Free-induction decay in the framework of sudden-modulation theory

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Abstract
Sudden-modulation theory is used for the calculation of stationary saturation and polarization of two-level systems. The randomly fluctuating frequency of the two-level system is assumed to be a noncorrelated, purely discontinuous Markovian process. The stationary probability of field-induced transitions is calculated exactly. It is shown that if the frequency modulation is fast (or if the field is strong enough) the transition probability coincides with that obtained in the framework of perturbation theory when the latter is developed in its integrodifferential non-Markovian version. This probability differs from the kinetic probability calculated by Markovian perturbation theory (with fluctuating frequency) in its corresponding spectral wing shape and in the field dependence of its corresponding resonance width. This field dependence is smoother than that in Markovian theory and stabilizes when the resonance width is not equal to the natural transition width. Nevertheless, in the Lorentzian approximation the free-induction decay rate in the framework of exact (or non-Markovian) theory increases with the field in nearly the same way as that in Markovian theory. Almost the same is true of the field dependence of the free-induction decay amplitude in either theory, provided that the signal correlation before and after the field is switched off is neglected. The conditions are found under which the Lorentzian approximation of the transition probability is valid. These conditions are shown to break down when the theory (in the fast-frequency-modulation limit) leads to agreement with experiments reported by De Voe and Brewer [ Phys. Rev. Lett. 50, 1269– 1272 ( 1983)].