Physicists finally measured an energy ladder predicted 40 years ago

Chains of up to 35 strontium atoms, each held in place by a tightly focused laser beam, have given Caltech physicists the first experimental look at an energy ladder that theorists calculated about 40 years ago. Nobody had measured the spacing between the ladder’s rungs in an experiment before, Caltech says, and the spacings turned out to match the theory’s predicted ratios.

The team, led on the experimental side by Manuel Endres and on the theory side by Jason Alicea, published the measurement in Nature on August 19, 2026, in a paper called “Observation of conformal field theory spectra in a quantum simulator.”

The prediction from conformal field theory

The ladder comes from conformal field theory, a mathematical framework for the universal behavior of quantum systems at a critical point, the knife-edge between two phases of matter. According to Caltech’s release, physicists have used these theories for about four decades to calculate how far apart the rungs of a system’s energy ladder should sit, and the spacings come in precise ratios.

The Nature paper places the prediction in the 1980s, crediting John Cardy with the insight that the pattern of low-energy levels in a finite system directly reveals the theory’s operator content. The paper builds on foundational conformal field theory work by Belavin, Polyakov and Zamolodchikov. Two theories are tested in the experiment: the Ising conformal field theory and the tricritical Ising theory, which describe two different kinds of quantum critical point.

Alicea explained why the ladder carries so much weight. In his words, the energy levels predicted by these theories are important because they encode profound information about the theories themselves, so a measured rung is a direct test of the underlying description and not a side effect of it.

The timeline explains the round number. A prediction made in the 1980s and tested in 2026 spans about four decades, which is how Caltech describes it, and the paper’s own date, August 19, 2026, precedes the later write-ups that circulated through late September. Caltech’s release frames the gap as a missing experimental realization rather than any doubt about the theories, which physicists have used routinely to calculate the spacings. What changed was the availability of simulators able to hold a chain of atoms at a critical point and read out its levels directly.

Strontium atoms and modulation spectroscopy

Caltech’s account describes the simulators as specialized systems that are simpler than general quantum computers, built to recreate one physical situation well. To reach two different quantum critical points, the group used a quantum simulator, a purpose-built system simpler than a general-purpose quantum computer. Caltech’s account, carried by ScienceDaily, says the atoms were arranged in lines with optical tweezers, and that the energy levels were detected with a technique called many-body modulation spectroscopy, in which the frequency of a laser is scanned while the response of the atoms is recorded.

The method resembles running a wet finger around the rim of a wine glass: the right frequency excites a particular resonance, and the resonances map out the rungs. The simulator also let the team vary the boundary conditions by adjusting the atoms at the ends of a chain, which changed the structure of the ladder.

Collaborators from Université Paris-Saclay and the Technical University of Munich contributed, and Xiangkai Sun, a Caltech graduate student, is a co-lead author on the paper. Funding came from the Department of Energy, the National Science Foundation and other agencies.

Ratios that collapsed onto universal curves

The measured ratios matched the predictions of both theories. In the group’s data, spectra taken at different system sizes collapsed onto universal curves once they were rescaled, which is the signature conformal field theory predicts: the microscopic details of the atoms wash out and only a few essential features survive. Alicea put it that way in the Caltech release, saying that the messy, microscopic details wash out and only a few essential features survive.

The experiment also revealed hidden families of excitations, according to that account, and let the team manipulate the ladder’s structure through the end atoms. SciTechDaily’s coverage and The Quantum Insider both repeat the central claim in nearly the same words, that for four decades researchers used these theories to calculate the spacings and that nobody had measured them in an experiment until this one.

Going in, the theory was trusted. Alicea said that even though they believed these theories to be true, it is important to have an experimental realization, something that can be poked and prodded, and that to see the predictions borne out is a beautiful thing. The result confirms the ratios for two theories in one-dimensional atom chains of up to 35 atoms in two specific theories, which is the scope of what the experiment establishes.

This article was produced with the assistance of AI and reviewed by Morning Overview editors prior to publication.

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