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Mixing of Bose and Fermi Superfluids

Trapped ultra-cold atom experiments provide a unique opportunity to understand Bose-Fermi superfluid mixtures occurring in contrasting areas of physics. At present there are several atom-trap experiments that could potentially explore this superfluid-mixture regime, thus warranting a detailed understanding of the occurrence and stability of various possible thermodynamic phases in the mixture. In the present work, we therefore construct the finite temperature phase diagram of an interacting atomic mixture of Bose and Fermi superfluids. Our study reveals a unique region of phase space, where the BCS instability of the Fermi surface coincides with dynamical instability of the homogeneous mixture towards phase separation through a first-order transition. We illustrate how this intriguing interplay manifests in a trapped configuration, thereby providing important constraints for observing superfluidity in experiments.