Bounded Collisional Resistivity and Lattice Unitarity

Optical lattices enable the simulation of condensed matter systems free from phonons and impurities, presenting an opportunity to study the high-temperature regime of the Fermi-Hubbard Model. Studies of transport are critical for understanding the microscopic mechanisms behind the current dissipation in strongly interacting systems. We report on direct measurements of the resistivity of a strongly interacting, yet weakly correlated, dilute gas of fermionic potassium-40 in a 3D optical lattice. We extract the complex resistivity via in-situ measurements of the center-of-mass response to an applied oscillatory force. The dominant source of dissipation in this defect-free system is two-body s-wave collisions, which we tune via a magnetic Feshbach resonance. In the strongly-interacting regime, we observe a saturation of current dissipation to a value independent of the scattering length, which qualitatively resembles the saturation of the collision rate in free space. According to the optical theorem, “lattice unitarity” is achieved when the scattering amplitude becomes purely imaginary. Contrary to free space, the unitary condition in the lattice depends on the center-of-mass momentum of colliding pairs. The bound cannot be saturated in a finite-temperature ensemble, however, it ensures a finite dissipation rate even in the limit of infinite scattering length. We also measure the temperature dependence of resistivity in the strongly-interacting regime. We compare our observations to a Boltzmann transport calculation and find good agreement, even in the strongly-interacting regime, by using a renormalized two-body scattering matrix. This work develops a microscopic understanding of resistivity in low-density Hubbard metals, and provides a foundation for extensions into higher density systems, lower dimensions, and the low-temperature Fermi liquid regime.