Advertisement

The European Physical Journal B

, Volume 68, Issue 3, pp 329–333 | Cite as

Collective excitations of harmonically trapped ideal gases

  • B. Van Schaeybroeck
  • A. LazaridesEmail author
Article
  • 60 Downloads

Abstract

We theoretically study the collective excitations of an ideal gas confined in an isotropic harmonic trap. We give an exact solution to the Boltzmann-Vlasov equation; as expected for a single-component system, the associated mode frequencies are integer multiples of the trapping frequency. We show that the expressions found by the scaling ansatz method are a special case of our solution. Our findings are most useful in case the trap contains more than one phase: we demonstrate how to obtain the oscillation frequencies in case an interface is present between the ideal gas and a different phase.

PACS

03.75.Ss Degenerate Fermi gases 03.75.Kk Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow 67.85.-d Ultracold gases, trapped gases 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.W. Zwierlein, A. Schirotzek, C.H. Schunck, W. Ketterle, Science 311, 492 (2006); M.W. Zwierlein, C.H. Schunck, A. Schirotzek, W. Ketterle, Nature 442, 54 (2006)Google Scholar
  2. G.B. Partridge, W. Li, R.I. Kamar, Y.A. Liao, R.G. Hulet, Science 311, 503 (2006); G.B. Partridge, W. Li, Y.A. Liao, R.G. Hulet, M. Haque, H.T.C. Stoof, Phys. Rev. Lett. 97, 190407 (2006)Google Scholar
  3. A. Lazarides, B. Van Schaeybroeck, Phys. Rev. A 77, 041602(R) (2008)Google Scholar
  4. S. Ospelkaus, C. Ospelkaus, L. Humbert, K. Sengstock, K. Bongs, Phys. Rev. Lett. 97, 120403 (2006)Google Scholar
  5. M. Zaccanti, C. D’Errico, F. Ferlaino, G. Roati, M. Inguscio, G. Modugno, Phys. Rev. A 74, 041605(R) (2006)Google Scholar
  6. B. Van Schaeybroeck, A. Lazarides, e-print arXiv:0804.1759 Google Scholar
  7. X. Du, L. Luo, B. Clancy, J.E. Thomas, e-print arXiv:0805.1036 Google Scholar
  8. C.J. Pethick, H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge Press, Cambridge, 2002); L.P. Pitaevskii, S. Stringari, Bose-Einstein Condensation (Clarendon Press, Oxford, 2003); S. Giorgini, L.P. Pitaevskii, S. Stringari, e-print arXiv:0706.3360 Google Scholar
  9. E.M. Lifshitz, L.P. Pitaevskii, Physical Kinetics (Pergamon Press, Oxford, UK)Google Scholar
  10. A.A. Abrikosov, I.M. Khalatnikov, Rep. Prog. Phys. 22, 329 (1959)Google Scholar
  11. Y. Kagan, E.L. Surkov, G. Shlyapnikov, Phys. Rev. A 54, R1753 (1996)Google Scholar
  12. Y. Castin, R. Dum, Phys. Rev. Lett. 77, 5315 (1996)Google Scholar
  13. M.J. Bijlsma, H.T.C. Stoof, Phys. Rev. A 60, 3973 (1999)Google Scholar
  14. D. Guéry-Odelin, F. Zambelli, J. Dalibard, S. Stringari, Phys. Rev. A 60, 4851 (1999)Google Scholar
  15. P. Pedri, D. Guéry-Odelin, S. Stringari, Phys. Rev. A 68, 043608 (2003)Google Scholar
  16. D. Guéry-Odelin, Phys. Rev. A 66, 033613 (1999)Google Scholar
  17. M. Amoruso, I. Meccoli, A. Minguzzi, M.P. Tosi, Eur. Phys. J. D 7, 441 (1999)Google Scholar
  18. L. Vichi, S. Stringari, Phys. Rev. A 60, 4734 (1999)Google Scholar
  19. G.M. Bruun, Phys. Rev. A 63, 043408 (2001)Google Scholar
  20. P. Capuzzi, A. Minguzzi, M.P. Tosi, Phys. Rev. A 68, 033605 (2003)Google Scholar
  21. D.H. Santamore, S. Gaudio, E. Timmermans, Phys. Rev. Lett. 93, 250402 (2004)Google Scholar
  22. T. Maruyama, G.F. Bertsch, Phys. Rev. A 77, 063611 (2008)Google Scholar
  23. D. Pines, P. Nozieres, Theory of Quantum Liquids (Benjamin, New York, 1966)Google Scholar
  24. B. Van Schaeybroeck, A. Lazarides, Phys. Rev. Lett. 98, 170402 (2007)Google Scholar
  25. G. Modugno, M. Modugno, F. Riboli, G. Roati, M. Inguscio, Phys. Rev. Lett. 89, 190404 (2002)Google Scholar
  26. F. Ferlaino, R.J. Brecha, P. Hannaford, F. Riboli, G. Roati, G. Modugno, M. Inguscio, J. Opt. B: Quantum Semiclass. Opt. 5, S3 (2003)Google Scholar
  27. I.L. Bekarevich, I.M. Khalatnikov, Zh. Eksperim. i. Teor. Fiz. 39, 1699 (1960) [Sov. Phys. JETP 12, 1187 (1961)]Google Scholar
  28. L. Landau, J. Phys. (USSR) 1, 25 (1946); N.A. Krall, A.W. Trivelpiece, Principles of Plasma Physics (McGraw-Hill, 1973)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  1. 1.Instituut voor Theoretische Fysica, Katholieke Universiteit LeuvenLeuvenBelgium

Personalised recommendations