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Quantum resonant effects in the delta-kicked rotor revisited

  • A. UllahEmail author
  • S.K. Ruddell
  • J.A. Currivan
  • M.D. Hoogerland
Regular Article

Abstract

We review the theoretical model and experimental realization of the atom optics δ-kicked rotor (AOKR), a paradigm of classical and quantum chaos. We have performed a number of experiments with an all-optical Bose-Einstein condensate (BEC) in a periodic standing wave potential in an AOKR system. We discuss results of the investigation of the phenomena of quantum resonances in the AOKR. An interesting feature of the momentum distribution of the atoms obtained as a result of short pulses of light, is the variance of the momentum distribution or the kinetic energy ⟨p 2⟩/2m in units of the recoil energy E rec  = ħω rec . The energy of the system is examined as a function of pulse period for a range of kicks that allow the observation of quantum resonances. In particular we study the behavior of these resonances for a large number of kicks. Higher order quantum resonant effects corresponding to the fractional Talbot time of (1/4)T T and (1/5)T T for five and ten kicks have been observed. Moreover, we describe the effect of the initial momentum of the atoms on quantum resonances in the AOKR.

Keywords

Atomic Physics 

References

  1. 1.
    A. Lichetenberg, M. Lieberman, Regular and Chaotic Dynamics (Springer, New York, 1992)Google Scholar
  2. 2.
    M.A. Lieberman, A.J. Lichtenberg, Phys. Rev. A 5, 1852 (1972)ADSCrossRefGoogle Scholar
  3. 3.
    I.P. Kornfeld, S.V. Fomin, Y.G. Sinai, Ergodic Theory (Springer, New York, 1982)Google Scholar
  4. 4.
    B.V. Chirikov, Phys. Rep. 52, 263 (1979)MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    G. Casati, B.V. Chirikov, J. Ford, F.M. Izraeliv, Lecture Notes in Physics (Springer, Berlin, Heidelberg, 1979)Google Scholar
  6. 6.
    B.V. Chirikov, F.M. Izrailev, D.L. Shepelyansky, Sov. Sci. Rev. C 2, 209 (1981)MathSciNetzbMATHGoogle Scholar
  7. 7.
    D.L. Shepelyanski, Physica D 8, 208 (1983)ADSCrossRefGoogle Scholar
  8. 8.
    F.L. Moore, J.C. Robinson, C.F. Bharucha, B. Sundaram, M.G. Raizen, Phys. Rev. Lett. 75, 4598 (1995)ADSCrossRefGoogle Scholar
  9. 9.
    H. Ammann, R. Gray, I. Shvarchuck, N. Christensen, Phys. Rev. Lett. 80, 4111 (1998)ADSCrossRefGoogle Scholar
  10. 10.
    H.J. Stöckmann, Quantum Chaos: An Introduction (Cambridge University Press, Cambridge, 1999)Google Scholar
  11. 11.
    S. Fishman, Quantum Localization, in Quantum Chaos, edited by G. Casati, I. Guarneri, U. Smilansky (North-Holland, New York, 1993), p. 187Google Scholar
  12. 12.
    F.M. Izrailev, D.L. Shepelyansky, Theor. Math. Phys. 43, 553 (1980)CrossRefGoogle Scholar
  13. 13.
    F.M. Izrailev, Physica D 1, 243 (1980)MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    M. Saunders, P.L. Halkyard, K.J. Challis, S.A. Gardiner, Phys. Rev. A 76, 043415 (2007)ADSCrossRefGoogle Scholar
  15. 15.
    P.L. Halkyard, M. Saunders, S.A. Gardiner, K.J. Challis, Phys. Rev. A 78, 063401 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    M. Saunders, P.L. Halkyard, S.A. Gardiner, K.J. Challis, Phys. Rev. A 79, 023423 (2009)ADSCrossRefGoogle Scholar
  17. 17.
    P. McDowall, A. Hilliard, M. McGovern, T. Grünzweig, M.F. Andersen, New J. Phys. 11, 123021 (2009)ADSCrossRefGoogle Scholar
  18. 18.
    F. Saif, Phys. Rep. 419, 207 (2005)ADSCrossRefGoogle Scholar
