Spontaneous emission of nondispersive Rydberg wave packets

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 58, Issue 1, 1998, Pages 466-477

  Delande, Dominique ^a   Zakrzewski, Jakub ^b  

^a LABORATOIRE KASTLER BROSSEL   (France)

^b JAGIELLONIAN UNIVERSITY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001082580     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.58.466     Document Type: Article

References (43)

1. I. Bialynicki-Birula, M. Kalinski, and J. H. Eberly, Phys. Rev. Lett. 73, 1777 (1994).PRLTAO
2. A. Buchleitner and D. Delande, Phys. Rev. Lett. 75, 1487 (1995).PRLTAO
3. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley, New York, 1992).
4. D. Delande, J. Zakrzewski, and A. Buchleitner, Europhys. Lett. 32, 107 (1995).EULEEJ
5. J. Zakrzewski, D. Delande, and A. Buchleitner, Phys. Rev. Lett. 75, 4015 (1995).PRLTAO
6. J. Zakrzewski, D. Delande, and A. Buchleitner, Phys. Rev. E 57, 1458 (1998).PLEEE8
7. Z. Bialynicka-Birula and I. Bialynicki-Birula, Phys. Rev. A 56, 3629 (1997).PLRAAN
8. P. Goy, J. M. Raimond, M. Gross, and S. Haroche, Phys. Rev. Lett. 50, 1903 (1983); PRLTAO
9. W. Jhe et al, Phys. Rev. Lett. 58, 666 (1987); PRLTAOfor a review see, e.g., S. Haroche in Fundamental Systems in Quantum Optics, Le Houches, Session LIII, 1990, edited by J. Dalibard, J. M. Raimond, and J. Zinn-Justin (Elsevier, Amsterdam, 1992).
10. For appropriate coupling the decay may become nonexponential, and the rates cannot be defined; see, e.g., M. Lewenstein, J. Zakrzewski, Th. W. Mossberg, and J. Mostowski, J. Phys. B 21, L9 (1988); JPAPEH
11. M. Lewenstein, J. Zakrzewski, and Th. W. Mossberg, Phys. Rev. A 38, 808 (1988).PLRAAN
12. K. Hornberger and A. Buchleitner, Europhys. Lett. 41, 383(1998).EULEEJ
13. J. H. Shirley, Phys. Rev. 138, B979 (1965).PRVBAK
14. M. Kalinski, J. H. Eberly, and I. Bialynicki-Birula, Phys. Rev. A 52, 2460 (1995).PLRAAN
15. M. Kalinski and J. H. Eberly, Phys. Rev. A 53, 1715 (1996).PLRAAN
16. I. Bialynicki-Birula and Z. Bialynicka-Birula, Phys. Rev. Lett. 78, 2539 (1997).PRLTAO
17. I. Bialynicki-Birula and Z. Bialynicka-Birula, Phys. Rev. Lett. 77, 4298 (1996).PRLTAO
18. D. Farrelly, E. Lee, and T. Uzer, Phys. Rev. Lett. 75, 972 (1995).PRLTAO
19. E. Lee, A. F. Brunello, and D. Farrelly, Phys. Rev. Lett. 75, 3641 (1995).PRLTAO
20. D. Farrelly, E. Lee, and T. Uzer, Phys. Lett. A 204, 359 (1995).PYLAAG
21. A. F. Brunello, T. Uzer, and D. Farrelly, Phys. Rev. Lett. 76, 2874 (1996).PRLTAO
22. E. Lee, A. F. Brunello, and D. Farrelly, Phys. Rev. A 55, 2203 (1997).PLRAAN
23. C. Cerjan, E. Lee, D. Farrelly, and T. Uzer, Phys. Rev. A 55, 2222 (1997).PLRAAN
24. D. Delande, J. Zakrzewski, and A. Buchleitner, Phys. Rev. Lett. 79, 3541 (1997).PRLTAO
25. We shall not consider typical quantum-mechanical effects important when the number of photons in the occupied mode is small, such as quantum revivals. The equivalence between dressed-state and Floquet pictures is obtained, let us recall, by neglecting the difference between (Formula presented) and (Formula presented) where (Formula presented) is the (very large) number of photons in the occupied mode.
26. In the context of quantum optics of a two-level system, the rotating wave approximation makes it possible to define a time-dependent unitary transformation producing a static Hamiltonian. As there is a formal analogy, this is known as passing to the “rotating frame,” although this is in general not a purely geometrical transformation. Only in the case of a circularly polarized field do the two acceptions of “rotating frame” coincide.
27. H. Klar, Z. Phys. D 11, 45 (1989).ZDACE2
28. J. Henkel and M. Holthaus, Phys. Rev. A 45, 1978 (1992); PLRAAN
29. M. Holthaus, Chaos Solitons Fractals 5, 1143 (1995), and references therein.CSFOEH
30. P. M. Koch and K. A. H. van Leeuven, Phys. Rep. 255, 289 (1995).PRPLCM
31. J. Zakrzewski and D. Delande, J. Phys. B 30, L87 (1997).JPAPEH
32. A. J. Lichtenberg and M. A. Lieberman, Irregular and Stochastic Motion (Springer-Verlag, New York, 1993).
33. A. Buchleitner, J. Zakrzewski, and D. Delande, in Proceedings of the 7th International Conference on Multiphoton Porcesses, edited by P. Lambropoulos and H. Walther (Institute of Physics and Physical Society, Bristol, 1997).
34. We have chosen the length gauge for the description of the empty modes of the electromagnetic field. Of course, one could use a different gauge, such as the velocity gauge. The matrix elements coming into play are different, but we checked that the decay rates of the various spontaneous transitions are — as they should be — gauge independent. Similarly, we could use another gauge to describe the driving microwave field. This produces a different Floquet Hamiltonian and a different static Hamiltonian in the rotating frame, and hence different creation and annihilation operators for the normal modes. However, the energy levels of the dressed atom — and consequently the frequencies of the normal modes — do not depend on the choice of gauge. The same is true for the decay rates. The “exact” computations shown in this paper have been performed in the velocity gauge.
35. The calculation is here done for the density of electromagnetic modes in free space. The decay rates can be substantially modified in the presence of a cavity, as could be used in a real experiment 8.
36. B. R. Mollow, Phys. Rev. 188, 1969 (1969); PHRVAO
37. S. Reynaud, Ann. Phys. (Paris) 8, 315 (1983); ZZZZZZ
38. C. Cohen-Tannoudji and S. Reynaud, J. Phys. B 10, 345 (1977).JPAMA4
39. In Ref. 7, the matrix elements of the dipole operator are calculated using explicit forms of the wave functions in configuration space. We prefer to use no explicit representation of the eigenstates and manipulate creation and annihilation operators in the normal modes: extension of the present results to the decay of “excited” nondispersive wave packets is much easier this way.
40. Note, however, that the spontaneous decay rate per Kepler period as given in Ref. 7 at the end of p. 3630 has a (Formula presented) factor wrongly placed. It is thus “only” four orders of magnitude smaller than the ionization rate.
41. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
42. H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One and Two-Electron Atoms (Springer, Berlin, 1957).
43. J. Zakrzewski, D. Delande, and A. Buchleitner, Z. Phys. B 103, 115 (1997). ZPCMDN