Features of Molecular Structure Beneficial for Optical Pumping

Fast and efficient state preparation of molecules can be accomplished by optical pumping. Molecular structure that most obviously facilitates cycling involves a strong electronic transition, with favorable vibrational branching (diagonal Franck-Condon factors, aka FCFs) and without any intervening electronic states. Here, we propose important adjustments to those criteria, based on our experience optically pumping SiO$^+$. Specifically, the preference for no intervening electronic states should be revised, and over-reliance on FCFs can miss important features. The intervening electronic state in SiO$^+$is actually found to be beneficial in ground rotational state preparation, by providing a pathway for population to undergo a parity flip. This contribution demonstrates the possibility that decay through intervening states may help state preparation of non-diagonal or polyatomic molecules. We also expand upon the definition of favorable branching. In SiO$^+$, we find that the off-diagonal FCFs fail to reflect the vibrational heating versus cooling rates. Since the branching rates are determined by transition dipole moments (TDMs) we introduce a simple model to approximate the TDMs for off-diagonal decays. We find that two terms, set primarily by the slope of the dipole moment function ($d\mu/dx$) and offset in equilibrium bond lengths ($\Delta x = r_e^g-r_e^e$), can add (subtract) to increase (decrease) the magnitude of a given TDM. Applying the model to SiO$^+$, we find there is a fortuitous cancellation, where decay leading to vibrational excitation is reduced, causing optical cycling to lead naturally to vibrational cooling.