  The problem analysis results made the author to draw a conclusion that the
nature of the resonance frequency long-term instability and drift at harmonic
excitation is related to the phase dynamics of the "atom + field" system in the
small vicinity of the resonance. The investigation is based on the strictly
substantiated asymptotic Krylov-Bogolyubov perturbation theory. A
time-dependent (drift) first-order correction of the perturbing field amplitude
to the resonance frequency was disclosed. It was found that this correction is
always present and is responsible for the frequency drift and long-term
instability. The necessary and sufficient conditions of accurate resonance, as
well as the conditions of realization of a stable (stationary, steady-state)
drift-free oscillation regime in a quantum system, are obtained.
