Dipole-Mode Spectrum and Hydrodynamic Crossover in a Resonantly Interacting Two-Species Fermion Mixture

Ultracold quantum-gas mixtures of fermionic atoms with resonant control of interactions offer a unique test-bed to explore few- and many-body quantum states with unconventional properties. The emergence of such strongly correlated systems, as for instance symmetry-broken superfluids, is usually accompanied by hydrodynamic collective behavior. Thus, experimental progress in this field naturally requires a deep understanding of hydrodynamic regimes. Here, we report on experiments employing a tunable Fermi-Fermi mixture of $^{161}$Dy and $^{40}$K near quantum degeneracy. We investigate the full spectrum of dipole modes across a Feshbach resonance and characterize the crossover from collisionless to deep hydrodynamic behavior in measurements of frequencies and damping rates. We compare our results with a theoretical model that considers the motion of the mass centers of the two species and we identify the contributions of friction and mean-field interaction. We show that one oscillating mode exists over the whole range of interactions, exhibiting striking changes of frequency and damping in the deep hydrodynamic regime. We observe the second oscillating mode to split into two purely exponential damping modes. One of these exponential modes shows very fast damping, faster than any other relevant timescale, and is largely insensitive against experimental imperfections. It provides an accurate measure for the interspecies drag effect, which generalizes the concept of spin drag explored in other experiments. We characterize the interspecies drag locally in terms of a microscopic friction coefficient and we discuss its unitarity-limited universal behavior on top of the resonance.