Quantum geometry has become central to understanding modern materials, underpinning phenomena from topology to electron localization. But until now, it has remained a largely theoretical concept, with no direct way to measure it.
In this work, we show that inelastic x-ray scattering (IXS) provides a direct, quantitative probe of quantum geometry in solids. By measuring the density response of materials, we extract key quantities like the quantum Fisher information and Bures metric, turning quantum geometry into an experimentally accessible property.
IXS spectra of diamond (top) and LiF (bottom) for various momentum transfer. The quasi-elastic peak, corresponding to data below 3 eV , have been set to zero. The vertical lines correspond to the q → 0 value of the band gap.
Along the way, we uncover an unexpected connection between quantum geometry and quantum information: the same measurements that reveal geometric structure also quantify how much quantum information is encoded in a material.
Comparing diamond and LiF, we find that covalent systems carry more quantum information, reflecting their more delocalized electronic structure.
This work establishes a new experimental route to quantum geometry and opens the door to studying it across a wide range of materials.
D. Bałut, B. Bradlyn, M. D. Collins, P. Abbamonte, Fundamental tests of quantum geometric bounds in ionic and covalent insulators using inelastic X-ray scattering, arXiv:2601.19054 (2026)
χ(q, ω) is a fundamental quantity that reveals the collective charge dynamics of the material. Despite decades of study, χ(q, ω), near a CDW transition, had never been measured at nonzero momentum, q, with energy resolution that is relevant for these quantum phases.
A divergent behavior observed in the real part of χ’(q, ω→0) near qCDW.
Using momentum-resolved electron energy loss spectroscopy (M-EELS), a technique uniquely sensitive to valence band charge excitations, we perform the first measurements of electron dynamics across a canonical CDW transition in ErTe3. We measured the dynamic charge susceptibility, χ(q, ω), across the CDW transition in ErTe3 and showed that the collective electron dynamics is purely relaxational and the real part of χ(q, ω→0) exhibits a divergent behavior, a long-predicted hallmark of CDWs.
In this study, we explore how quantum geometry and entanglement—usually thought of as purely theoretical concepts—can be directly measured in scattering experiments. We demonstrate a connection between the quantum Fisher information (QFI) and quantum weight, a measure of wavefunction geometry in insulators, and validate this relationship using inelastic x-ray scattering (IXS) data from LiF.
Both the QFI and the quantum weight are related to a material’s density-density response function. The QFI captures how rapidly the equilibrium density matrix responds to an external perturbation, offering a measure of the system’s intrinsic sensitivity. The quantum weight, on the other hand, is related to wave function geometry, reflecting bounds on fluctuation and localization, and in the limit of small momentum transfer and low temperature, can also be experimentally accessed via the density-density response function.
Our experimental results reveal that the quantum weight in LiF lies close to its theoretical upper bound. This suggests that, while LiF is a strongly localized ionic insulator, its electrons are nearly as delocalized, geometrically as quantum mechanics allows for a system with its material parameters.
This work bridges condensed matter and quantum information concepts, and also demonstrates a general strategy for experimentally accessing entanglement and quantum geometry in many-body systems where the charge density is measured.
We recently observed a new kind of collective excitation called a “demon”. This “particle” was predicted by David Pines in 1956, but it was never observed until we saw it in Sr2RuO4 in our momentum-resolved EELS experiments. Demons are interesting because they are massless and neutral, and do not couple to light, but can have strong influence over the low-energy properties of multiband metals. For example, Ihm, Cohen, and Tuan showed in a theoretical paper in 1981 that demons could mediate superconductivity. While not every multiband metal necessarily contains a demon, they are probably not rare, and represent a new phenomenon in condensed matter physics. For more details, see our paper in Nature.
Two undergraduates have left our group, Nathan Manning, who accepted a position at Bruker, a manufacturer of scientific instruments, and Solomon Michalak, who is entering the Ph.D. program at the University of Minnesota, and Muhammad (Mo) Fadag, who was hired as a patent examiner at the USPTO. This summer, we have a team of new undergraduate students actively working in our labs, one of whom is a fellow in the Open Quantum Initiative. Two of our graduate students are away participating in summer research programs. Cat is on a summer fellowship with the G. T. Seaborg Institute Graduate Research Program at Los Alamos National Laboratory, an extension to her last year’s fellowship, and Xuefei is an engineering intern at ASML/Cymer in San Diego.
