Magneto-optical trapping forces for atoms and molecules with complex level structures - M R Tarbutt (New Journal of Physics, 2015)
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 ${F_{{\rm l}}}\gt {F_{{\rm u}}}$ the polarizations must be reversed relative to cases where ${F_{{\rm u}}}\geqslant {F_{{\rm l}}}.$ 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 $^{2}Σ $ to $^{2}{{Π }_{1/2}}$ transition of a molecule. For some molecules, mixing of the excited $^{2}{{Π }_{1/2}}$ state with a nearby $^{2}Σ $ 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.