Skip to main content
SpringerLink
Log in

Ground state and excited states of a trapped dilute condensed Bose gas

  • Plenary and Invited Papers
  • Quantum Fluids and Solids
  • Published:
Czechoslovak Journal of Physics Aims and scope

Abstract

I review recent theoretical treatments of a dilute interacting condensed Bose gas in a trap. Bogoliubov's classic results for a uniform condensate are generalized to include the effect of a trap, using the Gross-Pitaevskii formalism (for the condensate) and the Bogoliubov equations (for the linearized small-amplitude excitations of the condensate). Several recent theoretical studies are discussed along with some open questions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. F. London,Superfluids (Dover, NY, 1964), Vol. II, provides a comprehensive account of the experimental and theoretical situation as of 1954, with very complete references.

    Google Scholar 

  2. The experimental summary of J. Wilks,The Properties of Liquid and Solid Helium (Clarendon Press, Oxford, 1967), Chaps. 1–8, remains remarkably up-to-date.

    Google Scholar 

  3. L. D. Landau and E. M. LifshitzFluid Mechanics (Pergamon, Oxford, 1987),2nd ed., Chap. XVI summarizes Landau's two-fluid hydrodynamics.

    MATH  Google Scholar 

  4. See also A. L. Fetter and J. D. WaleckaQuantum Theory of Many-Particle Systems (McGraw-Hill, NY, 1971), Sec. 54.

    Google Scholar 

  5. N. N. Bogoliubov, J. Phys. (USSR)11, 23 (1947).

    Google Scholar 

  6. Bogoliubov's seminal paper is reprinted in D. Pines,The Many-Body Problem (Benjamin, NY 1961) along with a brief historical summary and reprints of many of the central subsequent papers, specifically those by Lee, Huang, and Yang, by Beliaev and by Hugenholtz and Pines.

    Google Scholar 

  7. See also Ref., Chap. 6 and Sec. 35.

    Google Scholar 

  8. E. P. Gross, Nuovo Cimento20, 454 (1961); J. Math. Phys.46, 137 (1963).

    Article  MATH  Google Scholar 

  9. L. P. Pitaevskii, Zh. Eksp. Teor. Fiz.40, 646 (1961); Sov. Phys.-JETP13, 451 (1961).

    Google Scholar 

  10. See also Ref. [4],, Sec. 55.

    Google Scholar 

  11. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science269, 198 (1995).

    Article  ADS  Google Scholar 

  12. C. C. Bradley, C. A. Sackett, J. J. Tollett, and R. G. Hulet, Phys. Rev. Lett.75, 1687 (1995).

    Article  ADS  Google Scholar 

  13. K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett.75, 3969 (1995).

    Article  ADS  Google Scholar 

  14. M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, and W. Ketterle, Phys. Rev. Lett.77, 416 (1996).

    Article  ADS  Google Scholar 

  15. M. Tinkham,Introduction to Superconductivity (McGraw-Hill, NY, 1996),2nd ed., Sec. 3.5.

    Google Scholar 

  16. V. L. Ginzburg and L. P. Pitaevskii, Zh. Eksp. Teor. Fiz.34, 1240 (1958); Sov. Phys.-JETP7 858 (1958).

    MathSciNet  Google Scholar 

  17. See, for example, Ref.[4], Sec. 50 and Ref.[15]Introduction to Superconductivity (McGraw-Hill, NY, 1996),2nd ed. Chaps. 4 and 5.

    Google Scholar 

  18. V. V. Goldman, I. F. Silvera, and A. J. Leggett, Phys. Rev. B24, 2879 (1981).

    Article  ADS  Google Scholar 

  19. D. A. Huse and E. D. Siggia, J. Low Temp. Phys.46, 137 (1982).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. See, for example, Ref.[4] ), Sec. 56.

