  Periodically driven Floquet quantum systems provide a promising platform to
investigate novel physics out of equilibrium. Unfortunately, the drive
generically heats up the system to a featureless infinite temperature state.
For large driving frequency, the heat absorption rate is predicted to be
exponentially small, giving rise to a long-lived prethermal regime which
exhibits all the intriguing properties of Floquet systems. Here we
experimentally observe Floquet prethermalization using nuclear magnetic
resonance techniques. We first show the relaxation of a far-from-equilibrium
initial state to a long-lived prethermal state, well described by the
time-independent ''prethermal'' Hamiltonian. By measuring the autocorrelation
of this prethermal Hamiltonian we can further experimentally confirm the
predicted exponentially slow heating rate. More strikingly, we find that in the
timescale when the effective Hamiltonian picture breaks down, the Floquet
system still possesses other quasi-conservation laws. Our results demonstrate
that it is possible to realize robust Floquet engineering, thus enabling the
experimental observation of non-trivial Floquet phases of matter.
