Crossover of Quasiparticles and Statistics of Bose-Einstein Condensate with Increasing Interaction: from an Ideal Gas to a Thomas-Fermi Regime. The Case of a One-Dimensional Flat Trap

  • S. V. TarasovEmail author
  • Vl. V. Kocharovsky
  • V. V. Kocharovsky

A change-over of the quasiparticle wave functions and spectrum under a variation in an interparticle interaction in a Bose-Einstein condensed gas of bosons confined in a one-dimensional trap with a flat potential and impermeable walls is studied analytically and numerically. An efficient approximate method of analysis is developed. It yields a solution to the self-consistent Bogoliubov and Gross-Pitaevskii equations for quasiparticles and the condensate that describes a crossover from the regime of a gas of noninteracting bosons to the regime of a gas with the interaction being strong enough to reach a Thomas-Fermi asymptotics. As a result, the characteristic function of the total number of noncondensed particles is found which, for the first time, allows one to figure out how the quantum statistics of fluctuations of the number of particles in the condensate depends on its inhomogeneity and the interparticle interaction in the case of the flat trap. The qualitative features of this dependence as well as a possibility of an experimental observation of the predicted effects in the actual traps are discussed.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. D. Landau and E. M. Lifshitz, Statistical Physics, Pt. 1 Butterworth–Heinemann, Oxford (1980).Google Scholar
  2. 2.
    L. P. Pitaevskii and S. Stringari, Bose–Einstein Condensation, Oxford Univ. Press, Oxford (2003).zbMATHGoogle Scholar
  3. 3.
    C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases, Cambridge University Press, Cambridge (2002).Google Scholar
  4. 4.
    S. V. Tarasov, Vl. V. Kocharovsky, and V. V. Kocharovsky, J. Stat. Phys., 161, No. 4, 942 (2015).ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    S. A. Gardiner and S. A. Morgan, Phys. Rev. A, 75, No. 4, 043621 (2007).ADSCrossRefGoogle Scholar
  6. 6.
    T. P. Billam, P. Mason, and S. A. Gardiner, Phys. Rev. A, 87, No. 3, 033628 (2013).ADSCrossRefGoogle Scholar
  7. 7.
    V. V. Kocharovsky and Vl. V. Kocharovsky, Phys. Scr., 90, No. 10, 108002 (2015).ADSCrossRefGoogle Scholar
  8. 8.
    V. V. Kocharovsky, Vl. V. Kocharovsky, and M. O. Scully, Phys. Rev. A, 61, No. 5, 053606 (2000).ADSCrossRefGoogle Scholar
  9. 9.
    V. V. Kocharovsky and Vl. V. Kocharovsky, Phys. Rev. A, 81, No. 3, 033615 (2010).ADSCrossRefGoogle Scholar
  10. 10.
    S. V. Tarasov, Vl. V. Kocharovsky, and V. V. Kocharovsky, Phys. Rev. A, 90, No. 3, 033605 (2014).ADSCrossRefGoogle Scholar
  11. 11.
    S. V. Tarasov, Radiophys. Quantum Electron., 59, No. 6, 501 (2016).ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    R. Lopes, C. Eigen, N. Navon, et al., Phys. Rev. Lett., 119, No. 19, 190404 (2017).ADSCrossRefGoogle Scholar
  13. 13.
    M. A. Kristensen, M. B. Christensen, M. Gajdacz, et al., Phys. Rev. Lett., 122, No. 16, 163601 (2019).ADSCrossRefGoogle Scholar
  14. 14.
    M. Mehboudi, A. Lampo, C. Charelambous, et al., Phys. Rev. Lett., 122, No. 3, 030403 (2019).ADSCrossRefGoogle Scholar
  15. 15.
    S. Chatterjee and P. Diaconis, J. Phys. A, 47, No. 8, 085201 (2014).ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    S. Giorgini, L. P. Pitaevskii, and S. Stringari, Phys. Rev. Lett., 80, No. 23, 5040 (1998).ADSCrossRefGoogle Scholar
  17. 17.
    D. A. W. Hutchinson, E. Zaremba, and A. Griffin, Phys. Rev. Lett., 78, No. 10, 1842 (1997).ADSCrossRefGoogle Scholar
  18. 18.
    S. J. Garratt, C. Eigen, J. Zhang, et al., Phys. Rev. A, 99, No. 2, 021601 (2019).ADSCrossRefGoogle Scholar
  19. 19.
    W. Zwerger, Phys. Rev. Lett., 92, No. 2, 027203 (2004).ADSCrossRefGoogle Scholar
  20. 20.
    Z. Idziaszek, M. Gajda, and K. Rzazewski, Europhys. Lett., 86, No. 1, 10002 (2009).ADSCrossRefGoogle Scholar
  21. 21.
    H. Shi and A. Griffin, Phys. Rep., 304, Nos. 1–2, 1 (1998).ADSCrossRefGoogle Scholar
  22. 22.
    A. J. Leggett, Rev. Mod. Phys., 73, No. 2, 307 (2001).ADSCrossRefGoogle Scholar
  23. 23.
    S. V. Tarasov, Vl. V. Kocharovsky, and V. V. Kocharovsky, Entropy, 20, No. 3, 153 (2018).ADSCrossRefGoogle Scholar
  24. 24.
    M. Abramowitz and I. A. Steagun, eds., Handbook of Special Functions with Formulas, Graphs, and Tables, Dover, New York (1972).zbMATHGoogle Scholar
  25. 25.
    B. G. Englert, S. A. Fulling, and M. D. Pilloff, Opt. Commun., 208, Nos. 1–3, 139 (2002).ADSCrossRefGoogle Scholar
  26. 26.
    R. Lopes, C. Eigen, A. Barker, et al., Phys. Rev. Lett., 118, No. 21, 210401 (2017).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • S. V. Tarasov
    • 1
    Email author
  • Vl. V. Kocharovsky
    • 1
  • V. V. Kocharovsky
    • 1
    • 2
  1. 1.Institute of Applied Physics of the Russian Academy of SciencesNizhny NovgorodRussia
  2. 2.Texas A&M UniversityCollege StationUSA

Personalised recommendations