OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 9, Iss. 12 — Dec. 1, 1992
  • pp: 2163–2170

ac Stark shift of a two-photon transition induced by a model stochastic field

J. C. Camparo and P. P. Lambropoulos  »View Author Affiliations

JOSA B, Vol. 9, Issue 12, pp. 2163-2170 (1992)

View Full Text Article

Enhanced HTML    Acrobat PDF (1026 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We have investigated the ac Stark shift of a two-photon transition induced by a model stochastic field by using a Monte Carlo technique. The model field has a stochastic single mode, which can possess both colored amplitude and colored frequency fluctuations. The stochastic field’s modification of the ac Stark shift is quantified by a parameter M, which is the ratio of the Stark shift in the model stochastic field to the Stark shift that would be obtained in a phase-diffusion field of equivalent linewidth (i.e., a field with frequency fluctuations but no amplitude fluctuations). In the regime of weak fields, below saturation of the bound-bound transition, we find that M is greater than unity: the Stark shift is enhanced by the stochastic field. Moreover, in this regime M is an increasing function of the field’s degree of photon bunching. In strong fields, where the bound–bound transition is nearly saturated, the enhancement of the Stark shift is diminished, so much so that in extremely strong fields M is actually less than unity. Our calculations indicate that the ac Stark shift’s modification occurs through two distinct processes, depending on the strength of the field. In weak fields enhancement of a multiphoton transition’s Stark shift is influenced primarily by the intrinsic correlation between ac-Stark-shift fluctuations and Rabi-frequency fluctuations. In strong fields the fluctuating Stark shifts give rise to an asymmetric resonance line shape in a fashion analogous to inhomogeneous broadening. The line shape’s peak position then has a sublinear dependence on the stochastic field’s intensity, and this yields a diminished value of M.

© 1992 Optical Society of America

Original Manuscript: January 22, 1992
Revised Manuscript: April 7, 1992
Published: December 1, 1992

