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. In doing so, the team used a quantum gas microscope to make the individual atoms visible. The study, which was published in Science , provides an important foundation for future quantum simulations of nuclear physics and materials science.
Ultracold atoms are often employed to construct systems that resemble those found in solid-state physics. In this context, the fermionic atoms play the role of electrons in a solid. This system is unique in that it realizes a Hubbard model, which is one of the most important models for describing the interactions of fermions on a lattice. This approach is considered particularly promising for understanding high-temperature superconductivity.
The standard Hubbard model typically considers two spin states: spin-up and spin-down. A third component makes the system significantly more versatile, enabling researchers to investigate richer quantum mechanical phases.
"Although the Hubbard model is important and simple to write down, it isn't easy to solve. 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," said Kaden Hazzard , a Rice University associate professor of physics and astronomy and co-author on this work. "The experiments are a wonderful testing ground for the theoretical ideas. [First name] Sohail and I were able to compare sophisticated numerical calculations to the experiments, which are already pushed to the boundaries of our capabilities. These comparisons will feed back into helping us refine our theoretical tools. It's an exciting and fast-developing time."
Ultracold atoms in an optical lattice are an excellent platform for quantum simulations. The atoms in the lowest energy state of the lattice form a quantum system in which they tunnel from one lattice site to another, effectively swapping places. Identical fermions cannot occupy the same location, but if distinguishable fermions meet at a single location, an magnetic-field-dependent interaction energy arises.
In the current study, the team led by Peter Schauss, who is conducting research at the University of Hamburg and in the Cluster of Excellence "CUI: Advanced Imaging of Matter," realized for the first time a three-component Hubbard model using ultracold atoms with tunable interactions. The team also sought to detect fundamental states and phases in the experiment.
"It was particularly important to us to observe a so-called Mott state, in which the interactions suppress the double occupation of sites," Schauss said. In this case, strong interactions prevent particles from flowing freely between lattice sites, leading to insulating behavior. Paradoxically, it is near Mott states that high-temperature superconductivity emerges.
The researchers used a quantum gas microscope, which can detect each individual atom with spatial resolution. By utilizing atoms in different internal states, the experiment was able to realize various types of fermions, allowing the team to ultimately use three distinct states. This results in a system that, while very different from the electrons on a lattice known from solid-state physics, resembles nuclear physics, where quarks can have three different colors.
"It turned out that the experimental realization is surprisingly stable," Schauss said. "Usually, one fears that three-body collisions could quickly destroy the system. Despite this potential danger, we were able to successfully carry out the measurements and observe a Mott insulator."
In addition, the researchers identified many other phases. These depend on the strength of the interactions between the three states in each case. For example, it was found that in the same system, both ferromagnetic correlations between two states and antiferromagnetic correlations between two others can occur.
In addition, the researchers developed a method of determining the number of triple-occupied lattice sites. The measured values agreed with the results of numerical calculations, performed by collaborators at Rice. The researchers plan to further refine the interactions in their model, so they can study lattice models of quantum chromodynamics in the laboratory.
This work was funded by the the National Science Foundation (PHY-1848304 and DGE-2346014), the Robert A. Welch Foundation (C-1872) and the W. M. Keck Foundation (995764).
