Limitation of single-repumping schemes for laser cooling of Sr atoms

We explore the efficacy of two single-repumping schemes, 5s5p \,³P₂ - 5p² \,³P₂ (481\,nm) and 5s5p \,³P₂ - 5s5d \,³D₂ (497\,nm), for a magneto-optical trap (MOT) of Sr atoms. We reveal that the enhancement in the MOT lifetime is limited to $26.9(2)$ for any single-repumping scheme. Our investigation indicates that the primary decay path from the 5s5p \,¹P₁ state to the 5s5p \,³P₀ state proceeds via the 5s4d \,³D₁ state, rather than through the upper states accessed by the single-repumping lasers. We estimate that the branching ratio for the 5s5p \,¹P₁ → 5s4d \,³D₁ → 5s5p \,³P₀ decay path is 1:3.9 × 10⁶ and the decay rate for the transition from the 5s5p \,¹P₁ state to the 5s4d \,³D₁ state is 83(32)\,s⁻¹. This outcome underscores the limitation on atom number in the MOT for long loading times (1 \,s) when employing a single-repumping scheme. These findings will contribute to the construction of field-deployable optical lattice clocks.