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Sum-rule approaches to the elementary excitation spectrum of interacting gases of finite bosons in harmonic potentials

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Abstract.

Based on the corrected sum rules and generalized virial identities, we derive an expression for all modes of excitation spectrum of interacting Bose gases at finite atom numbers in axially anisotropic potentials, in terms of the N-body ground state average. Using the variational Gaussian calculation for the ground-state wave function, its explicit analytic formulas are obtained. These results show clearly the dependence of excitation spectrum on the interaction strength parameter \(p = \sqrt{2/\pi}({a_{\rm sc}}/{a_{\rm ho}})(N-1)\) and trap geometry parameter \( \lambda \) for the system with N = 1 through \(N\rightarrow \infty \). For \( \lambda = 0\) and 1 the dependences have simple and intuitive physical interpretations. We compare the low-lying excitation spectra with the existing numerical results and make quantitative predications for future experiments and numerical simulation for higher-lying excitation modes.

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References

  1. M.H. Anderson et al. , Science 269, 198 (1995); K.B. Doris et al. , Phys. Rev. Lett. 75, 3969 (1995); C.C. Bradley et al. , Phys. Rev. Lett. 75, 1687 (1995)

    Google Scholar 

  2. C.N. Yang, C.P. Yang, Phys. Rev. 150, 321 (1966); Phys. Rev. 150, 327 (1966); Phys. Rev. 151, 258 (1966); J. Math. Phys. 10, 1115 (1969)

    Article  Google Scholar 

  3. E.H. Lieb, Phys. Rev. Lett. 18, 692 (1967)

    Article  Google Scholar 

  4. S. Stringari, Phys. Rev. Lett. 77, 2360 (1996)

    Article  Google Scholar 

  5. Y.L. Ma, S.T. Chui, Phys. Rev. A 65, 053610 (2002)

    Article  Google Scholar 

  6. M. Fliesser et al. , Phys. Rev. A 56, 4879 (1997); A. Csordás, R. Graham, Phys. Rev. A 56, 1477 (1997)

    Article  Google Scholar 

  7. L. Pitaevskii, S. Stringari, Phys. Rev. Lett. 81,4541 (1998); E. Braaten, J. Pearson, Phys. Rev. Lett. 82, 255 (1999)

    Google Scholar 

  8. Y.L. Ma, S.T. Chui, J.C. Kimball, J. Low Temp. Phys. 129, 79 (2002); Y.L. Ma, S.T. Chui, J. Phys.: Condens. Matter 14, 10105 (2002)

    Article  Google Scholar 

  9. M. Marinescu, A.F. Starace, Phys. Rev. A 56, 570 (1997)

    Article  Google Scholar 

  10. V.M. Peréz-García et al. , Phys. Rev. Lett. 77, 5320 (1996); Phys. Rev. A 56, 1424 (1997)

    Article  Google Scholar 

  11. M. Edwards et al. , Phys. Rev. Lett. 77, 1671 (1996); Phys. Rev. A 53, R1950 (1996)

    Article  Google Scholar 

  12. K.G. Singh, D.S. Rokhsar, Phys. Rev. Lett. 77, 1667 (1996)

    Article  Google Scholar 

  13. D.A.W. Hutchinson, E. Zaremba, A. Griffin, Phys. Rev. Lett. 78, 1842 (1997); D.A.W. Hutchinson, E. Zaremba, Phys. Rev. A 57, 1280 (1998)

    Article  Google Scholar 

  14. Yu. Kagan, E.L. Surkov, G.V. Shlyapnikov, Phys. Rev. A 55, R18 (1997)

  15. P.A. Ruprecht et al. , Phys. Rev. A 54, 4178 (1996)

    Article  Google Scholar 

  16. L. You, W. Hoston, M. Lewenstein, Phys. Rev. A 55, R1581 (1997)

  17. F. Zambelli, S. Stringari, Phys. Rev. Lett. 81 , 1754 (1998)

    Google Scholar 

  18. Y.L. Ma, S.T. Chui, J. Low Temp. Phys. 131, 51 (2003)

    Article  Google Scholar 

  19. O. Bohigas et al. , Phys. Rep. 51, 267 (1997); P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer, New York, 1980); E. Lipparini, S. Stringari, Nucl. Phys. A 371, 430 (1981); S. Stringari, Phys. Lett. B 108, 232 (1982); G. Eckart, G. Holzwarth, Phys. Lett. B 118, 9 (1982); M. Casas, J. Martorell, Nucl. Phys. A 490, 329 (1988); E. Lipparini, S. Stringari, Phys. Rep. 175, 103 (1989)

    Google Scholar 

  20. F. Dalfovo, L.P. Pitaevskii, S. Stringari, Phys. Rev. A 54, 4213 (1996)

    Article  Google Scholar 

  21. G. Baym, C.J. Pethick, Phys. Rev. Lett. 76, 6 (1996)

    Article  Google Scholar 

  22. A.L. Fetter, J. Low Temp. Phys. 106, 643 (1997)

    Google Scholar 

  23. D.S. Jin et al. , Phys. Rev. Lett. 77, 420 (1996)

    Article  Google Scholar 

  24. T. Kimura, H. Saito, M. Ueda, J. Phys. Soc. Jap. 68, 1477 (1999)

    Google Scholar 

  25. F. Dalfovo, S. Stringari, Phys. Rev. A 53, 2477 (1996)

    Google Scholar 

  26. Y.L. Ma, Z.Z. Chen, Chin. Phys. Lett. 20, 1434 (2003)

    Article  Google Scholar 

  27. Y.L. Ma, S.T. Chui, Phys. Rev. A 66, 053611 (2002)

    Article  Google Scholar 

  28. T. Miyakawa, T. Suzuki, H. Yabu, Phys. Rev. A 62, 063613 (2000)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Fudan University, 200433, Shanghai, P.R. China

    Y. L. Ma

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  1. Y. L. Ma
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Correspondence to Y. L. Ma.

Additional information

Received: 18 February 2004, Published online: 20 April 2004

PACS:

67.40.Db Quantum statistical theory; ground state, elementary excitations - 67.90. + z Other topics in quantum fluids and solids; liquid and solid helium

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Ma, Y.L. Sum-rule approaches to the elementary excitation spectrum of interacting gases of finite bosons in harmonic potentials. Eur. Phys. J. D 29, 415–427 (2004). https://doi.org/10.1140/epjd/e2004-00055-9

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