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.