This article has been reviewed according to Science X's editorial process and policies. Editors have highlighted the following attributes while ensuring the content's credibility: 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? Our answer was a programmable photonic integrated circuit.
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