Features of molecular structure beneficial for optical pumping

Abstract

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 (FCFs)] and without any intervening electronic states. Here, we propose important adjustments to those criteria, based on our experience optically pumping ${\mathrm{SiO}}^{+}$. 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 ${\mathrm{SiO}}^{+}$ 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 nondiagonal or polyatomic molecules. We also expand upon the definition of favorable branching. In ${\mathrm{SiO}}^{+}$, 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 ($d\ensuremath{\mu}/dx$) and offset in equilibrium bond lengths ($\mathrm{\ensuremath{\Delta}}x={r}_{e}^{g}\ensuremath{-}{r}_{e}^{e}$), can add (subtract) to increase (decrease) the magnitude of a given TDM. Applying the model to ${\mathrm{SiO}}^{+}$, we find there is a fortuitous cancellation, where decay leading to vibrational excitation is reduced, causing optical cycling to lead naturally to vibrational cooling.