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Landau damping and frequency-shift of monopole mode in an elongated-rubidium Bose-Einstein condensate

Chai Zhao-Liang Zhou Yu Ma Xiao-Dong

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Landau damping and frequency-shift of monopole mode in an elongated-rubidium Bose-Einstein condensate

Chai Zhao-Liang, Zhou Yu, Ma Xiao-Dong
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  • 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.
    • 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).
    [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

  • [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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Publishing process
  • Received Date:  23 January 2013
  • Accepted Date:  11 March 2013
  • Published Online:  05 July 2013

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