Interaction between atom and radiation with sinusoidally shaped amplitude: Applications to frequency standards

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.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