Sub-Doppler spectroscopy in a thin film of resonant vapor

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 59, Issue 5, 1999, Pages 3723-3735

  Briaudeau, Stephan ^a   Bloch, Daniel ^a   Ducloy, Martial ^a  

^a UNIVERSITÉ PARIS 13   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000099020     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.59.3723     Document Type: Article

References (45)

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13. Laser Phys.A. Ch. Izmailov3, 507 (1993).
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24. According to various experimental studies, it appears that an alkali-metal atom can remain adsorbed on a standard window (glass or sapphire) for a time largely exceeding the typical time of flight between the walls, corresponding to atomic desorption: see, e.g., D. Bloch, M. Oria, M. Fichet, and M. Ducloy, Ann. Phys. (Paris) 15, 107 (1990)
25. or A. M. Bonch-Bruevich, Yu. M. Maksimov, and V. V. Khromov, Opt. Spektrosk. 58, 1392 (1985) [Opt. Spectrosc. 58, 854 (1985)]; and
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27. As shown in 8, the interferometric dependence is conveniently evidenced by considering the derivative (Formula presented) Indeed, the velocity integration can then be carried out in the large Doppler approximation, and the real part in the complex exponential appearing from Eq. (2) exhibits an interferometric dependence. For cell thicknesses small enough so that the atoms with thermal velocity u are far from reaching the steady sate of interaction (i.e., for (Formula presented)), the interferometric dependence turns out to be a simple thickness modulation of the absorption coefficient: (Formula presented) with the first term simply related to the (frequency derivative) macroscopic linear absorption, and the second one to the transient effect.
28. A. M. Akul’shin, V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. V. Sautenkov, E. K. Yurkin, and N. V. Senkov, Pis’ma Zh. Eksp. Teor. Fiz. 36, 247 (1982) [JETP Lett. 36, 303 (1982)].
29. Note the following misprint in Ref. 4: a “(Formula presented)” factor is missing in Eq. (3) of Ref. 4.
30. Note that in the linear two-level model signal, in the absence of FM, the logarithmic singularity also corresponds to such “soft” velocity selection, with (Formula presented)
31. From asymptotic calculations, and in the frame of FM absorption (i.e., frequency derivative of the absorption line shape), one estimates that competition with the linear regime occurs when (Formula presented) In a large range of value for (Formula presented) this can be approximated in a simple way: (Formula presented) with ɛ on the order of 0.1–1. As expected, the competition is not solely dependent upon the intensity, but also on the cell length.
32. B. Dahmani, L. Hollberg, and R. Drullinger, Opt. Lett. 12, 876 (1987).
33. We generally assume that the atomic density is governed by the usual Langmuir-Taylor formulas, although such formulas are only established at the interface between condensed systems and a large volume vapor. Note, by the way, that in some cases, drops of metallic Cs were visible along the trajectory between the Cs reservoir and the thin vapor region. This supports the possibility of a gradient in the atomic density, which would not be governed only by the temperature of the coldest point.
34. Witout any special selection of the slowest atoms, the transit time for thermal atoms is ∼50 ns for a 10-μm cell and 500 ns for a 100-μm cell, to be compared with the 30-ns lifetime of the Cs (Formula presented) level.
35. The calculation assumes a thermal Maxwell-Boltzmann velocity distribution, and takes into account the theoretical ratios for the strength of the various hyperfine components. The difference between a steady-state model and a model taking into account the two-level transient regime is very weak and cannot be discriminated experimentally. The small differences observed between the experimental spectra on the short cell and on the 1-cm-thick cell are attributed to the slight change in the Doppler broadening: the temperature conditions are indeed modified in order to make the absorption comparable.
36. The early sign change observed on noncycling transitions does not necessarily define the transition from the linear regime to the nonlinear regime of optical pumping: for a relatively weak intensity, depending on the atomic interaction, the optical pumping induces simultaneously a hyperfine transfer, which decreases the absorption and a Zeeman sublevel redistribution, which tends to an increased absorption.
37. In this last case, the beam diameter was expanded up to 20 mm in order to keep ensuring the anisotropic design of the cell, and to compensate—at least partly—for the drop in the atomic density.
38. In the model developed in 9, following calculations by A. Ch. Izmailov (unpublished), one essentially assumes a relaxation affecting specifically the slower atoms. Such an approach should also be valid to deal with interatomic collisions. Alternately, a simplified approach has been used, yet yielding neighboring results: it consists of integrating a steady-state saturated atomic response, assuming that the saturation is velocity-dependent, due to time-of-flight limitation. Hence (Formula presented) with (Formula presented) the time-of-flight limited saturation, following a dependence (Formula presented) where τ is the time of flight, given by (Formula presented) in the simple cases.
39. As it is well known, in the special cases of a (Formula presented) or (Formula presented) transition, the interaction strength remains independent of the coupled sublevels, due to the particular symmetry involved in these transitions. In these cases, any elliptical polarization is an eigenstate for nonlinear propagation, independent of the light intensity.
40. It is also well known (and predicted with thin cells) that the line shapes in polarization spectroscopy may become antisymmetric and dispersionlike. This would require a larger amount of transmission through the analyzer, while in the present case the experiments were always conducted in the conditions of nearly optimal extinction.
41. For such a comparison, it is crucial to compensate as much as possible for the variations of the angular beam deflection with the (tunable) frequency shift. In our measurements, we normalized the signal level by keeping constant the amplitude of a resonance associated to “fast” atoms, normally insensitive to slight changes in the pump-probe frequency shift.
42. R. H. Romer and R. H. Dicke, Phys. Rev. 99, 532 (1955).
43. To feel the particular statistics involved, one may first notice that the desorbing atoms see an infinite horizon—in the limit of an infinite light beam size—so that the “mean” atomic free flight diverges. Alternately, one may note, in the limit of extremely low density vapor (i.e., atoms leave the surface one by one), that the relatively important, but infrequent, contribution of the very slow atoms (see the end of Sec. II) will be observable only after a long observation time: more precisely, increasing the accuracy can be accomplished at the expense of an unlimited increase of the required observation time. Only the intrinsic truncature at (Formula presented) or the experimental truncature imposed by the finite beam diameter, prevents divergence in the observation time, and sets a limit to come back to a “normal” law. Such a behavior appears related with a truncated Lévy walk distribution [for more details on these statistics problems, see, e.g., Lévy Flights and Related Topics in Physics, edited by M. F. Shlesinger, G. M. Zaslavsky, and U. Frisch, Lecture Notes in Physics Vol. 450 (Springer, Berlin 1995) or
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