Ultracold molecules promise a revolutionary test bed for quantum science with applications ranging from experiments that probe the nature of our universe, to hosting new platforms for quantum computing. Cooling and trapping molecules in the ultracold regime is the first step to unlocking the wide array of proposed applications, and developing these techniques to control molecules is a key but challenging research field. In this thesis, we describe progress towards a new apparatus designed to cool and trap barium monohydride (BaH), a molecule that is amenable to laser cooling and has prospects as a precursor for ultracold atomic hydrogen. The same complexity that makes molecules interesting objects of study creates challenges for optical control. To mitigate some of these challenges, we first cool the molecules using cryogenic techniques and technologies. Our apparatus uses a cryogenic buffer gas to thermalize BaH within a contained cell. The molecules are extracted into a beam with millikelvin transverse temperature, and forward velocities <100 m/s. The BaH beam in this work is the brightest hydride beam to date, with molecule density and kinetic characteristics well suited for laser cooling and trapping.
A counterintuitive scheme to produce ultracold hydrogen via fragmentation of laser cooled diatomic hydrides is presented where the final atomic H temperature is inversely proportional to the mass of the molecular parent. In addition, the critical density for formation of a Bose-Einstein condensate (BEC) at a fixed temperature is reduced by a factor (mH/mMH)3/2 over directly cooled hydrogen atoms. The narrow Feshbach resonances between a 1S0 atom and hydrogen are well suited to a tiny center of mass energy release necessary during fragmentation. With the support of ab initio quantum chemistry, it is demonstrated that BaH is an ideal diatomic precursor that can be laser cooled to a Doppler temperature of $\ensuremath{\sim}26\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{K}$ with just two rovibronic transitions, the simplest molecular cooling scheme identified to date. Preparation of a hydrogen atom gas below the critical BEC temperature Tc is feasible with present cooling technology, with optical pulse control of the condensation process.