Exceptional points, or EPs for short, are among the phenomena of modern Physics. These are special points or locations at which the properties of matter, space or time change. In a new theoretical study, researchers from the Institute for Photonic Quantum Systems (PhoQS) at Paderborn University, in collaboration with researchers from the University of Arizona, have now shown that ‘exceptional points’ in non-linear systems follow a universal geometric order – something that was previously unclear. Their findings have now been published in the prestigious journal *Nature Communications*.
‘Exceptional points’ are points in physical systems at which not only two eigenvalues but also the corresponding states merge. Such phenomena occur in so-called non-Hermitian systems, which are characterised, for example, by amplification, loss or interactions with their environment. They are the subject of intensive research in fields including optics, lasers, quantum systems and polariton condensates. Until now, EPs have mainly been studied in linear systems. In such systems, they can often be described as isolated points in parameter space. However, many real physical systems are non-linear: their properties depend on the intensity, occupation or state of the system itself.
“We were able to show that non-linear ‘exceptional’ points do not follow just any geometry,” explains Prof. Dr Stefan Schumacher, in whose research group the work was carried out. The theoretical study was driven forward largely by Prof. Dr Nai Kwong of the University of Arizona, as well as Jan Wingenbach in Schumacher’s research group and Dr. Laura Ares in the research group of Prof. Dr Jan Sperling, also from Paderborn University. Close collaboration with Prof. Dr Rolf Binder and Prof. Dr Nai H. Kwong of the University of Arizona was essential to the success of the work. Commenting on the findings, Jan Wingenbach says: “The discovery of a universal cone-and-cusp structure came as a surprise. It shows that we can now understand the physics of non-linear ‘exceptional points’ much better. This is a crucial step towards making targeted use of these phenomena for future applications, for example in sensor technology or in functional photonic systems.” Prof. Schumacher adds: “Very different physical systems can exhibit the same characteristic structure in the vicinity of an ‘exceptional point’. This universal topology provides a kind of roadmap for identifying such points more precisely in future, understanding them and making them usable for applications.”
The study thus offers a new perspective on known linear EPs and demonstrates how they are embedded in non-linear systems. ‘Exceptional points’ are considered promising for highly sensitive sensors because systems in their vicinity can react particularly strongly to small disturbances. At the same time, with non-linear systems, it is crucial to understand what amplification is actually achievable and where the fundamental limits lie. The new topological description can help to determine such limits mathematically with precision and to design robust, highly sensitive components for various physical platforms. In the long term, the work thus points to a deeper unity within non-linear, non-Hermitian Physics: different systems can exhibit the same universal topological signature despite differing microscopic details.
The paper is available at: https://www.nature.com/articles/s41467-026-72854-2
This text was translated automatically.
