可编程光子芯片在能量泄漏时仍能读出光中的隐藏拓扑

by Ali W. Elshaari

When I explain topology to students, I start with a knot in a rope. You can stretch it, twist it or shake it, but the knot stays until you cut the rope. Physicists have found that some materials and devices carry similar "knots" in how waves move through them. These are topological properties, labeled by whole numbers that don't change under small imperfections. That robustness is why topology has become one of the central ideas in modern physics. It promises electronics, photonics and quantum devices that tolerate defects and noise.

There is a catch that has always bothered us. These topological numbers live in what physicists call momentum space. It's an abstract space that describes how a wave travels, not where it is.

In most experiments, nobody looks at momentum space directly. Instead, we infer the topology from its consequences, such as special states appearing at the edges of a carefully fabricated sample. That works, but it is a bit like working out whether a rope is knotted by looking only at its ends.

The problem becomes even harder in "non-Hermitian" systems, which lose energy to their surroundings. Every real device is like this, and lossy systems turn out to host some of the richest and strangest physics. But strong loss shrinks the very signal that carries the topological information. So we asked ourselves: Can we read out topology directly in momentum space, even when dissipation is strong?

A programmable chip as a physics simulator

Our answer was a programmable photonic integrated circuit. It's a small chip in which light travels through a reconfigurable network of waveguides, and we can control the paths electrically.

Instead of fabricating a physical lattice, we program the chip to reproduce how the system behaves at one point in momentum space. Then we reprogram it for the next point, and so on, until we have scanned the whole space. The same chip can describe a trivial system one moment and a topological one the next.

Loss was the trickier part. Light on our chip naturally evolves without loss, while the systems we wanted to study do lose energy. We used a mathematical technique called unitary dilation, which embeds the lossy evolution inside a larger, loss-free one. In practice, we add extra "helper" channels on the chip that absorb what would otherwise be lost. The signal channels then behave exactly like the lossy system we want to study.

To read out the hidden information, we use interferometry. We mix the light with reference light at four different phase shifts and measure the output intensities. From those four simple measurements, we reconstruct both the strength and the phase of the signal. The phase is where the topology hides.

Our findings are published in the journal Physical Review Letters.

What we saw

We first tested the method on a classic model of a lossy topological chain, the non-Hermitian Su–Schrieffer–Heeger model. The chip clearly told the two phases apart. The topological quantity we extracted, called the Zak phase, came out close to π for the topological case (we measured 1.02π) and close to zero for the ordinary one, just as theory predicts.

We also looked at something unique to lossy systems: an exceptional point. It's a special point where the system's normal modes merge and conventional intuition breaks down. When we traced a loop around the signature of this point in our measured signal, the phase wound once, giving +1 in one direction and −1 in the other. I find it striking that such an exotic feature leaves such a clean fingerprint in a few intensity measurements.

Finally, we extended the idea to a two-dimensional synthetic space by slowly cycling the system's parameters, a scheme known as a Rice–Mele pump. Here the relevant topological number, the Chern number, came out as 1 for the topological cycle and 0 for the trivial one.

Why this matters, and what's next

For me, the most exciting part is the flexibility. Exploring a whole family of topological phases would normally require fabricating many different samples. With a programmable chip, we can simply change the settings and traverse the entire "map" of phases on one device, even in the strongly lossy regime that is hardest to access.

There are, of course, limits. The chip simulates these systems; it isn't a real material. When the signal becomes very weak, the phase becomes hard to determine. And larger, more complex models will need chips with more channels. But programmable photonic chips are scaling quickly. I see this as a step toward using them as versatile laboratories for topological and non-Hermitian physics that fixed-geometry devices cannot reach.

This work was carried out by doctoral student Andrea Cataldo in the Q-Photon group at KTH Royal Institute of Technology, led by Ali W. Elshaari. We collaborated with Emil J. Bergholtz at Stockholm University, Daniel Leykam at the Singapore University of Technology and Design, and Jun Gao at Huazhong University of Science and Technology.

This story is part of Science X Dialog, where researchers can report findings from their published research articles. Visit this page for information about Science X Dialog and how to participate.

Publication details

Andrea Cataldo et al, Interferometric readout of momentum-space topology in a programmable dissipative photonic circuit, Physical Review Letters (2026). DOI: 10.1103/xkht-64kc. On arXiv: arxiv.org/abs/2609.38352

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Andrea Cataldo is a Ph.D. student in the Quantum Nano Photonics group at KTH Royal Institute of Technology in Stockholm, Sweden, supervised by Ali W. Elshaari. Andrea's research uses programmable photonic integrated circuits to explore topological and non-Hermitian physics.

Ali W. Elshaari is an associate professor in the Department of Applied Physics at KTH Royal Institute of Technology, where he works in the Quantum Nano Photonics group. His research focuses on integrated quantum photonics, including programmable photonic circuits, on-chip quantum light sources and hybrid quantum photonic devices. His work ranges from fundamental studies of topological and non-Hermitian physics to scalable photonic technologies for quantum information processing. He is a member of the Wallenberg Center for Quantum Technology (WACQT) and a Marie Curie Fellow.

Citation: Reading hidden topology in light, even when energy leaks away (2026, October 3) retrieved 17 October 2026 from https://phys.org/news/2026-10-hidden-topology-energy-leaks.html

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