  We show that a composite spin-1/2 Kondo system can be formed by coupling a
superconducting quantum interference device (SQUID) to the internal hyperfine
states of a trapped ultracold atomic Fermi gas. Here, the SQUID, or flux qubit,
acts as an effective magnetic impurity that induces spin-flip scattering near
the Fermi energies of the trapped gas. Although the ultracold gas and SQUID are
at vastly different temperatures, the formation of a strongly correlated Kondo
state between the two systems is found when the gas is cooled below the Kondo
temperature; this temperature regime is within current experimental limits.
Furthermore, the momentum distribution of the trapped fermions is calculated.
We find that it clearly contains an experimental signature of this correlated
state and the associated Kondo screening length. In addition to probing Kondo
physics, the controllability of this system can be used to systematically
explore the relaxation and equilibration of a strongly correlated system that
has been initially prepared in a selected nonequilibrium state.
