Modeling magneto-optical trapping of CaF molecules

Magneto-optical trapping forces for molecules are far weaker than for alkali atoms because the photon scattering rate is reduced when there are multiple ground states, and because of optical pumping into dark states. The force is further reduced when the upper state has a much smaller Zeeman splitting than the lower state. We use a rate model to estimate the strength of the trapping and damping forces in a magneto-optical trap (MOT) of CaF molecules, using either the A$^{2}\Pi_{1/2}$ - X$^{2}\Sigma^{+}$ transition or the B$^{2}\Sigma^{+}$ - X$^{2}\Sigma^{+}$ transition. We identify a new mechanism of magneto-optical trapping that arises when, in each beam of the MOT, two laser components with opposite polarizations and different detunings address the same transition. This mechanism produces a strong trapping force even when the upper state has little or no Zeeman splitting. It is the main mechanism responsible for the trapping force when the A$^{2}\Pi_{1/2}$ - X$^{2}\Sigma^{+}$ transition is used.