Determination of CaOH and CaOCH$_3$ vibrational branching ratios for direct laser cooling and trapping

Alkaline earth monoalkoxide free radicals (MORs) have molecular properties conducive to direct laser cooling to sub-millikelvin temperatures. Using dispersed laser induced fluorescence (DLIF) measurements from a pulsed supersonic molecular beam source we determine vibrational branching ratios and Franck-Condon factors for the MORs CaOH and CaOCH$_{3}$. With narrow linewidth continuous-wave dye laser excitation, we precisely measure fluorescence branching for both $\tilde{X}-\tilde{A}$ and $\tilde{X}-\tilde{B}$ electronic systems in each molecule. Weak symmetry-forbidden decays to excited bending states with non-zero vibrational angular momentum are observed. Normal mode theoretical analysis combined with ab initio structural calculations are performed and compared to experimental results. Our measurements and analysis pave the way for direct laser cooling of these (and other) complex nonlinear polyatomic molecules. We also describe a possible approach to laser cooling and trapping of molecules with fewer symmetries like chiral species.