, Miesner H J, Inouye S, Andrews M R, Ketterle W 1998 Phys.Rev. Lett. 81 500
[21]	Onofrio R, Durfee D S, Raman C, Köhl M, Kuklewicz C E, Ketterle W 2000 Phys. Rev. Lett. 84 810
[22]	Maragó O, Hechenblaikner J, Hodby E, Foot C 2001 Phys. Rev. Lett. 86 3938
[23]	Mewes M O, Andrews M R, Druten N J V, Kurn D M, Durfee D S, Townsend C G, Ketterle W 1996 Phys. Rev. Lett. 77 988
[24]	Zaremba E, Griffin A, Nikuni T 1998 Phys. Rev. A 57 4695
[25]	Zaremba E, Nikuni T, Griffin A 1999 J. Low Temp. Phys. 116 277
[26]	Jackson B, Zaremba E 2002 Phys. Rev. Lett. 88 180402
[27]	Jackson B, Zaremba E 2002 Phys. Rev. Lett. 89 150402
[28]	Morgan S A, Rusch M, Hutchinson D A W, Burnett K 2003 Phys. Rev. Lett. 91 250403
[29]	Morgan S A 2004 Phys. Rev. A 69 023609
[30]	Giorgini S 1998 Phys. Rev. A 57 2949
[31]	Giorgini S 2000 Phys. Rev. A 61 063615
[32]	Pitaevskii L P, Stringari S 1997 Phys. Lett. A 235 398
[33]	Fedichev P O, Shlyapnikov G V, Walraven J T M 1998 Phys. Rev. Lett. 80 2269
[34]	Reidl J, Csordás A, Graham R, Szépfalusy P 2000 Phys. Rev. A 61 043606
[35]	Tsuchiya S, Griffin A 2005 Phys. Rev. A 72 053621
[36]	Guilleumas M, Pitaevskii L P 2003 Phys. Rev. A 67 053607
[37]	Guilleumas M, Pitaevskii L P 1999 Phys. Rev. A 61 013602
[38]	Ma X, Ma Y L, Huang G 2007 Phys. Rev. A 75 013628
[39]	Ma X, Zhou Y, Ma Y L, Huang G 2006 Chin. Phys. 15 1871
[40]	Ma X, Ma Y L, Huang G 2007 Chin. Phys. Lett. 24 616
[41]	Ma X, Yang Z, Lu J, Wei W 2011 Chin. Phys. B 20 070307
[42]	Yang Z, Chai Z, Li C, Ma X 2012 Commun. Theor. Phys. 57 789

施引文献

[1]	Pethick C J, Smith H 2008 Bose-Einstein Condensation in Dilute Gases (2nd Edn.) (Cambridge University Press)
[2]	Stringari S 1996 Phys. Rev. Lett. 77 2360
[3]	Fetter A L 1996 Phys. Rev. A 53 4245
[4]	Ruprecht P A, Edwards M, Burnett K, Clark C W 1996 Phys. Rev. A 54 4178
[5]	Dalfovo F, Minniti C, Pitaevskii L P 1997 Phys. Rev. A 56 4855
[6]	Morgan S A, Choi S, Burnett K, Edwards M 1998 Phys. Rev. A 57 3818
[7]	Hechenblaikner G, Maragó O M, Hodby E, Arlt J, Hopkins S, Foot C J 2000 Phys. Rev. Lett. 85 692
[8]	Hodby E, Maragó O M, Hechenblaikner G, Foot C J 2001 Phys. Rev. Lett. 86 2196
[9]	Maragó O M, Hopkins S A, Arlt J, Hodby E, Hechenblaikner G, Foot C J 2000 Phys. Rev. Lett. 84 2056
[10]	Khawaja U Al, Stoof H T C 2001 Phys. Rev. A 65 013605
[11]	Hechenblaikner G, Morgan S A, Hodby E, Maragó O M, Foot C J 2002 Phys. Rev. A 65 033612
[12]	Liu W M, Fan W B, Zheng W M, Liang J Q, Chui S T 2002 Phys. Rev. Lett. 88 170408
[13]	Ma Y L, Chui S T 2002 Phys. Rev. A 65 053610
[14]	Hu B, Huang G, Ma Y L 2004 Phys. Rev. A 69 063608
[15]	Huang G, Szeftel J, Zhu S 2002 Phys. Rev. A 65 053605
[16]	Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198
[17]	Jin D S, Matthews M R, Ensher J R, Wieman C E, Cornell E A 1997 Phys. Rev. Lett. 78 764
[18]	Jin D S, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1996 Phys. Rev. Lett. 77 420
[19]	Chevy F, Bretin V, Rosenbusch P, Madison K W, Dalibard J 2002 Phys. Rev. Lett. 88 250402
[20]	Stamper-Kurn D M, Miesner H J, Inouye S, Andrews M R, Ketterle W 1998 Phys.Rev. Lett. 81 500
[21]	Onofrio R, Durfee D S, Raman C, Köhl M, Kuklewicz C E, Ketterle W 2000 Phys. Rev. Lett. 84 810
[22]	Maragó O, Hechenblaikner J, Hodby E, Foot C 2001 Phys. Rev. Lett. 86 3938
[23]	Mewes M O, Andrews M R, Druten N J V, Kurn D M, Durfee D S, Townsend C G, Ketterle W 1996 Phys. Rev. Lett. 77 988
[24]	Zaremba E, Griffin A, Nikuni T 1998 Phys. Rev. A 57 4695
[25]	Zaremba E, Nikuni T, Griffin A 1999 J. Low Temp. Phys. 116 277
[26]	Jackson B, Zaremba E 2002 Phys. Rev. Lett. 88 180402
[27]	Jackson B, Zaremba E 2002 Phys. Rev. Lett. 89 150402
[28]	Morgan S A, Rusch M, Hutchinson D A W, Burnett K 2003 Phys. Rev. Lett. 91 250403
[29]	Morgan S A 2004 Phys. Rev. A 69 023609
[30]	Giorgini S 1998 Phys. Rev. A 57 2949
[31]	Giorgini S 2000 Phys. Rev. A 61 063615
[32]	Pitaevskii L P, Stringari S 1997 Phys. Lett. A 235 398
[33]	Fedichev P O, Shlyapnikov G V, Walraven J T M 1998 Phys. Rev. Lett. 80 2269
[34]	Reidl J, Csordás A, Graham R, Szépfalusy P 2000 Phys. Rev. A 61 043606
[35]	Tsuchiya S, Griffin A 2005 Phys. Rev. A 72 053621
[36]	Guilleumas M, Pitaevskii L P 2003 Phys. Rev. A 67 053607
[37]	Guilleumas M, Pitaevskii L P 1999 Phys. Rev. A 61 013602
[38]	Ma X, Ma Y L, Huang G 2007 Phys. Rev. A 75 013628
[39]	Ma X, Zhou Y, Ma Y L, Huang G 2006 Chin. Phys. 15 1871
[40]	Ma X, Ma Y L, Huang G 2007 Chin. Phys. Lett. 24 616
[41]	Ma X, Yang Z, Lu J, Wei W 2011 Chin. Phys. B 20 070307
[42]	Yang Z, Chai Z, Li C, Ma X 2012 Commun. Theor. Phys. 57 789

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