Magnetic trapping and coherent control of laser-cooled molecules

We demonstrate coherent microwave control of the rotational, hyperfine and Zeeman states of ultracold CaF molecules, and the magnetic trapping of these molecules in a single, selectable quantum state. We trap about $5\times 10^{3}$ molecules for 2 s at a temperature of 65(11) $\mu$K and a density of $1.2 \times 10^{5}$ cm$^{-3}$. We measure the state-specific loss rate due to collisions with background helium.