Physicists realize three-flavor Hubbard model with ultracold lithium-6 and image each flavor in a lattice

An international team of physicists has extended quantum gas microscopy to lithium-6 Fermi gases with three internal states in an optical lattice, according to a study in Science. The group studied the phase diagram of the three-flavor Hubbard model. They report signatures of flavor-selective localization and selective pairing at temperatures down to the tunneling energy scale science.orgSciencescience.orgOpen source ↗. The measurements were compared with numerical linked-cluster expansion calculations.

The standard Hubbard model describes interacting electrons with two spin states, up and down. Despite its simple form, it remains very hard to solve. A third component could reveal new quantum behavior, but three-body collisions can remove atoms from the system and make experiments difficult to sustain.

Setup and measurements

The atoms sit in an optical lattice, an artificial crystal made of laser light with regularly spaced sites. They can tunnel between neighboring sites. Three internal quantum states of lithium-6 represent three distinct fermionic components. By adjusting the magnetic field, the researchers tuned the interactions between each pair of components independently, which gave three separate interaction strengths.

A flavor-resolved quantum gas microscope distinguished the three components and located individual atoms. With it the team examined how particles occupied lattice sites. They identified a Mott insulating state, in which strong interactions suppress multiple occupancy of sites and restrict particle movement. They did so by measuring fluctuations in atomic occupancy and the response of the system to changes in density. Peter Schauss, a physics professor at the University of Virginia and one of the authors, said observing the Mott state was a particular goal of the work.

Results and limits

Depending on the interaction strengths, some pairs of components showed ferromagnetic correlations, while others showed antiferromagnetic ones. The researchers also measured triply occupied sites, where all three components share one location. These data agreed with numerical calculations by collaborators at Rice University.

Three-body collisions still cause atom losses, and heating makes it hard to reach the low temperatures needed for more delicate quantum phases. Even so, Schauss said the realization proved surprisingly stable, and the measurements were carried out successfully.

The authors state that a further increase of phase space density may allow observation of a distinct pair Mott phase at half filling. They also see it as a path toward studying color superfluidity and other aspects of quantum chromodynamics science.orgSciencescience.orgOpen source ↗. The team plans to refine the interactions, look for the paired Mott state and explore triangular and kagome lattices.