Attractively Interacting Fermions in an Optical Lattice

Mixtures of ultracold fermionic species in optical lattices can serve as a tool to test condensed matter physics models, a prominent example being the Fermi-Hubbard-Hamiltonian. We study a balanced spin mixture of $^{40}$K in $|F,m_F \rangle=|\frac{9}{2},-\frac{9}{2} \rangle$ and $|\frac{9}{2},-\frac{7}{2}\rangle$ in a three dimensional blue detuned optical lattice, where the interaction between the spin states can be tuned via a Feshbach resonance. Changing the scattering length allows us to go from non-interacting to attractive states and finally to a strongly paired system. For small attractive interactions, the cloud size shrinks upon increasing the interactions, but surprisingly we find a minimal cloud size for medium attractive interactions. For stronger interactions the cloud size increases again. This anomalous increase can be understood with a straightforward entropy argument. We compare the experimental data with the prediction of an exact calculation in the zero-tunneling limit and with a high temperature expansion theory.