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The theoretical description of the external degrees of freedom of atomstrapped inside a magneto-optical trap (MOT) often relies on the decoupling ofthe evolution of the internal and external degrees of freedom. That is possiblethanks to much shorter timescales typically associated with the first ones. Theelectronic structure of alkaline-earth atoms, on the other hand, presentsultra-narrow transitions and metastable states that makes such an approximationinvalid in the general case. In this article, we report on a model based onopen Bloch equations for the evolution of the number of atoms in amagneto-optical trap. With this model we investigate the loading of thestrontium blue magneto-optical trap under different repumping schemes, eitherdirectly from a Zeeman slower, or from an atomic reservoir made of atoms in ametastable state trapped in the magnetic quadrupolar field. The fluorescenceobserved on the strong 461~nm transition is recorded and quantitativelycompared with the results from our simulations. The comparison betweenexperimental results and calculations within our model allowed to identify theexistence of the decay paths between the upper level of the repumpingtransition and the dark strontium metastable states, which could not beexplained by electric dipole transition rates calculated in the literature.Moreover, our analysis pinpoints the role of the atomic movement in limitingthe efficiency of the atomic repumping of the Sr metastable states.

Comparison between 403 nm and 497 nm repumping schemes for strontium magneto-optical traps