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

Abstract

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}\Sigma $ to $^{2}{{\Pi }_{1/2}}$ transition of a molecule. For some molecules, mixing of the excited $^{2}{{\Pi }_{1/2}}$ state with a nearby $^{2}\Sigma $ 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.

Keywords

• laser cooling
• magneto-optical trap
• cold molecules