Towards Doppler cooling of SiO$^{+}$

Extending the techniques of Doppler cooling from atoms to molecules is challenging due to the complex nature of molecular structure. ~Rotation and vibration of the molecule result in additional dark states which may require repumping, and higher order processes such as photodissociation and predissociation may terminate the cycling transition. ~We identify SiO$^{+}$ as a promising candidate for laser cooling, which differs from previous candidates in that the cycling scheme involves three electronic states. ~ Using a rate-equation approach, we model the cooling process and find that the intervening electronic state does not require additional repumping, since decay out of it is sufficiently fast. ~ We also present our current efforts towards Doppler cooling of SiO$^{+}$.