By manipulating ultrafast quantum particles under extreme conditions, researchers have begun to probe growth dynamics in unprecedented detail.
Why do patterns emerge as surfaces grow, whether in crystals, flames, or living systems? Physicists have long turned to the Kardar–Parisi–Zhang (KPZ) equation, proposed in 1986, as a unifying description of these processes. This theory captures how randomness and nonlinear effects shape growth across vastly different systems, from spreading bacterial colonies to data-driven algorithms.
Now, researchers at the University of Würzburg have taken a major step toward confirming just how universal this idea really is. After earlier success in one dimension, they have demonstrated for the first time that KPZ behavior also governs growth in two-dimensional systems, a milestone that had remained experimentally out of reach.
Würzburg Research Team Achieves Breakthrough in 2D Quantum System
“When surfaces grow—whether crystals, bacteria, or flame fronts—the process is always nonlinear and random. In physics, we describe such systems as being out of equilibrium,” explains Siddhartha Dam, a postdoctoral researcher in the Würzburg–Dresden Cluster of Excellence ctd.qmat at the University of Würzburg’s Chair of Technical Physics. “Engineering a system capable of simultaneously measuring how a non-equilibrium process evolves in space and time is extremely challenging—especially because these processes unfold on ultrashort timescales. That’s why verifying the KPZ model in two dimensions has taken so long. We have now succeeded in controlling a non-equilibrium quantum system in the laboratory—something that has only recently become technically feasible.”
To carry out the experiment, the team cooled a gallium arsenide (GaAs) semiconductor to −269.15°C (−452.47°F) and continuously illuminated it with a laser. This setup produced polaritons, hybrid particles made from light and matter, within a carefully engineered layer of the material. These particles exist only under non-equilibrium conditions. They are created by laser excitation and disappear within a few picoseconds.
Tracking Growth at the Quantum Level
“We can precisely track where the polaritons are in the material. When we pump the system with light, polaritons are created—they grow. Using advanced experimental techniques, we were able to quantify both the spatial and temporal evolution of this growing quantum system and found that it follows the KPZ model,” Dam explains.
The concept of testing a universal growth theory in a quantum system using polaritons was developed by Sebastian Diehl, a professor at the University of Cologne and a member of the team. His group established the theoretical basis in 2015.
In 2022, researchers in Paris observed KPZ behavior experimentally, but only in a one-dimensional system. “The experimental demonstration of KPZ universality in two-dimensional material systems highlights just how fundamental this equation is for real non-equilibrium systems,” Diehl says.
Targeted Materials Design Enables Injection of Polaritons
To generate polaritons, the team built a highly specialized structure. Reflective mirror layers trap photons inside a central “quantum film,” where they interact with excitons in the gallium arsenide to form polaritons that can be observed as they evolve.
“By precisely controlling the thickness of individual material layers using molecular beam epitaxy, we were able to tune their optical properties and hence fabricate the necessary highly reflective mirrors under ultra-high vacuum conditions,” explains Simon Widmann, a doctoral researcher at the Chair of Engineering Physics, who conducted the experiments together with Siddhartha Dam. “We control how the material grows atom by atom and can fine-tune all experimental parameters—for example, the laser, which must excite the sample with micrometer precision. This level of control was essential for successfully demonstrating KPZ universality.”
Reference: “Observation of Kardar-Parisi-Zhang universal scaling in two dimensions” by Simon Widmann, Siddhartha Dam, Johannes Düreth, Christian G. Mayer, Romain Daviet, Carl Philipp Zelle, David Laibacher, Monika Emmerling, Martin Kamp, Sebastian Diehl, Simon Betzold, Sebastian Klembt and Sven Höfling, 9 April 2026, Science.
DOI: 10.1126/science.aeb4154
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