J. C. Camparo and P. P. Lambropoulos, "ac Stark shift of a two-photon transition induced by a model stochastic field," J. Opt. Soc. Am. B 9, 2163-2170 (1992)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Arditi, T. R. Carver, “Pressure, light, and temperature shifts in optical detection of 0–0 hyperfine resonance of alkali metals,” Phys. Rev. 124, 800 (1961). [CrossRef]
  2. J. P. Barrat, C. Cohen-Tannoudji, “Elargissement et deplacement des raies de resonance magnetique causes par une excitation optique,” J. Phys. 22, 443 (1961).
  3. B. S. Mathur, H. Tang, W. Happer, “Light shifts in the alkali atoms,” Phys. Rev. 171, 11 (1968), and references therein. [CrossRef]
  4. See, for example, G. Busca, M. Tetu, J. Vanier, “Light shift and light broadening in the 87Rb maser,” Can. J. Phys. 13, 1379 (1973);C. H. Volk, R. P. Frueholz, “The role of long-term lamp fluctuations in the random walk of frequency behavior of the rubidium frequency standard: a case study,” J. Appl. Phys. 57, 980 (1985);J. C. Camparo, R. P. Frueholz, “Fundamental stability limits for the diode-laser-pumped atomic frequency standard,” J. Appl. Phys. 59, 3313 (1986). [CrossRef]
  5. J. S. Barkos, “ac Stark effect and multiphoton processes in atoms,” Phys. Rep. 31, 209 (1977). [CrossRef]
  6. C. Lecompte, G. Mainfray, C. Manus, F. Sanchez, “Laser temporal-coherence effects on multiphoton ionization processes,” Phys. Rev. A 11, 1009 (1975). [CrossRef]
  7. A. T. Georges, P. Lambropoulos, “Aspects of resonant multiphoton processes,” Adv. Electron. Electron Phys. 54, 191 (1980), and references therein. [CrossRef]
  8. N. B. Delone, V. A. Kovarskii, A. V. Massalov, N. F. Perel’man, “An atom in the radiation field of a multifrequency laser,” Sov. Phys. Usp. 23, 472 (1980). [CrossRef]
  9. R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, 1973).
  10. L.-A. Lompre, G. Mainfray, C. Manus, J. P. Marinier, “Laser light statistics and bandwidth effects in resonant multiphoton ionisation of caesium atoms at 1.059 μ m,” J. Phys. B14, 4307 (1981). [CrossRef]
  11. J. Morellec, D. Normand, G. Petite, “Resonance shifts in the multiphoton ionization of cesium atoms,” Phys. Rev. A 14, 300 (1976). [CrossRef]
  12. P. Zoller, “Stark shifts and resonant multiphoton ionisation in multimode laser fields,” J. Phys. B 15, 2911 (1982). [CrossRef]
  13. Y. Gontier, M. Trahin, “Multiphoton ionisation and light statistics: application to the cesium atom,” J. Phys. B 12, 2123 (1979). [CrossRef]
  14. P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, M. D. Levenson, “Saturation effects in resonant three-photon ionisation of sodium with a nonmonochromatic field,” J. Phys. B 11, 1733 (1978). [CrossRef]
  15. P. Zoller, P. Lambropoulos, “Laser temporal coherence effects in two-photon resonant three-photon ionisation,” J. Phys. B 13, 69 (1980). [CrossRef]
  16. L. R. Brewer, F. Buchinger, M. Ligare, D. E. Kelleher, “Resonance-enhanced multiphoton ionization of atomic hydrogen,” Phys. Rev. A 39, 3912 (1989). [CrossRef] [PubMed]
  17. Most high-power pulsed lasers operate in many modes, and it is known that in the limit of many modes a multimode field becomes a chaotic field. On a more pragmatic level, a chaotic field’s nth-order coherence function may be written in terms of products of first-order coherence functions, which aids in the analytical evaluation of atomic averages.
  18. L. A. Westling, M. G. Raymer, “Intensity autocorrelation measurements and spontaneous FM phase locking in a multimode pulsed dye laser,” J. Opt. Soc. Am. B 3, 911 (1986). [CrossRef]
  19. J. C. Camparo, P. Lambropoulos, “Monte Carlo simulations of field fluctuations in strongly driven resonant transitions,” submitted to Phys. Rev. A.
  20. M. D. MacLaren, G. Marsaglia, “Uniform random number generators,” J. Assoc. Comput. Mach. 12, 83 (1965). [CrossRef]
  21. J. H. Ahrens, U. Dieter, “Computer methods for sampling from the exponential and normal distributions,” Commun. Assoc. Comput. Mach. 15, 873 (1972).
  22. M. J. Levin, “Generation of a sampled Gaussian time series having a specified correlation function,” IRE Trans. Inf. Theory IT-6, 545 (1960). [CrossRef]
  23. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1984).
  24. P. Zoller, P. Lambropoulos, “Non-Lorentzian laser lineshapes in intense field–atom interaction,” J. Phys. B 12, L547 (1979). [CrossRef]
  25. A. T. Georges, P. Lambropoulos, J. H. Marburger, “Theory of third-harmonic generation in metal vapors under two-photon resonance conditions,” Phys. Rev. A 15, 300 (1977). [CrossRef]
  26. P. W. Milonni, J. H. Eberly, “Temporal coherence in multi-photon absorption. Far off-resonance intermediate states,” J. Chem. Phys. 68, 1602 (1978). [CrossRef]
  27. Actually, this procedure is repeated twice: once for a positive value of κ and once for a negative value of κ. These two ac Stark shifts are then averaged in order to account for the stochastic realization shift, as discussed in Ref. 28.
  28. J. C. Camparo, P. Lambropoulos, “The stochastic realization shift,” Opt. Commun. 85, 213 (1991). [CrossRef]
  29. In the Monte Carlo simulations of the present study a random change in the field’s amplitude and frequency was made every 0.01 time units, and in the time between random changes the field characteristics were stable. If the time scale for some process was shorter than 0.01 time units, then for that process the field would have had monochromatic character. It might therefore be argued that with ω1= 56 and ω1= 100 and with random changes occurring every 0.01 time units, we were not simulating the stochastic field accurately enough for our simulation to be sensitive to the field’s degree of photon bunching. However, if this systematic effect were the explanation for the Stark shift enhancement’s ciritical |g2(0)| value, then there should have also been a critical |g2(0)| value for amplitude enhancement. Because this was not the case, it seems unlikely that a systematic effect of our Monte Carlo simulation can be the cause of the Stark shift enhancement’s critical |g2(0)| value.
  30. S. Jacobs, “How monochromatic is laser light?” Am. J. Phys. 47, 597 (1979). [CrossRef]
  31. J. G. Powles, “The adiabatic fast passage experiment in magnetic resonance,” Proc. Phys. Soc. London 71, 497 (1958). [CrossRef]
  32. J. C. Camparo, R. P. Frueholz, “Parameters of adiabatic rapid passage in the 0–0 hyperfine transition of 87Rb,” Phys. Rev. A 30, 803 (1984). [CrossRef]
  33. See, for example, A. Messiah, Quantum Mechanics (Wiley, New York, 1961), Vol. II;B. Holstein, “The adiabatic propagator,” Am. J. Phys. 57, 714 (1989). [CrossRef]
  34. A. T. Georges, P. Lambropoulos, “Saturation and stark splitting of an atomic transition in a stochastic field,” Phys. Rev. A 20, 991 (1979). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited