Grating magneto-optical traps with complicated level structures

We study the forces and optical pumping within grating magneto-optical traps (MOTs) operating on transitions with non-trivial level structure. In contrast to the standard six-beam MOT configuration, rate equation modelling predicts that the asymmetric laser geometry of a grating MOT will produce spin-polarized atomic samples. Furthermore, the Land\'e $g$-factors and total angular momenta of the trapping transition strongly influence both the confinement and equilibrium position of the trap. Using the intuition gained from the rate equation model, we realize a grating MOT of fermionic $^{87}$Sr and observe that it forms closer to the center of the trap's quadrupole magnetic field than its bosonic counterpart. We also explore the application of grating MOTs to molecule laser cooling, where the rate equations suggest that dual-frequency operation is necessary, but not sufficient, for stable confinement for type-II level structures. To test our molecule laser cooling models, we create grating MOTs using the $D_1$ line of $^7$Li and see that only two of the four possible six-beam polarization configurations operate in the grating geometry. Our results will aid the development of portable atom and molecule traps for time keeping, inertial navigation, and precision measurement.