The results of simulations of cooling based on Sawtooth-Wave Adiabatic Passage (SWAP) are presented including the possibility of population leaking to states outside of the cycling transition. The amount of population leaking can be substantially suppressed compared to Doppler cooling, which could be useful for systems that are difficult to repump back to the cycling transition. The suppression of the leaked population was more effective when simulating the slowing of a beam than in cooling a thermal distribution. As expected, calculations of the leaked population versus branching ratio of spontaneous emission show that the suppression is more effective for narrow linewidth transitions. In this limit, using SWAP to slow a beam may be worth pursuing even when the branching ratio out of the cycling transition is greater than 10%.
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