When exposed to intense light of approximately 580 nm, the ground stat
e of K shifts up in energy, passing through two photon resonances with
Rydberg states, and finally crossing the two-photon ionization limit.
We have used laser pulses of varying duration to study the nature of
the population transfer from the ground state to the excited state due
to the intensity-tuned resonances encountered during the rising edge
of the pulse. A dynamic Floquet approach in which the resonances are t
reated as avoided crossings of the Floquet energy levels is used to mo
del the population transfer and gives excellent agreement with the dat
a. The model is extended into the strong-coupling regime where the gro
und state interacts with many excited states simultaneously, and we sh
ow that this model can be used to describe multiphoton ionization as a
series of avoided crossings with the continuum.