  We investigate dynamics of atomic and molecular systems exposed to intense,
shaped chaotic fields and a weak femtosecond laser pulse theoretically. As a
prototype example, the photoionization of a hydrogen atom is considered in
detail. The net photoionization undergoes an optimal enhancement when a
broadband chaotic field is added to the weak laser pulse. The enhanced
ionization is analyzed using time-resolved wavepacket evolution and the
population dynamics of the atomic levels. We elucidate the enhancement produced
by spectrally-shaped chaotic fields of two different classes, one with a
tunable bandwidth and another with a narrow bandwidth centered at the first
atomic transition. Motivated by the large bandwidth provided in the high
harmonic generation, we also demonstrate the enhancement effect exploiting
chaotic fields synthesized from discrete, phase randomized, odd-order and
all-order high harmonics of the driving pulse. These findings are generic and
can have applications to other atomic and simple molecular systems.
