  The advent of ultrafast laser science offers the unique opportunity to
combine Floquet engineering with extreme time resolution, further pushing the
optical control of matter into the petahertz domain. However, what is the
shortest driving pulse for which Floquet states can be realised remains an
unsolved matter, thus limiting the application of Floquet theory to pulses
composed by many optical cycles. Here we ionized Ne atoms with few-femtosecond
pulses of selected time duration and show that a Floquet state can be
established already within 10 cycles of the driving field. For shorter pulses,
down to 2 cycles, the finite lifetime of the driven state can still be
explained using an analytical model based on Floquet theory. By demonstrating
that the population of the Floquet sidebands can be controlled not only with
the driving laser pulse intensity and frequency, but also by its duration, our
results add a new lever to the toolbox of Floquet engineering.
