Physicists Build First Tunable Three-Flavor Hubbard System and Image Every Atom

For the first time, an international team of researchers from Germany, Thailand, India, China and the United States has created a three-component Hubbard system with tunable interactions in the laboratory and watched it atom by atom. The study, published in Science (DOI: 10.1126/science.adv1247), provides a foundation for future quantum simulations in nuclear physics and materials science. The team is led by Peter Schauss, who works at the University of Hamburg and the Cluster of Excellence "CUI: Advanced Imaging of Matter."

The Hubbard model is one of the most important tools for describing how fermions interact on a lattice, and it is considered especially promising for understanding high-temperature superconductivity. Physicists often study it with ultracold atoms held in an optical lattice, where fermionic atoms play the role of electrons in a solid. They tunnel from one lattice site to the next, effectively swapping places. Identical fermions cannot occupy the same site, but when distinguishable fermions meet, a magnetic-field-dependent interaction energy appears.

The standard model usually considers just two spin states, up and down. Adding a third makes the system far more versatile and allows richer quantum phases. "Although the Hubbard model is important and simple to write down, it isn't easy to solve," said Kaden Hazzard, an associate professor of physics and astronomy at Rice University and a co-author. "Theorists have been banging our heads on the two-component Hubbard model for decades, yet there are still major open questions. Adding a third tunable component lets us see how the two-component model reacts to it, potentially helping us answer these major questions."

The team used a quantum gas microscope, which detects each individual atom with spatial resolution. By preparing atoms in different internal states, the experiment realized different types of fermions, allowing three distinct states in one lattice. The result is very different from electrons in a crystal, but it resembles nuclear physics, where quarks come in three different colors.

A key goal was to see a Mott state, in which strong interactions suppress double occupation of lattice sites and particles can no longer flow freely, producing insulating behavior. Schauss noted that, paradoxically, high-temperature superconductivity emerges near Mott states. Schauss said the setup proved more stable than feared. "Usually, one fears that three-body collisions could quickly destroy the system," he said. "Despite this potential danger, we were able to successfully carry out the measurements and observe a Mott insulator."

The researchers identified several other phases that depend on the strength of the interactions between each pair of states. In the same system, they found ferromagnetic correlations between two of the states and antiferromagnetic correlations between two others. They also developed a method for counting the number of triply occupied lattice sites, and their measured values agreed with numerical calculations performed by collaborators at Rice.

Hazzard said the comparison runs both ways. "The experiments are a wonderful testing ground for the theoretical ideas," he said. He and co-author Sohail were able to compare sophisticated numerical calculations with experiments that are already at the edge of what is possible, and those comparisons will help refine theoretical tools. The team now plans to fine-tune the interactions further so it can study lattice models of quantum chromodynamics, the theory of the strong force, directly in the laboratory. The work, first posted to arXiv in 2025, shows that ultracold-atom simulators can reach beyond condensed matter toward the physics that binds atomic nuclei.