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

TL;DR

This paper demonstrates the realization of the fermionic Hubbard model with ultracold atoms in a 3D optical lattice, measuring compressibility and observing phase transitions from metal to Mott insulator.

Contribution

It introduces a new in-situ imaging method for measuring compressibility and compares experimental results with theoretical calculations to map phase evolution.

Findings

Observation of metal to insulator transition with increasing confinement.

Evidence for emergent Mott insulating phase at strong interactions.

Quantitative agreement with dynamical mean field theory calculations.

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.