Researchers at the universities of Jena and Regensburg have revealed an optical method using ultrashort laser pulses to measure Berry curvature in a tungsten diselenide monolayer. Published in the journal Nature Photonics, the technique extracts a local quantum property in a few hundred femtoseconds, matching theoretical calculations.
Electrons moving through a crystal do not travel along simple, predictable tracks. Instead, their paths are shaped by quantum mechanical states within the material’s momentum space. One key geometric property governing these states is Berry curvature, which dictates how electrons react when exposed to light or electric fields. Until recently, determining this parameter relied primarily on theoretical calculations or experimentally complex methods.
A collaborative team working across the Institute of Solid State Physics at Friedrich Schiller University Jena and the University of Regensburg altered that approach. By combining optical measurements with an analytical model, researchers successfully obtained a quantitative estimate of local Berry curvature in an atomically thin semiconductor.
Optical Measurements Inside Tungsten Diselenide
The experiment focused on tungsten diselenide, a material belonging to a family of semiconductors that interact strongly with light when reduced to a single atomic layer (less than one nanometre thick). This strong interaction makes such materials ideal for nonlinear optics, where emitted light frequencies differ from incoming signals.
To capture the measurement, the research team directed two ultrashort laser pulses at the sample. The first pulse—a circularly polarized pump beam—temporarily modified the material’s electronic energy levels. The second pulse served to optically detect this change, generating light at twice the frequency of the incident light.
By adjusting the timing between the pump and probe pulses, researchers isolated the brief light-induced response from the rest of the material’s behavior. The entire process operated on a timescale of a few hundred femtoseconds, where a femtosecond represents one millionth of a billionth of a second.
Connecting Light Polarization to Quantum Geometry
The experiment relied on two distinct electronic regions known as valleys, positioned at opposite momenta and designated as +K and −K. Without the pump pulse, the optical contributions of these valleys balance out, causing the measured difference between opposite circular polarizations to vanish.
Reversing the direction of rotation of the first circularly polarized laser pulse caused the sign of the measured signal to flip. The team measured the difference between left- and right-circularly polarized components of the generated second-harmonic light, which supplied the experimental signal for the model.
We wanted to make a quantum property accessible that has so far been difficult to determine experimentally.
Nele Tornow, lead author at the University of Jena
Lead author Nele Tornow noted that the primary innovation rests on pairing an optical experiment with a theoretical model to derive a concrete value for the property. Co-researcher Giancarlo Soavi, affiliated with the Institute of Solid State Physics and the Abbe Centre of Photonics at the University of Jena, emphasized the broader utility of the breakthrough.
Using this optical method, we can investigate such properties on extremely short time scales.
Giancarlo Soavi, University of Jena and Abbe Centre of Photonics
Future Applications Beyond Tungsten Diselenide
While the initial demonstration utilized tungsten diselenide, the research team reports that the underlying measurement principle is not restricted to a single material class. Both the experimental setup and the analytical model developed alongside Regensburg researchers can be applied to other materials.
The findings, detailed in the journal Nature Photonics, establish a strategy for tracking rapid changes in electronic quantum states. The method offers a pathway to observe how material quantum geometry shifts during rapid optical processes.