Hidden Order in Quantum Chaos: The Pseudogap
Physicists have uncovered a link between magnetism and a mysterious phase of matter called the pseudogap, which appears in certain quantum materials just above the temperature at which they become superconducting. The findings could help researchers design new materials with sought-after properties such as high-temperature superconductivity, in which electric current flows without resistance.
Using a quantum simulator chilled to just above absolute zero, the researchers discovered a universal pattern in how electrons — which can have spin up or down — influence their neighbors’ spins as the system is cooled. The findings represent a significant step toward understanding unconventional superconductivity, and were the result of a collaboration between experimentalists at the Max Planck Institute of Quantum Optics in Germany and theoretical physicists, including Antoine Georges, director of the Center for Computational Quantum Physics (CCQ) at the Simons Foundation’s Flatiron Institute in New York City.
The international research team published their results the week of January 19 in the Proceedings of the National Academy of Sciences.
Superconductivity has driven decades of research and holds the promise to revolutionize everything from long-distance power transmission to quantum computing. However, superconductivity is still not fully understood. In many high-temperature superconductors, the transition to the superconducting state does not emerge out of a conventional metallic state. Instead, the material first enters a curious intermediate regime known as the pseudogap, in which electrons start behaving in unusual ways, and fewer electronic states are available for electrons to flow through the material. Understanding the pseudogap is widely considered essential for unraveling the mechanisms behind superconductivity and designing materials with improved properties.
In materials containing an unaltered number of electrons, the electrons arrange themselves in an orderly, alternating magnetic pattern known as antiferromagnetism. In this pattern, neighboring electron spins point in opposite directions — like dancers following a precise left-right rhythm.
But when electrons are removed through a process known as doping, this magnetic order becomes strongly disrupted. For a long time, researchers assumed that doping destroyed long-range magnetic order entirely. The new study in PNAS, however, shows that at extremely low temperatures, a subtle form of organization remains, hidden beneath the apparent disorder. These experiments were informed by theoretical work on the pseudogap conducted at the CCQ that resulted in a 2024 paper in Science.
From Chaos to Universal Order
The experimental research team turned to the Fermi-Hubbard model, a well-established theoretical framework that captures the interaction of electrons within a solid. Rather than working with real materials, the team re-created the model using lithium atoms cooled to billionths of a degree above absolute zero. The atoms were arranged in a precisely controlled optical lattice made of laser light.
Such ultracold atom quantum simulators enable scientists to mimic complex materials under controlled conditions, a feat impossible in traditional solid-state experiments. Using a quantum gas microscope — a device capable of imaging individual atoms and their magnetic orientation — the research team took more than 35,000 high-resolution snapshots of individual atoms. These images revealed both the spatial positions and the magnetic correlations of atoms across a wide range of temperatures and doping levels.
“It is remarkable that quantum analog simulators based on ultracold atoms can now be cooled down to temperatures where intricate quantum collective phenomena show up,” says Georges.
The results were striking: “Magnetic correlations follow a single universal pattern when plotted against a specific temperature scale,” explains lead author Thomas Chalopin of the Max Planck Institute of Quantum Optics. “And this scale is comparable to the pseudogap temperature, the point at which the pseudogap emerges.” In other words, the pseudogap is linked to the subtle magnetic patterns that lie beneath the apparent chaos.
The study also revealed that electrons in this regime do not simply interact in pairs. Instead, they form complex, multiparticle correlated structures. Even a single dopant can disrupt magnetic order over a surprisingly large area. Unlike previous studies, which focused on correlations between two electrons at a time, the new study measured correlations involving up to five particles simultaneously — a level of detail achieved by only a handful of labs worldwide.
Revealing Hidden Correlations
For theorists, these results provide a new benchmark for models of the pseudogap. More broadly speaking, the new findings bring scientists closer to understanding how high-temperature superconductivity emerges from the collective behavior of interacting, ‘dancing’ electrons. “By revealing the hidden magnetic order in the pseudogap, we are uncovering one of the mechanisms that may ultimately be related to superconductivity,” Chalopin explains.
The study also highlights the power of collaboration between experiment and theory. By combining detailed theoretical predictions with highly controlled quantum simulations, the researchers were able to identify patterns that would otherwise have remained concealed.
The research is the result of an international collaboration that combines experimental and theoretical expertise. Future experiments will further cool the system, search for new forms of order and develop novel ways of observing quantum matter from fresh perspectives.
“Analog quantum simulations are entering a new and exciting stage, which challenges the classical algorithms that we develop at CCQ,” says Georges. “At the same time, those experiments require guidance from theory and classical simulations. Collaboration between theorists and experimentalists is more important than ever.”
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