Spectroscopy of a driven solid-state qubit coupled to a structured environment

Mesoscopic Physics

Abstract.

We study the asymptotic dynamics of a driven spin-boson system where the environment is formed by a broadened localized mode. Upon exploiting an exact mapping, an equivalent formulation of the problem in terms of a quantum two-state system (qubit) coupled to a harmonic oscillator which is itself Ohmically damped, is found. We calculate the asymptotic population difference of the two states in two complementary parameter regimes. For weak damping and low temperature, a perturbative Floquet-Born-Markovian master equation for the qubit-oscillator system can be solved. We find multi-photon resonances corresponding to transitions in the coupled quantum system and calculate their line-shape analytically. In the complementary parameter regime of strong damping and/or high temperatures, non-perturbative real-time path integral techniques yield analytic results for the resonance line shape. In both regimes, we find very good agreement with exact results obtained from a numerical real-time path-integral approach. Finally, we show for the case of strong detuning between qubit and oscillator that the width of the n-photon resonance scales with the nth Bessel function of the driving strength in the weak-damping regime.

References

  1. Y. Nakamura, Yu.A. Pashkin, J.S. Tsai, Nature 398, 786 (1999) Google Scholar
  2. J.M. Martinis, S. Nam, J. Aumentado, C. Urbina, Phys. Rev. Lett. 89, 117901 (2002) PubMedGoogle Scholar
  3. Yu.A. Pashkin, T. Yamamoto, O. Astafiev, Y. Nakamura, D.V. Averin, J.S. Tsai, Nature 421, 823 (2003) PubMedGoogle Scholar
  4. D. Vion, A. Aassime, A. Cottet, P. Joyez, H. Pothier, C. Urbina, D. Esteve, M.H. Devoret, Science 296, 886 (2002) PubMedGoogle Scholar
  5. I. Chiorescu, Y. Nakamura, C.J.P.M. Harmans, J.E. Mooij, Science 299, 1869 (2003) PubMedGoogle Scholar
  6. I. Chiorescu, P. Bertet, K. Semba, Y. Nakamura, C.J.P.M. Harmans, J.E. Mooij, Nature 431, 159 (2004) PubMedGoogle Scholar
  7. C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom-Photon Interactions (Wiley, New York, 1992) Google Scholar
  8. U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 1999) Google Scholar
  9. M. Grifoni, P. Hänggi, Phys. Rep. 304, 229 (1998) Google Scholar
  10. L. Tian, S. Lloyd, T.P. Orlando, Phys. Rev. B 65, 144516 (2002) Google Scholar
  11. M. Thorwart, L. Hartmann, I. Goychuk, P. Hänggi, J. Mod. Opt. 47, 2905 (2000) Google Scholar
  12. A.Yu. Smirnov, Phys. Rev. B 67, 155104 (2003) Google Scholar
  13. M. Thorwart, E. Paladino, M. Grifoni, Chem. Phys. 296, 333 (2004) Google Scholar
  14. F.K. Wilhelm, S. Kleff, J. von Delft, Chem. Phys. 296, 345 (2004) Google Scholar
  15. S. Kleff, S. Kehrein, J. von Delft, Phys. Rev. B 70, 014516 (2004) Google Scholar
  16. S. Saito, M. Thorwart, H. Tanaka, M. Ueda, H. Nakano, K. Semba, H. Takayanagi, Phys. Rev. Lett. 93, 037001 (2004) PubMedGoogle Scholar
  17. M.C. Goorden, F.K. Wilhelm, Phys. Rev. B 68, 012508 (2003) Google Scholar
  18. M.C. Goorden, M. Thorwart, M. Grifoni, Phys. Rev. Lett. 93, 267005 (2004) PubMedGoogle Scholar
  19. A. Garg, J.N. Onuchic, V. Ambegaokar, J. Chem. Phys. 83, 4491 (1985) Google Scholar
  20. R. Blümel, R. Graham, L. Sirko, U. Smilansky, H. Walther, K. Yamada, Phys. Rev. Lett. 62, 341 (1989) PubMedGoogle Scholar
  21. S. Kohler, T. Dittrich, P. Hänggi, Phys. Rev. E 55, 300 (1997) Google Scholar
  22. J.H. Shirley, Phys. Rev. 138, B979 (1965) Google Scholar
  23. I. Shavit, L.T. Redmon, J. Chem. Phys. 73, 5711 (1980) Google Scholar
  24. N. Makri, D.E. Makarov, J. Chem. Phys. 102, 4600 (1995) Google Scholar
  25. M. Thorwart, P. Reimann, P. Jung, R.F. Fox, Chem. Phys. 235, 61 (1998) Google Scholar
  26. M. Thorwart, P. Reimann, P. Hänggi, Phys. Rev. E 62, 5808 (2000) Google Scholar
  27. L. Hartmann, I. Goychuk, M. Grifoni, P. Hänggi, Phys. Rev. E 61, R4687 (2000) Google Scholar
  28. S.M. Girvin, R.-S. Huang, A. Blais, A. Wallraff, R.J. Schoelkopf, in Proceedings of Les Houches Summer School, Session LXXIX, Quantum Entanglement and Information Processing (2003); see also cond-mat/0310670 Google Scholar
  29. A. Wallraff, D.I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S.M. Girvin, R.J. Schoelkopf, Nature 431, 162 (2004) PubMedGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Authors and Affiliations

  1. 1.Instituut-Lorentz, Universiteit LeidenLeidenThe Netherlands
  2. 2.Institut für Theoretische Physik IV, Heinrich-Heine-Universität DüsseldorfDüsseldorfGermany
  3. 3.Institut für Theoretische Physik, Universität RegensburgRegensburgGermany

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