The complex network of Floquet states that results from an application
of an external ac electric field to a collection of atoms is investig
ated. It is shown that precision dc Stark spectroscopy can reveal the
details of the quasienergy states, Floquet states, spawned by the appl
ication of a rf field. Transitions to the Floquet sidebands of quadrat
ic (dc) Stark states are found to have absorption intensities in good
agreement with theory. This combination of dc and ac fields applied to
atoms, Floquet spectroscopy, is then used to determine accurately the
scalar and tensor polarizabilities of the 65p 2P state of sodium. Dev
iations from quadratic behavior are investigated as well as the relati
onship of our measured polarizability to previous measurements at lowe
r principal quantum numbers.