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We describe the effects of disorder on the critical temperature of s-wavesuperfluids from the BCS to the BEC regime, with direct application toultracold Fermi atoms. In the BCS regime the pair breaking and phase coherencetemperature scales are essentially the same allowing strong correlationsbetween the amplitude and phase of the order parameter. As non-pair breakingdisorder is introduced the largely overlapping Cooper pairs conspire tomaintain phase coherence such that the critical temperature remains essentiallyunchanged. However, in the BEC regime the pair breaking and phase coherencetemperature scales are very different such that non-pair breaking disorder canaffect dramatically phase coherence, and thus the critical temperature, withoutthe requirement of breaking tightly-bound fermion pairs simultaneously.Finally, we find that the superfluid is more robust against weak disorder inthe intermediate region between the two regimes.

Disorder effects during the evolution from BCS to BEC superfluidity