Journal of Experimental and Theoretical Physics

, Volume 118, Issue 1, pp 124–132 | Cite as

Quasi-energy of single quantum particles and a Bose-Einstein condensate in a dynamical trap

Order, Disorder, and Phase Transition in Condensed System


The quasi-energy states have been found analytically for single quantum particles and an atomic Bose-Einstein condensate in a trap with periodically oscillating walls with a small modulation depth. A resonance is shown to exist as the modulation frequency approaches the difference of the frequencies corresponding to the levels in the unperturbed problem. Quasi-energy splitting and, accordingly, beats with a periodic population exchange between two levels in resonance have been found in the resonant case. Bistability of the response to trap size modulation, when the sustenance (depending on the initial conditions) of various quasi-energy states is possible under the same conditions, has been found for a Bose-Einstein condensate under resonance conditions.


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  1. 1.
    V. N. Krasil’nikov, Parametric Wave Phenomena in the Classical Electrodynamics (St. Petersburg State University, St. Petersburg, 1996) [in Russian].Google Scholar
  2. 2.
    S. N. Gurbatov, O. V. Rudenko, and A. I. Saichev, Waves and Structures in Nonlinear Nondispersive Media (Fizmatlit, Moscow, 2008; Springer, New York, 2012).Google Scholar
  3. 3.
    P. E. Toschek, in Proceedings of the Les Houches Summer School on Theoretical Physics: New Trends in Atomic Physics, Session XXXVIII, Les Houches, France, June 28–July 29, 1982, Ed. by G. Grynberg and R. Stora (Elsevier, Amsterdam, The Netherlands, 1984), Vol. 1, p. 383.Google Scholar
  4. 4.
    K. Hammerer, M. Wallquist, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, P. Zoller, J. Ye, and H. J. Kimble, Phys. Rev. Lett. 103, 063005 (2009).ADSCrossRefGoogle Scholar
  5. 5.
    S. Camerer, M. Korppi, A. Jöckel, D. Hunger, T. W. Hänsch, and P. Treutlein, Phys. Rev. Lett. 107, 223001 (2011).ADSCrossRefGoogle Scholar
  6. 6.
    J. D. Teufel, T. Donner, M. A. Castellanos-Beltran, J. W. Harlow, and K. W. Lehnert, Nat. Nanotechnol. 4, 820 (2009).ADSCrossRefGoogle Scholar
  7. 7.
    D. Meiser and P. Meystre, Phys. Rev. A: At., Mol., Opt. Phys. 73, 033417 (2006).ADSCrossRefGoogle Scholar
  8. 8.
    Y. Chang, T. Shi, Y. X. Liu, C. P. Sun, and F. Nori, Phys. Rev. A: At., Mol., Opt. Phys. 83, 063826 (2011).ADSCrossRefGoogle Scholar
  9. 9.
    M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).ADSCrossRefGoogle Scholar
  10. 10.
    L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Volume 3: Quantum Mechanics: Non-Relativistic Theory (Nauka, Moscow, 1974; Butterworth-Heinemann, Oxford, 1981).Google Scholar
  11. 11.
    Ya. B. Zel’dovich, Sov. Phys. JETP 24(5), 1006 (1966).Google Scholar
  12. 12.
    V. I. Ritus, Sov. Phys. JETP 24(5), 1041 (1966).ADSGoogle Scholar
  13. 13.
    A. I. Baz’, Ya. B. Zel’dovich, and A. M. Perelomov, Scattering, Reactions, and Decays in Nonrelativistic Quantum Mechanics (Israel Program for Scientific Translation, Jerusalem, 1969; Nauka, Moscow, 1971).Google Scholar
  14. 14.
    L. P. Pitaevskii, Phys.-Usp. 49(4), 333 (2006).ADSCrossRefGoogle Scholar
  15. 15.
    N. N. Rosanov, V. A. Smirnov, and S. V. Fedorov, J. Exp. Theor. Phys. 102(5), 703 (2006).ADSCrossRefGoogle Scholar
  16. 16.
    J. Kaspzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymaska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, Nature (London) 443, 409 (2006).ADSCrossRefGoogle Scholar
  17. 17.
    H. Gibbs, Optical Bistability: Controlling Light With Light (Academic, London, 1985; Mir, Moscow, 1988).Google Scholar
  18. 18.
    P. N. Pigurnov, N. N. Rozanov, and V. A. Smirnov, Opt. Spectrosc. 68(1), 119 (1990).ADSGoogle Scholar
  19. 19.
    N. N. Rozanov, Optical Bistability and Hysteresis in Distributed Nonlinear Systems (Nauka, Moscow, 1997) [in Russian].Google Scholar

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© Pleiades Publishing, Inc. 2014

Authors and Affiliations

  1. 1.Vavilov State Optical InstituteSt. PetersburgRussia
  2. 2.St. Petersburg National Research University of Information Technologies, Mechanics, and OpticsSt. PetersburgRussia
  3. 3.Ioffe Physicotechnical InstituteRussian Academy of SciencesSt. PetersburgRussia

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