  Recent experiments have revitalized the interest in a Fermi gas of ultracold
atoms with strong repulsive interactions. In spite of its seeming simplicity,
this system exhibits a complex behavior, resulting from the competing action of
two distinct instabilities: ferromagnetism, which promotes spin
anticorrelations and domain formation; and pairing, that renders the repulsive
fermionic atoms unstable towards forming weakly bound bosonic molecules. The
breakdown of the homogeneous repulsive Fermi liquid arising from such
concurrent mechanisms has been recently observed in real time through
pump-probe spectroscopic techniques [A. Amico et al., Phys. Rev. Lett. 121,
253602 (2018)]. These studies also lead to the discovery of an emergent
metastable many-body state, an unpredicted quantum emulsion of anticorrelated
fermions and pairs. Here, we investigate in detail the properties of such an
exotic regime by studying the evolution of kinetic and release energies, the
spectral response and coherence of the unpaired fermionic population, and its
spin-density noise correlations. All our observations consistently point to a
low-temperature heterogeneous phase, where paired and unpaired fermions
macroscopically coexist while featuring micro-scale phase separation. Our
findings open new appealing avenues for the exploration of quantum emulsions
and also possibly of inhomogeneous superfluid regimes, where pair condensation
may coexist with magnetic order.
