  Near-resonant periodic driving of quantum systems promises the implementation
of a large variety of novel effective Hamiltonians. The challenge of Floquet
engineering lies in the preparation and measurement of the desired quantum
state. We address these aspects in a model system consisting of interacting
fermions in a periodically driven array of double wells created by an optical
lattice. The singlet and triplet fractions and the double occupancy of the
Floquet states are measured, and their behavior as a function of the
interaction strength is analyzed in the high- and low-frequency regimes. We
demonstrate full control of the Floquet state population and find suitable
ramping protocols and time-scales which adiabatically connect the initial
ground state to different targeted Floquet states. The micromotion which
exactly describes the time evolution of the system within one driving cycle is
observed. Additionally, we provide an analytic description of the model and
compare it to numerical simulations.
