  Synthetic quantum systems with interacting constituents play an important
role in quantum information processing and in elucidating fundamental phenomena
in many-body physics. Following impressive advances in cooling and trapping
techniques, ensembles of ultracold polar molecules have emerged as a promising
synthetic system that combines several advantageous properties. These include a
large set of internal states for encoding quantum information, long nuclear and
rotational coherence times and long-range, anisotropic interactions. The latter
are expected to allow the exploration of intriguing phases of correlated
quantum matter, such as topological superfluids, quantum spin liquids,
fractional Chern insulators and quantum magnets. Probing correlations in these
phases is crucial to understand their microscopic properties, necessitating the
development of new experimental techniques. Here we use quantum gas microscopy
to measure the site-resolved dynamics of quantum correlations in a gas of polar
molecules in a two-dimensional optical lattice. Using two rotational states of
the molecules, we realize a spin-1/2 system where the particles are coupled via
dipolar interactions, producing a quantum spin-exchange model. Starting with
the synthetic spin system prepared far from equilibrium, we study the evolution
of correlations during the thermalization process for both spatially isotropic
and anisotropic interactions. Furthermore, we study the correlation dynamics in
a spin-anisotropic Heisenberg model engineered from the native spin-exchange
model using Floquet techniques. These experiments push the frontier of probing
and controlling interacting systems of ultracold molecules, with prospects for
exploring new regimes of quantum matter and characterizing entangled states
useful for quantum computation and metrology.
