Competition of fermion pairing, magnetism, and charge order in the spin-doped attractive Hubbard gas

Abstract

The tension between fermion pairing and magnetism affects numerous strongly correlated electron systems, from high-temperature cuprates to twisted bilayer graphene. Exotic forms of fermion pairing and superfluidity are predicted when attraction between fermions competes with spin doping. Here, we follow the evolution of fermion pairing and charge and spin order in a spin-imbalanced attractive Hubbard gas of fermionic $^{40}$K atoms, covering a wide range of densities, magnetizations, and interactions with single-atom resolution. At low spin imbalance and weak interactions, we find a mixture of nonlocal fermion pairs coexisting with itinerant excess fermions. For stronger interactions an effective hard-core Bose-Fermi mixture emerges. Spin doping drives a crossover from charge-density wave correlations to a Fermi liquid of polarons. Beyond a certain spin imbalance and interaction strength, we find evidence for the onset of combined spin- and pair-density wave order, a possible precursor for the existence of magnetized superfluidity in the attractive Hubbard system.