Magneto-optical trapping forces for atoms and molecules with complex level structures

Laser cooling and magneto-optical trapping of molecules typically involves multiple transitions driven by several laser frequencies. We analyze how magneto-optical trapping forces depend on the angular momenta, F l and F u , and the g -factors, g l and g u , of the lower and upper states. When the polarizations must be reversed relative to cases where The correct choice of circular polarization depends on the sign of g u but not on the sign of g l . If g u is zero there is no trapping force, and the trapping force is very weak whenever g u is small compared to g l , which it usually is when the cooling transition is the to transition of a molecule. For some molecules, mixing of the excited state with a nearby excited state can greatly increase g u , leading to stronger trapping forces. A strong trapping force can also be produced by rapidly and synchronously reversing both the magnetic field and the laser polarizations. We simulate a recent experiment on magneto-optical trapping of SrF molecules, and suggest that an alternative choice of laser beam polarizations will strengthen the trapping force.