Imagine an orchestra where every musician plays their own part without listening to the others. Suddenly, without any visible command, neighboring musicians begin to sync perfectly, yet there is still no overall melody. Something similar happens in certain materials when they are cooled: electrons lose energy as if preparing for superconductivity, but they never actually make the transition. This state is called the pseudogap, and it has remained a puzzle for decades.
The authors of the study looked at the problem through the lens of entanglement — a quantum connection in which particles cease to be independent. Using a simulator made of ultracold atoms (a cloud of particles cooled to nearly absolute zero), they measured how the electrons' spins, their tiny magnetic moments, become entangled. It turned out that a special type of entanglement, where the spins of two neighbors form a pair with zero total moment, arises exactly when the pseudogap appears. And, unlike ordinary correlations, it does not extend beyond nearest neighbors.
This result deals a blow to theories that explained the pseudogap through classical fluctuations — for example, oscillations in charge density. If the fluctuations were classical, entanglement would not be limited to neighbors. Now scientists will have to build models where quantum connections between nearest atoms play the central role. So the electron orchestra, not yet playing the symphony of superconductivity, is already tuning up in pairs, and this tuning is a purely quantum effect.
as written by the authors arXiv:2605.31240
Despite decades of intense theoretical and experimental investigation, the two-dimensional Fermi-Hubbard model still resists a complete microscopic understanding. Conventional approaches typically probe global observables and locally resolved correlation functions. Here, we develop a complementary perspective based on the measurement of entanglement. Using both an ultracold-atom quantum simulator and numerical simulations based on the dynamical vertex approximation, we find that entanglement is closely tied to the onset of the enigmatic pseudogap regime: spin-singlet entanglement emerges only as the pseudogap sets in and, in contrast to classical correlations, remains confined to nearest-neighbour sites in this regime. Our results, therefore, disfavour purely classical-fluctuation theories of the pseudogap and constrain microscopic models to those that develop nearest-neighbour spin-singlet entanglement at the pseudogap onset.
The ultracold atoms in the simulator are cooled to temperatures a billionth of a degree above absolute zero — colder than interstellar space.