Metallic and Insulating Phases of Repulsively Interacting Fermions in a 3D Optical Lattice

TLDR

The fermionic Hubbard model is central to describing strongly correlated materials. The study realizes this Hamiltonian with a repulsively interacting spin mixture of ultracold $^{40}$K atoms in a three‑dimensional optical lattice. Compressibility is measured via in‑situ imaging with independently tunable confinement and lattice depth, and the results are compared to dynamical mean‑field theory to follow the system’s evolution from a compressible metal through a Fermi liquid to a band insulator. The measurements show a compressibility transition from a dilute metal to a Fermi liquid and then to a band insulator, and at strong interactions evidence an emergent incompressible Mott insulating phase.

Abstract

The fermionic Hubbard model plays a fundamental role in the description of strongly correlated materials. Here we report on the realization of this Hamiltonian using a repulsively interacting spin mixture of ultracold $^{40}$K atoms in a 3D optical lattice. We have implemented a new method to directly measure the compressibility of the quantum gas in the trap using in-situ imaging and independent control of external confinement and lattice depth. Together with a comparison to ab-initio Dynamical Mean Field Theory calculations, we show how the system evolves for increasing confinement from a compressible dilute metal over a strongly-interacting Fermi liquid into a band insulating state. For strong interactions, we find evidence for an emergent incompressible Mott insulating phase.