Publication: Location of crossings in the Floquet spectrum of a driven two-level system
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2004-01
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American Physical Society
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Abstract
The calculation of the Floquet quasi-energies of a system driven by a time-periodic field is an efficient way to understand its dynamics. In particular, the phenomenon of dynamical localization can be related to the presence of close approaches between quasienergies (either crossings or avoided crossings). Here we consider a driven two-level system and study how the locations of crossings in the quasienergy spectrum alter as the field parameters are changed. A perturbational scheme provides a direct connection between the form of the driving field and the quasienergies which is exact in the limit of high frequencies. We first obtain relations for the quasienergies for some common types of applied field in the high-frequency limit, and then show how the locations of the crossings drift as the frequency is reduced. We find a simple empirical formula which describes this drift extremely well in general, and which we conjecture is exact for the specific case of square-wave driving
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©2003 The American Physical Society.
This research was supported by the EU through the TMR program ‘‘Quantum Electron Transport in the Frequency and Time Domains.’’ The author thanks Gloria Platero for discussions, and acknowledges the hospitality of the International Institute for Applied Systems Analysis (IIASA) in Vienna, where part of this work was carried out.
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1. C.H. Bennett and D.P. DiVincenzo, Nature (London) 404, 247 (20009.
2. D. Vion, A. Aassime, A. Cottet, P. Joyez, H. Pothier, C. Urbina, D. Esteve, and M.H. Devoret, Science 296, 886 (2002).
3. B.E. Cole, J.B. Williams, B.T. King, M.S. Sherwin, and C.R. Stanley, Nature (London) 410, 60 (20019.
4. R.H. Blick, D. Pfannkuche, R.J. Haug, K. von Klitzing, and K. Eberl, Phys. Rev. Lett. 80, 4032 (1998).
5. T.H. Oosterkamp, T. Fujisawa, W.G. van der Wiel, K. Ishibashi, R.V. Hijman, S. Tarucha, and L.P. Kouwenhoven, Nature (London) 395, 873 (1998).
6. Jon H. Shirley, Phys. Rev. 138, B979 (1965).
7. F. Grossmann, T. Dittrich, P. Jung, and P. Hänggi, Phys. Rev. Lett. 67, 516 (1991).
8. F. Grossmann and P. Hänggi, Europhys. Lett. 18, 571 (1992).
9. Martin Holthaus, Phys. Rev. Lett. 69, 1596 (1992).
10. K. Drese and M. Holthaus, Eur. Phys. J. D 5, 119 (1999).
11. J.C.A. Barata and W.F. Wreszinski, Phys. Rev. Lett. 84, 2112 (2000).
12. Marco Frasca, Phys. Rev. A 60, 573 (1999).
13. V. Delgado and J.M. Llorente, J. Phys. B 33, 5403 (2000).
14. It should be noted, however, that although quasienergy degeneracy is necessary to produce CDT it is not sufficient. For example, if the Floquet states themselves have a large amplitude of oscillation, the particle will not be localized on short time scales, and thus CDT will not occur.
15. J. von Neumann and E. Wigner, Phys. Z 30, 467 (1929).
16. M. Holthaus, Z. Phys. B: Condens. Matter 89, 251 (1992).
17. C.E. Creffield and G. Platero, Phys. Rev. B 65, 113304 (20029.
18. Hideo Sambe, Phys. Rev. A 7, 2203 (1973).
19. J.M. Villas-Bôas, Wei Zhang, Sergio E. Ulloa, P.H. Rivera, and Nelson Studart, Phys. Rev. B 66, 085325 (20029.
20. Ming Jun Zhu, Xian-Geng Zhao, and Qian Niu, J. Phys.: Condens. Matter 11, 4527 (1999).
21. Xian-Geng Zhao, J. Phys.: Condens. Matter 6, 4527 (1994).
22. M.M. Dignam and C. Martijn de Sterke, Phys. Rev. Lett. 88, 046806 (2002).
23. Handbook of Mathematical Functions, edited by M. Abramowitz and I.A. Stegun (Dover, New York, 1972).