  Superconductivity and superfluidity of fermionic and bosonic systems are
remarkable many-body quantum phenomena. In liquid helium and dilute gases, Bose
and Fermi superfluidity has been observed separately, but producing a mixture
in which both the fermionic and the bosonic components are superfluid is
challenging. Here we report on the observation of such a mixture with dilute
gases of two Lithium isotopes, 6Li and 7Li. We probe the collective dynamics of
this system by exciting center-of-mass oscillations that exhibit extremely low
damping below a certain critical velocity. Using high precision spectroscopy of
these modes we observe coherent energy exchange and measure the coupling
between the two superfluids. Our observations can be captured theoretically
using a sum-rule approach that we interpret in terms of two coupled
oscillators.
