Abstract
The study of the evolution of a two-level atom crossing an electromagnetic field with a sinusoidally shaped amplitude is of interest in frequency metrology because a few Cs beam standards share this type of realization. The Magnus expansion method helps to find a solution to this problem giving approximate analytical results, which are made easy to handle by a series expansion in the detuning between atom resonance and radiation frequency. Numerical checks show that rather simple expressions provide an accuracy better than 10−3 in the matrix elements of the evolution operator for useful ranges of power levels and frequency differences. Two examples concerned with Cs beam standards are discussed.
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A. Bauch, K. Dorenwendt, T. Heindorff: Metrologia 24, 199 (1987)
A. De Marchi, R.E. Drullinger, J.H. Shirley: 44th Frequency Control Symp., Philadelphia 34 (1990)
W. Magnus: Commun. Pure Appl. Math. 7, 649 (1954)
D.W. Robinson: Helv. Phys. Acta 36, 140 (1963)
D.P. Burum: Phys. Rev. B 24, 3684 (1981)
W.R. Salzman: J. Chem. Phys. 82, 822 (1985)
S. Klarsfeld, J.A. Oteo: Phys. Rev. A 39, 3270 (1989)
W.R. Salzman: J. Chem. Phys. 85, 4605 (1986)
W.R. Salzman: Chem. Phys. Lett. 124, 531 (1986)
W.R. Salzman: Phys. Rev. A 36, 5074 (1987)
M.M. Maricq: J. Chem. Phys. 86, 5647 (1987)
F.M. Fernandez, J. Echave, E.A. Castro: J. Math. Phys. 31, 338 (1990)
R.M. Wilcox: J. Math. Phys. 8, 962 (1967)
N. Rosen, C. Zener: Phys. Rev. 40, 502 (1932)
N.F. Ramsey: Molecular Beams (Clarendon, Oxford 1956) pp. 124–134
J. Vanier, C. Audoin: The Quantum Physics of Atomic Frequency Standards (Adam Hilgher, Bristol, Philadelphia 1989) pp. 636–647
P. Thomann: Proc. 22nd PTTI, NASA Conf. publ. 3116 (Vienna, V 1990) p. 331
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At the time of this work A.G. Shahian was a guest at Politecnico di Milano, with a grant of the Ministry for Foreign Affairs of Italy
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Bava, E., Shahian, A.G. Interaction between atom and radiation with sinusoidally shaped amplitude: Applications to frequency standards. Appl. Phys. B 54, 500–505 (1992). https://doi.org/10.1007/BF00325516
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DOI: https://doi.org/10.1007/BF00325516