  Polar molecules confined in an optical lattice are a versatile platform to
explore spin-motion dynamics based on strong, long-range dipolar interactions.
The precise tunability of Ising and spin-exchange interactions with both
microwave and dc electric fields makes the molecular system particularly
suitable for engineering complex many-body dynamics. Here, we used Floquet
engineering to realize interesting quantum many-body systems of polar
molecules. Using a spin encoded in the two lowest rotational states of
ultracold KRb molecules, we mutually validated XXZ spin models tuned by a
Floquet microwave pulse sequence against those tuned by a dc electric field
through observations of Ramsey contrast dynamics, setting the stage for the
realization of Hamiltonians inaccessible with static fields. In particular, we
observed two-axis twisting mean-field dynamics, generated by a
Floquet-engineered XYZ model using itinerant molecules in 2D layers. In the
future, Floquet-engineered Hamiltonians could generate entangled states for
molecule-based precision measurement or could take advantage of the rich
molecular structure for quantum simulation of multi-level systems.
