Model-independent measurements of the excited state fraction in a sodium magneto-optical trap*

We perform a model-independent measurement of the excited-state population of a sodium (Na) magneto-optical trap (MOT) in a hybrid ion-neutral trap. By photoionizing the the excited Na atoms within our MOT, we separately measure the photoionization rate using MOT-fluorescence detection and by directly detecting the photoionized ions trapped in the LPT. A comparison of these two measurements yields a model-independent measurement of the excited state fraction. We found that below a critical trapping-laser intensity the excited-state fraction is accurately predicted by a two-level model with an experimentally determined effective saturation intensity. Under a wide range of trapping conditions, we measured the effective saturation intensity to be $I_{\mathrm{se}} = 22.9(3)\;\textrm{mW}/\textrm{cm}^2$ for the type-I MOT and $I_{\mathrm{se}} = 48.9\;\textrm{mW}/\mathrm{cm}^2$ for the type-II MOT. These effective saturation intensities are both larger than the theoretically predicted value of $I_{\mathrm{sat}} = 13.4144(45)\;\textrm{mW}/\textrm{cm}^2$ for isotropically-polarized light. Beyond the critical trapping-laser intensity, we find that the excited state fraction deviates from the two-level model as a function of repump-laser power and magnetic field gradient.