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Physicists have developed a method to detect hidden topological properties in light, even when energy leaks away from the system. Topology describes features like knots that remain unchanged despite stretching or twisting. In physics, these properties are labeled by whole numbers that stay constant under small imperfections. This robustness makes topology vital for future electronics and quantum devices that can tolerate defects. However, studying this is difficult because topological numbers exist in momentum space, an abstract area describing wave behavior rather than physical location. Most experiments currently infer topology indirectly by observing edge states, which is like judging a knot only by looking at the rope’s ends.

To solve this, researchers created a programmable photonic integrated circuit. This chip uses light traveling through reconfigurable waveguides controlled electrically. Instead of building a fixed physical lattice, scientists program the chip to simulate specific points in momentum space sequentially. To handle energy loss, which shrinks signals in real devices, they used a mathematical technique called unitary dilation. This method embeds the lossy evolution inside a larger, loss-free system by adding extra "helper" channels on the chip that absorb potential lost energy, allowing the signal channels to behave exactly like the target lossy system.

The team read out the hidden information using interferometry, mixing light with reference beams at four phase shifts to measure output intensities. From these measurements, they reconstructed the signal’s phase, where topology hides. They tested this on a non-Hermitian Su–Schrieffer–Heeger model and found the Zak phase close to π for topological cases and zero for ordinary ones. They also identified an exceptional point, a unique feature in lossy systems where modes merge, observing a distinct phase winding pattern. Finally, they extended the method to a two-dimensional space using a Rice–Mele pump, successfully measuring the Chern number as 1 for topological cycles and 0 for trivial ones.

This work was led by doctoral student Andrea Cataldo at KTH Royal Institute of Technology in Stockholm, Sweden, under supervisor Ali W. Elshaari. The research team included collaborators from Stockholm University, the Singapore University of Technology and Design, and Huazhong University of Science and Technology. Their findings were published in Physical Review Letters in 2026. Cataldo notes that while the chip simulates systems rather than being a real material, its flexibility allows researchers to traverse entire maps of topological phases on one device without fabricating multiple samples.