A collaborative team spanning Caltech, Université Paris-Saclay, and the Technical University of Munich executed landmark experiments probing two distinct conformal field theories with quantum simulators–specialized quantum systems engineered for dedicated computational tasks. Their results were published in Nature.
This AI image shows a chain of strontium atoms (orange), each held in an optical tweezer (blue cones). The chain sits within a modulated laser field. The evenly spaced lines above represent the ladder of excitation energies predicted by conformal field theory, whose rungs the team measured. Image Credit: AI-generated artwork by Stephan Naus
As various substances shift between phases, for instance, water boiling or a magnet ceasing to attract metals, a notable phenomenon occurs: They start exhibiting identical behavior, adhering to the same mathematical principles.
Physicists call this trait universality - the messy, microscopic details wash out and only a few essential features survive.
Jason Alicea, William K. Davis Professor of Theoretical Physics, California Institute of Technology
The mathematical basis for these pervasive characteristics is typically articulated through a theoretical construct known as conformal field theory.
Caltech physics professor Manuel Endres led the experimental team, along with Jason Alicea's theoretical research group.
Using novel technology developed for these quantum simulators, the research group reports the first direct measurement of energy levels in synthetic quantum matter, as predicted by the Ising and tricritical Ising conformal field theories. (Ising is named after Ernst Ising, a physicist who, in the 1920s, resolved an early model of magnetism.)
These theories characterize universal behavior that appears when a quantum system, displaying unusual properties like entanglement and superposition, sits at a critical juncture between two states, with one more ordered than the other.
Unlike everyday transitions, such as water turning into steam, this transition is driven not by heat but by quantum phenomena at temperatures near absolute zero. At that critical juncture, lasers can stimulate the system to reach a sequence of distinct energy levels, like steps on a ladder.
The energy levels predicted by these theories are important because they encode profound information about the theories themselves.
Jason Alicea, William K. Davis Professor of Theoretical Physics, California Institute of Technology
For forty years, scientists have used conformal field theories to determine the intervals between these levels, which exhibit exact proportions, yet no one had empirically observed them until now.
"Our new tools borrow from quantum computing platforms," says Xiangkai Sun, a co-lead author of the study and a graduate student at the Endres lab. "Over the past 10 years, people have been learning to control these systems, and now we are at the point where we can use them to do fundamental physics research."
The quantum setup examined in this research utilizes platforms from the Endres laboratory, which constructs quantum computers: configurations of neutral atoms held by lasers known as optical tweezers. A similar neutral-atom system within the lab recently achieved a significant feat by confining 6,100 atoms in one array. While the optical tweezer methodology for these arrays was primarily conceived for quantum computing, the group redirected it in this novel investigation to address a core inquiry in fundamental physics.
For this test, the scientists employed optical tweezers to confine strontium atoms linearly. They used additional lasers to excite the atoms into higher-energy Rydberg states, causing adjacent atoms to interact strongly. As a result, the atomic chain behaved as a single unit rather than separate particles. Following this, the scientists adjusted the lasers to position the chain precisely at its critical threshold.
To determine the energy ladder, the group utilized a novel instrument created for these investigations, known as many-body modulation spectroscopy. Using this technique, the scientists subtly vibrated the whole chain by adjusting the lasers at a selected frequency, subsequently gauging the intensity of the atomic reaction.
By scanning across frequencies and observing where the reaction peaked, the group could delineate the ladder's steps.
We repeated the experiment on chains of up to 35 atoms, and the rungs came out as predicted by the Ising conformal field theory: the spectra collapsed onto a single universal curve once rescaled for size. We then tuned to the tricritical point and measured the lowest levels of its distinct spectrum, which came out in the different ratios theory predicts.
Xiangkai Sun, Study Co-Lead Author and Graduate Student, California Institute of Technology
Because each atom in the array is individually addressable, the team could also perform feats far more difficult with conventional materials. The excitations were categorized by their symmetry, uncovering a second family of rungs that the initial measurement had not detected. Moreover, by manipulating the atoms at the chain's two ends, they modified the ladder's arrangement, each configuration generated a distinct pattern foreseen by the tricritical Ising theory.
"Even though we believed these theories to be true, it's important to have an experimental realization, something you can poke and prod. To see those predictions borne out is a beautiful thing," Alicea says.
For future work, the team intends to utilize an even larger quantum system to investigate conformal field theories, employing atoms not only in a line but also in a grid.
"In two dimensions, the conformal field theories are not as well understood, so this is an exciting opportunity," Sun adds.
"What excites me is that the technique doesn't require knowing the answer in advance. Here we could check our measurements against exact predictions. The next step is to point this at systems where nobody knows the response of the system quantitatively - including regimes that classical computers can't reach," Endres notes.
The study received funding from the US Department of Energy, specifically its Quantum Systems Accelerator and Quantum Science Center; the National Science Foundation, encompassing the Institute for Quantum Information and Matter at Caltech (IQIM); the Army Research Office; the Defense Advanced Research Projects Agency; the Air Force Office of Scientific Research; the Gordon and Betty Moore Foundation; and the Deutsche Forschungsgemeinschaft.
Other Caltech contributors include Yuan Le, Stephen Naus, Richard Bing-Shiun Tsai, and Lewis Picard, who is currently employed at the Caltech-affiliated startup Oratomic. Further authors are Sara Murciano from the Université Paris-Saclay (formerly a postdoctoral scholar at Caltech) and Michael Knap from the Technical University of Munich and the Munich Center for Quantum Science and Technology.
Journal Reference:
Sun, X., et al. (2026) Observation of conformal field theory spectra in a quantum simulator. Nature. DOI:10.1038/s41586-026-10904-x. https://www.nature.com/articles/s41586-026-10904-x.