Magnetic trapping of ultracold molecules at high density

Trapping ultracold molecules in conservative traps is essential for applications -- such as quantum state-controlled chemistry, quantum simulations, and quantum information processing. These applications require high densities or phase-space densities. We report magnetic trapping of NaLi molecules in the triplet ground state at high density ($\approx 10^{11} \; \rm{cm}^{-3}$) and ultralow temperature ($\approx 1\;{\rm \mu K}$). Magnetic trapping at these densities allows studies on both atom-molecule and molecule-molecule collisions in the ultracold regime in the absence of trapping light, which has often lead to undesired photo-chemistry. We measure the inelastic loss rates in a single spin sample and spin-mixtures of fermionic NaLi as well as spin-stretched NaLi$+$Na mixtures. We demonstrate sympathetic cooling of NaLi molecules in the magnetic trap by radio frequency evaporation of co-trapped Na atoms and observe an increase in the molecules' phase-space density by a factor of $\approx 16$.