Engineering the sub-Doppler force in molecular magneto-optical traps

Current dual-frequency magneto-optical traps for ultracold molecules are plagued by sub-Doppler heating effects, making them vastly inferior to standard atomic MOTs. Here we demonstrate theoretically that the sub-Doppler effects in such a MOT can be engineered to provide cooling instead of heating. We give an intuitive picture how to achieve such cooling and show the cooling and trapping force results of the 16 level optical Bloch equations for the case of CaF molecules. From three-dimensional Monte Carlo simulations we estimate the temperature and density of our MOT to be $40 \mu K$ and $4 \times 10^8 cm^{-3}$ respectively for a molecule number of $10^5$.