  We present generalized adiabatic theorems for closed and open quantum systems
that can be applied to slow modulations of rapidly varying fields, such as
oscillatory fields that occur in optical experiments and light induced
processes. The generalized adiabatic theorems show that a sufficiently slow
modulation conserves the dynamical modes of time dependent reference
Hamiltonians. In the limiting case of modulations of static fields, the
standard adiabatic theorems are recovered. Applying these results to periodic
fields shows that they remain in Floquet states rather than in energy
eigenstates. More generally, these adiabatic theorems can be applied to
transformations of arbitrary time-dependent fields, by accounting for the
rapidly varying part of the field through the dynamical normal modes, and
treating the slow modulation adiabatically. As examples, we apply the
generalized theorem to (a) predict the dynamics of a two level system driven by
a frequency modulated resonant oscillation, a pathological situation beyond the
applicability of earlier results, and (b) to show that open quantum systems
driven by slowly turned-on incoherent light, such as biomolecules under natural
illumination conditions, can only display coherences that survive in the steady
state.
