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We analyse a Bose-Einstein condensate (BEC) mixed with a superfluid two-component Fermi gas in the whole BCS-BEC cross-over. Using a quasiparticle random phase approximation combined with Beliaev theory to describe the Fermi superfluid and the BEC respectively, we show that the single particle and collective excitations of the Fermi gas give rise to an induced interaction between the bosons, which varies strongly with momentum and frequency. It diverges at the sound mode of the Fermi superfluid, resulting in a sharp avoided crossing feature and a corresponding sign change of the interaction energy shift in the excitation spectrum of the BEC. In addition, the excitation of quasiparticles in the Fermi superfluid leads to damping of the excitations in the BEC. Besides studying induced interactions themselves, these prominent effects can be used to systematically probe the strongly interacting Fermi gas.
In this letter we show that the vortex lattice structure in the Bose-Fermi superfluid mixture can undergo a sequence of structure transitions when the Fermi superfluid is tuned from the BCS regime to the BEC regime. This is due to different vortex co
Cooper pairing caused by an induced interaction represents a paradigm in our description of fermionic superfluidity. Here, we present a strong coupling theory for the critical temperature of $p$-wave pairing between spin polarised fermions immersed i
The recent experimental realization of Bose-Fermi superfluid mixtures of dilute ultracold atomic gases has opened new perspectives in the study of quantum many-body systems. Depending on the values of the scattering lengths and the amount of bosons a
We investigate magnetoassociation of ultracold fermionic Feshbach molecules in a mixture of $^{40}$K and $^{87}$Rb atoms, where we can create as many as $7times 10^4$ $^{40}$K$^{87}$Rb molecules with a conversion efficiency as high as 45%. In the per
We report on the realization of a Fermi-Fermi mixture of ultracold atoms that combines mass imbalance, tunability, and collisional stability. In an optically trapped sample of $^{161}$Dy and $^{40}$K, we identify a broad Feshbach resonance centered a