Driving the resonant quantum kicked rotor via extended initial conditions

  • A. RomanelliEmail author
  • G. Hernández
Quantum Optics Regular Article


We study the resonances of the quantum kicked rotor subjected to an extended initial distribution. For the primary resonances we obtain the dispersion relation for the map of this system. We find an analytical dependence of the statistical moments on the shape of the initial distribution. For the secondary resonances we obtain numerically a similar dependence. This allows us to devise an extended initial condition which produces an average angular momentum pointing in a preset direction which increases with time with a preset ratio.


Angular Momentum Dispersion Relation Group Velocity Primary Resonance Quantum Walk 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    G. Casati, B.V. Chirikov, F.M. Izrailev, J. Ford, Lect. Notes Phys. 93, 334 (1979)MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    H. Schomerus, E. Lutz, Phys. Rev. Lett. 98, 260401 (2007)ADSCrossRefGoogle Scholar
  3. 3.
    H. Schomerus, E. Lutz, Phys. Rev. A 77, 062113 (2008)ADSCrossRefGoogle Scholar
  4. 4.
    J.-A. Currivan, A. Ullah, M.D. Hoogerland, Europhys. Lett. 85, 30005 (2009)ADSCrossRefGoogle Scholar
  5. 5.
    M. Sadgrove, A. Hilliard, T. Mullins, S. Parkins, R. Leonhardt, Phys. Rev. E 70, 036217 (2004)ADSCrossRefGoogle Scholar
  6. 6.
    M. Saunders, P.L. Halkyard, K.J. Challis, S.A. Gardiner, Phys. Rev. A 76, 043415 (2007)ADSCrossRefGoogle Scholar
  7. 7.
    P.L. Halkyard, M. Saunders, S.A. Gardiner, Phys. Rev. A 78, 063401 (2008)ADSCrossRefGoogle Scholar
  8. 8.
    S. Chaudhury, A. Smith, B.E. Anderson, S. Ghose, P.S. Jessen, Nature 461, 768 (2009)ADSCrossRefGoogle Scholar
  9. 9.
    F.M. Izrailev, Phys. Rep. 196, 299 (1990)MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    J.W. Goodman, Introduction to Fourier optics (Roberts and Company Publishers, 2005)Google Scholar
  11. 11.
    K. Patorski, Progress in Optics, edited by E. Wolf (Elsevier Science, Amsterdam, 1989), Vol. XXVII, pp. 1 − 108Google Scholar
  12. 12.
    F.L. Moore, J.C. Robinson, C. Bharucha, P.E. Williams, M.G. Raizen, Phys. Rev. Lett. 73, 274 (1994)CrossRefGoogle Scholar
  13. 13.
    J.C. Robinson, C. Bharucha, F.L. Moore, R. Jahnke, G.A. Georgakis, Q. Niu, M.G. Raizen, B. Sundaram, Phys. Rev. Lett. 74, 3963 (1995)ADSCrossRefGoogle Scholar
  14. 14.
    F.L. Moore, J.C. Robinson, C.F. Bharucha, B. Sundaram, M.G. Raizen, Phys. Rev. Lett. 75, 4598 (1995)ADSCrossRefGoogle Scholar
  15. 15.
    J.C. Robinson, C.F. Bharucha, K.W. Madison, F.L. Moore, B. Sundaram, S.R. Wilkinson, M.G. Raizen, Phys. Rev. Lett. 76, 3304 (1996)ADSCrossRefGoogle Scholar
  16. 16.
    C.F. Bharucha, J.C. Robinson, F.L. Moore, B. Sundaram, Q. Niu, M.G. Raizen, Phys. Rev. E 60, 3881 (1999)ADSCrossRefGoogle Scholar
  17. 17.
    W.H. Oskay, D.A. Steck, V. Milner, B.G. Klappauf, M.G. Raizen, Opt. Commun. 179, 137 (2000)ADSCrossRefGoogle Scholar
  18. 18.
    J.F. Kanem, S. Maneshi, M. Partlow, M. Spanner, A.M. Steinberg, Phys. Rev. Lett.98, 083004 (2007)Google Scholar
  19. 19.
    G.J. Valcárcel, E. Roldán, A. Romanelli, New J. Phys. 12, 123022 (2010)CrossRefGoogle Scholar
  20. 20.
    A. Romanelli, R. Siri, V. Micenmacher, Phys. Rev. E 76, 037202 (2007)ADSCrossRefGoogle Scholar
  21. 21.
    A. Romanelli, Phys. Rev. E 79, 056209 (2008)ADSCrossRefGoogle Scholar
  22. 22.
    A. Romanelli, Phys. Rev. A 80, 022102 (2009)MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    A. Romanelli, A.C. Sicardi Schifino, R. Siri, G. Abal, A. Auyuanet, R. Donangelo, Physica A 338, 395 (2004)MathSciNetADSCrossRefGoogle Scholar
  24. 24.
    A. Romanelli, A. Auyuanet, R. Siri, G. Abal, R. Donangelo, Physica A 352, 409 (2005)MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    A. Romanelli, A. Auyuanet, R. Siri, V. Micenmacher, Phys. Lett. A 365, 200 (2007)ADSCrossRefGoogle Scholar
  26. 26.
    A. Romanelli, Phys. Lett. A 80, 042332 (2009)MathSciNetGoogle Scholar
  27. 27.
    I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals Series and Products (Academic Press, New York, 1994), p. 987Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Instituto de Física, Facultad de Ingeniería, Universidad de la RepúblicaMontevideoUruguay

Personalised recommendations