Optically trapped ultracold polar molecules offer a rapidly maturing platform for quantum
science. Due to their strong, long-range, and tunable dipolar interactions, these systems are particularly
suitable for realizing spin-motion models with rich many-body physics. However, the additional
complexity of molecules compared with single atoms makes production of ultracold gases
and control of interactions challenging.
In this thesis, I discuss our efforts to improve production and control of ultracold molecules
and to explore the many-body physics arising from their interactions. Using a spin encoded in
rotational states of fermionic 40K87Rb molecules, we demonstrated tuning of Heisenberg XXZ
models with electric fields and Floquet engineering of XYZ models with microwave pulse sequences.
By additionally regulating motion with optical lattices, we realized highly tunable generalized
t-J models, relevant to quantum simulation of strongly correlated materials. We used Ramsey
spectroscopy to explore the out-of-equilibrium dynamics of these systems, observing one- and twoaxis
twisting at short times, and dephasing due to dipolar interactions and their coupling to motion
at longer times. These methods could be used to generate spin-squeezed states relevant to precision
metrology.
In addition to controlling interactions, observing new dynamics and phases predicted for these
models requires preparing low-entropy initial states in bulk or lattice systems. I present progress
towards producing a deeply degenerate Fermi gas in an isolated 2D layer, enabling control of the
anisotropy of the dipolar interactions. Using a tunable-spacing optical lattice, we compressed a
K-Rb mixture into a quasi-2D geometry, producing 2D molecular gases below the Fermi temperature.
I discuss prospects for improving molecule production and evaporative cooling into deep
degeneracy.
