We present a detailed experimental study of the frequency-modulated ex
citation of a two-level atom, using a microwave herd to drive transiti
ons between two Rydberg Stark states of potassium. Zn the absence of a
modulation the interaction is the standard model of the Rabi problem,
producing sinusoidal oscillations of the population between the two s
tates. In the presence of a frequency modulation of the interacting fi
eld, however the time evolution of the system is significantly modifie
d, producing square wave oscillations of the population, sinusoidal os
cillations at a different frequency, or even sinusoidal oscillations b
uilt up in a series of stair steps. The three responses described abov
e are each found in a different regime for the frequency of the modula
tion with respect to the unmodulated Rabi frequency: the low-, high-,
and intermediate-frequency regimes, respectively.