Atoms and molecules in the ultracold regime have emerged as promising platforms for quantum simulation of strongly-correlated matter.  In this talk, I will describe recent progress on two fronts to study quantum many-body physics with ultracold gases.  First, using ultracold fermionic atoms immersed in a Bose-Einstein condensate (BEC), we realized a paradigmatic quasiparticle in condensed matter physics, the Bose polaron.  Using radiofrequency spectroscopy, we probed the strong-coupling polaron in its quantum critical regime. Its inverse lifetime, given by the spectral width, was observed to increase linearly with temperature at the Planckian scale k_BT/ħ , a hallmark of quantum critical behavior. Close to the BEC critical temperature, the spectral width exceeds the binding energy of the impurities, signaling a breakdown of the quasiparticle picture.

Next, I will describe progress in creating and controlling an ultracold dipolar gas of ²³Na⁴⁰K, toward the goal of molecule-based quantum simulation.  Molecules have richer internal structures and more tunable interactions compared to atoms, yet coherent control over their degrees of freedom presents a far greater challenge.  At the single-molecule level, we have demonstrated a second-scale spin coherence time between two nuclear spin states of NaK.  Controlling NaK-NaK interactions was the natural further step; recent work on inducing resonant dipolar collisions by microwave dressing will be discussed.  This technique has led to the strongest collision rates observed to date in an ultracold molecular gas, and is general to all dipolar molecules, providing an ideal way to tune interactions in tailored quantum many-body systems.