New laser technique reveals electrons' hidden quantum geometry

Physicists have long struggled to measure a particular quantum property of electrons—one that shapes how they behave when exposed to light or electric fields. This property, called Berry curvature, describes the geometric character of the quantum states electrons occupy inside a crystal. Until now, researchers either calculated it theoretically or relied on cumbersome experimental techniques. A team at Friedrich Schiller University Jena and the University of Regensburg has found a cleaner path: they used ultrashort laser pulses to observe it directly, and published their findings in Nature Photonics in October 2026.

The challenge lies in the nature of electrons themselves. Inside a crystal, they do not behave like tiny balls rolling along a track. Instead, their motion is governed by quantum mechanics, which means their behavior emerges from abstract quantum states. Berry curvature is a number that captures something essential about the geometry of these states—a kind of curvature in the mathematical space where electrons live. It matters because it determines, in part, how electrons will respond when light hits them or when an electric field is applied.

The Jena and Regensburg researchers took a different approach than their predecessors. Rather than trying to measure Berry curvature in isolation, they combined optical measurements with a theoretical model, allowing them to extract a quantitative value for the property. Nele Tornow, the lead author from Jena's Institute of Solid State Physics, explained that the innovation was in this hybrid method: "We wanted to make a quantum property accessible that has so far been difficult to determine experimentally. What makes our approach special is that we combine an optical experiment with a theoretical model to obtain a specific value for the Berry curvature."

The experiment itself is elegantly simple in concept, though demanding in execution. The team worked with tungsten diselenide, a semiconductor material that exists as a single atomic layer—less than one nanometer thick. Such atomically thin materials have a particular advantage: they interact strongly with light, making them ideal for the kind of nonlinear optical experiments the researchers needed to perform. They fired two ultrashort laser pulses at the sample in sequence. The first pulse, circularly polarized, disturbed the electronic states of the material for a fraction of a second—specifically, a few hundred femtoseconds, where a femtosecond is one millionth of a billionth of a second. The second pulse then detected this disturbance optically. The result was light at twice the frequency of the original pulses. By analyzing the polarization of this light—the way it oscillates—the researchers extracted information about the Berry curvature.

The measurement proved consistent with theoretical predictions. When the team reversed the direction of rotation of the first laser pulse, the sign of the measured signal flipped as well, confirming the method's reliability. Giancarlo Soavi, also from Jena's Institute of Solid State Physics and the Abbe Centre of Photonics, noted the practical significance: "Using this optical method, we can investigate such properties on extremely short time scales. This will enable us in the future to track how the quantum geometry of a material changes during very rapid processes."

What makes this work particularly valuable is its potential generality. Although the researchers demonstrated the technique using tungsten diselenide, they emphasize that the underlying principle is not limited to this one material. The measurement approach and the theoretical model, developed in collaboration with colleagues at the University of Regensburg, can in principle be adapted to other semiconductors and materials. This opens a path toward deeper investigation of how electrons behave in materials under extreme conditions—when processes happen so fast that conventional measurement methods cannot follow. Over time, the technique could reshape how physicists understand the relationship between quantum geometry and the optical properties of matter.