    Google Scholar 

  22. A. L. Fetter, Ann. Phys. (N.Y.)70, 67 (1972).

    Article  ADS  Google Scholar 

  23. P. G. de Gennes,Superconductivity of Metals and Alloys (Benjamin, NY, 1966) Chap. 5.

    MATH  Google Scholar 

  24. See also Ref.[15], Sec. 10.1.

    Google Scholar 

  25. A. L. Fetter, Phys. Rev. A53, 4245 (1996).

    Article  ADS  Google Scholar 

  26. W.-C. Wu and A. Griffin, cond-mat/9606076 (unpublished).

  27. See, for example, Ref.[4], Chaps. 5 and 9.

    Google Scholar 

  28. D. S. Jin, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett.77, 420 (1996).

    Article  ADS  Google Scholar 

  29. M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, Phys. Rev. Lett.77, 988 (1996).

    Article  ADS  Google Scholar 

  30. See http://amo.phy.gasou.edu./bec.html/ for an updated bibliography on Bose-Einstein condensation (and other relevant information).

  31. M. Edwards and K. Burnett Phys. Rev. A51, 1382 (1995).

    Article  ADS  Google Scholar 

  32. P. A. Ruprecht, M. J. Holland, K. Burnett, and M. Edwards, Phys. Rev. A51, 4704 (1995).

    Article  ADS  Google Scholar 

  33. M. Edwards, R. J. Dodd, C. W. Clark, P. A. Ruprecht, and K. Burnett, Phys. Rev. A53, R1950 (1996).

    Article  ADS  Google Scholar 

  34. F. Dalfovo and S. Stringari, Phys. Rev. A53, 2477 (1996).

    Article  ADS  Google Scholar 

  35. K. N. Ilinski and A. Moroz, cond-mat/9512155 (to appear in J. Res. NIST).

  36. A. L. Fetter, cond-mat/9607177 (unpublished).

  37. F. Dalfovo, L. P. Pitaevskii, and S. Stringari, cond-mat/9604069 (unpublished).

  38. A. L. Fetter, inThe Physics of Liquid and Solid Helium, edited by K. H. Bennemann and J. B. Ketterson (Wiley, NY, 1976), Part I, p. 207.

    Google Scholar 

  39. R. J. Donnelly,Quantized Vortices in Helium II (Cambridge Press, Cambridge, 1991).

    Google Scholar 

  40. M. Edwards, P. A. Ruprecht, K. Burnett, R. J. Dodd, and C. W. Clark, Phys. Rev. Lett.77, 1671 (1996).

    Article  ADS  Google Scholar 

  41. S. Stringari, Phys. Rev. Lett.77, XXX (1996).

    Article  Google Scholar 

  42. R. E. Packard and T. M. Sanders, Jr. Phys. Rev. Lett.22, 823 (1969); Phys. Rev. A6, 799 (1972).

    Article  ADS  Google Scholar 

  43. E. J. Yarmchuk, M. J. V. Gordon, and R. E. Packard, Phys. Rev. Lett.43, 214 (1979).

    Article  ADS  Google Scholar 

  44. E. J. Yarmchuk and R. E. Packard, J. Low Temp. Phys.46, 479 (1982).

    Article  ADS  Google Scholar 

  45. A. L. Fetter, J. Low Temp. Phys.16, 533 (1974).

    Article  ADS  Google Scholar 

  46. K. DeConde and R. E. Packard, Phys. Rev. Lett.35, 732 (1975).

    Article  Google Scholar 

  47. A. L. Fetter, Phys. Rev.138, A709 (1965).

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departments of Physics and Applied Physics, Stanford University, 94305-4060, Stanford, California, USA

    Alexander L. Fetter

Authors
  1. Alexander L. Fetter
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported in part by the National Science Foundation under Grant No. DMR 94-21888.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fetter, A.L. Ground state and excited states of a trapped dilute condensed Bose gas. Czech J Phys 46 (Suppl 6), 3063–3069 (1996). https://doi.org/10.1007/BF02548111

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02548111

Keywords

Search

Navigation