  19. 19.
    S. Wimberger, I. Guarneri, S. Fishman, Nonlinearity 16, 1381 (2003)MathSciNetADSCrossRefzbMATHGoogle Scholar
  20. 20.
    S. Wimberger, M. Sadgrove, J. Phys. A 38, 10549 (2005)MathSciNetADSCrossRefzbMATHGoogle Scholar
  21. 21.
    L. Deng, E.W. Hagley, J. Denschlag, J.E. Simsarian, M. Edwards, C.W. Clark, K. Helmerson, S.L. Rolston, W.D. Phillips, Phys. Rev. Lett. 83, 5407 (1999)ADSCrossRefGoogle Scholar
  22. 22.
    M.K. Oberthaler, R.M. Godun, M.B. d’Arcy, G.S. Summy, K. Burnett, Phys. Rev. Lett. 83, 4447 (1999)ADSCrossRefGoogle Scholar
  23. 23.
    P. Szriftgiser, J. Ringot, D. Delande, J.C. Garreau, Phys. Rev. Lett. 89, 224101 (2002)ADSCrossRefGoogle Scholar
  24. 24.
    G.J. Duffy, S. Parkins, T. Müller, M. Sadgrove, R. Leonhardt, A.C. Wilson, Phys. Rev. E 70, 056206 (2004)ADSCrossRefGoogle Scholar
  25. 25.
    P.H. Jones, M. Goonasekera, D.R. Meacher, T. Jonckheere, T.S. Monteiro, Phys. Rev. Lett. 98, 073002 (2007)ADSCrossRefGoogle Scholar
  26. 26.
    S.A. Wayper, W. Simpson, M.D. Hoogerland, Eur. Phys. Lett. 79, 60006 (2007)ADSCrossRefGoogle Scholar
  27. 27.
    J.A. Currivan, A. Ullah, M.D. Hoogerland, Eur. Phys. Lett. 85, 30005 (2009)ADSCrossRefGoogle Scholar
  28. 28.
    A. Ullah, M.D. Hoogerland, Phys. Rev. E 83, 046218 (2011)ADSCrossRefGoogle Scholar
  29. 29.
    S. Fishman, D.R. Grempel, R.E. Prange, Phys. Rev. Lett. 49, 509 (1982)MathSciNetADSCrossRefGoogle Scholar
  30. 30.
    C. Ryu, M.F. Andersen, A. Vaziri, M.B. d’Arcy, J.M. Grossman, K. Helmerson, W.D. Phillips, Phys. Rev. Lett. 96, 160403 (2006)ADSCrossRefGoogle Scholar
  31. 31.
    Y.B. Ovchinnikov, J.H. Müller, M.R. Doery, E.J.D. Vredenbregt, K. Helmerson, S.L. Rolston, W.D. Phillips, Phys. Rev. Lett. 83, 284 (1999)ADSCrossRefGoogle Scholar
  32. 32.
    M. Lepers, V. Zehnlé, J.C. Garreau, Phys. Rev. A 77, 043628 (2008)ADSCrossRefGoogle Scholar
  33. 33.
    H.F. Talbot, Philos. Mag. 9, 401 (1836)Google Scholar
  34. 34.
    M. Saunders, Ph.D. thesis, Durham University, 2009Google Scholar
  35. 35.
    M.P. Sadgrove, Ph.D. thesis, The University of Auckland, 2005Google Scholar
  36. 36.
    W.H. Oskay, D.A. Steck, V. Milner, B.G. Klappauf, M.G. Raizen, Opt. Commun. 179, 137 (2000)ADSCrossRefGoogle Scholar
  37. 37.
    M. Sadgrove, T. Mullins, S. Parkins, R. Leonhardt, Physica E 29, 369 (2005)ADSCrossRefGoogle Scholar
  38. 38.
    Y.C. Wenas, M.D. Hoogerland, Rev. Sci. Instrum. 79, 053101 (2008)ADSCrossRefGoogle Scholar
  39. 39.
    L.E. Reichl, The Transition to Chaos in Conservative Classical Systems: Quantum Manifestations (Springer-Verlag, Berlin, 1992)Google Scholar
  40. 40.
    M. Berry, I. Marzoli, W. Schleich, Phys. World 14, 39 (2001)Google Scholar
  41. 41.
    M. Sadgrove, M. Horikoshi, T. Sekimura, K. Nakagawa, Phys. Rev. Lett. 99, 043002 (2007)ADSCrossRefGoogle Scholar
  42. 42.
    I. Dana, V. Ramareddy, I. Talukdar, G.S. Summy, Phys. Rev. Lett. 100, 024103 (2008)ADSCrossRefGoogle Scholar
  43. 43.
    M. Sadgrove, S. Kumar, K. Nakagawa, Phys. Rev. Lett. 101, 180502 (2008)ADSCrossRefGoogle Scholar
  44. 44.
    R.A. Horne, R.H. Leonard, C.A. Sackett, Phys. Rev. A 83, 063613 (2011)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • A. Ullah
    • 1
    Email author
  • S.K. Ruddell
    • 1
  • J.A. Currivan
    • 1
  • M.D. Hoogerland
    • 1
  1. 1.Department of PhysicsUniversity of AucklandAucklandNew Zealand

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