Connecting few-body inelastic decay to many-body correlations: a weakly coupled impurity in a resonant Fermi gas

We study three-body recombination in an ultracold Bose-Fermi mixture. We first show theoretically that, for weak inter-species coupling, the loss rate is proportional to Tan's contact. Second, using a 7 Li/ 6 Li mixture we probe the recombination rate in both the thermal and dual superfluid regimes. We find excellent agreement with our model in the BEC-BCS crossover. At unitarity where the fermion-fermion scattering length diverges, we show that the loss rate is proportional the 4/3 power of the fermionic density. Our results demonstrate that impurity-induced losses can be used as a quantitative probe of many-body correlations.