When physical materials undergo radical transformations—such as water boiling into steam or a permanent magnet losing its magnetic properties at high temperatures—the microscopic mechanisms driving these changes are wildly diverse. Yet, physicists have long observed a profound and counterintuitive phenomenon: entirely unrelated systems frequently begin to obey the exact same underlying mathematical rules. In the lexicon of modern theoretical physics, this unifying trait is known as universality. During these critical transitions, the messy, complex details of microscopic particles wash away, leaving only a few essential, universal features that dictate the macro-level behavior of the system.
For decades, researchers have relied on an advanced mathematical framework called conformal field theory (CFT) to describe this universal behavior. However, rigorously testing these theoretical frameworks in a controlled laboratory setting has historically remained an elusive goal. Now, in a groundbreaking study published in the scientific journal Nature, an international collaboration of researchers has successfully carried out the first direct experimental observations of conformal field theory spectra using advanced quantum simulators.
The multi-institutional research effort brought together the experimental physics group led by Manuel Endres at the California Institute of Technology (Caltech), theoretical physicists under the guidance of Jason Alicea at Caltech, alongside academic partners at Université Paris-Saclay and the Technical University of Munich. By leveraging newly matured quantum hardware, the team has bridged a decades-long gap between abstract theoretical predictions and empirical physics, opening unprecedented pathways for exploring matter near absolute zero.
The Chronology of a Breakthrough: From 1920s Magnetism to Modern Lasers
The intellectual lineage of this recent discovery stretches back nearly a century. In the 1920s, physicist Ernst Ising formulated an early mathematical model designed to understand the microscopic origins of magnetism. Known today as the Ising model, it simplifies materials into a grid of interacting magnetic moments, or spins, that point either up or down. By the latter half of the 20th century, physicists expanded upon these concepts to formulate conformal field theories, predicting that systems at critical phase transition points should exhibit distinct, highly organized energy spectra.
For approximately 40 years, theoretical physicists utilized CFT calculations to map out how far apart these energy states—often conceptualized as the rungs of an invisible ladder—should be positioned. Theory dictated that these energy levels must appear in precise, unyielding mathematical ratios. Despite the elegance of these calculations, direct empirical confirmation remained out of reach because conventional materials are inherently difficult to isolate, manipulate, and measure at such granular levels.
The turning point arrived over the past decade, concurrent with the rapid engineering boom in quantum computing technologies. While general-purpose quantum computers continue to battle challenges related to error correction and scalability, scientists recognized that specialized quantum simulators could be constructed to mimic specific quantum behaviors. The Caltech-led team capitalized on this trajectory, spending recent years refining neutral-atom platforms capable of exerting exquisite individual control over large numbers of atoms. The culmination of this technological evolution led directly to the recent Nature publication, marking a transition from theoretical extrapolation to direct, empirical observation of quantum criticality.
Methodology: Trapping Atoms and Measuring the Quantum Ticking Point
To execute the experiment, the research team utilized an experimental apparatus built upon optical tweezer arrays—a cutting-edge technology wherein tightly focused laser beams act as microscopic tweezers capable of holding, moving, and organizing individual neutral atoms in space. Demonstrating the rapid scalability of this platform, a related neutral-atom setup in the Endres laboratory recently achieved a monumental milestone by successfully trapping 6,100 atoms within a single array.
For the conformal field theory study, the researchers arranged a precise line of strontium atoms using the optical tweezer technology. Secondary lasers were then introduced to excite the atoms into exceptionally high energy states known as Rydberg states. When atoms enter a Rydberg state, their outermost electrons are pushed far from the nucleus, causing neighboring atoms to interact with immense strength.
These powerful interactions force the entire chain of atoms to function collectively as a unified quantum system, rather than as a collection of isolated particles. By dynamically adjusting the laser parameters, the researchers coaxed the atomic chain toward a specific quantum tipping point. Unlike conventional phase transitions driven by thermal energy—such as heating water until it boils—this quantum phase transition occurs near absolute zero and is governed entirely by quantum fluctuations and entanglement.
To observe and record the predicted energy ladder of this system, the team developed an innovative experimental protocol termed many-body modulation spectroscopy. The researchers applied a gentle, rhythmic disturbance across the entire atomic chain by modulating the laser fields at a specific frequency, subsequently measuring how the atoms responded.
This mechanism is conceptually analogous to running a wet finger around the rim of a crystal wine glass. When the motion of the finger precisely matches the natural resonant frequency of the glass, the structure rings out clearly, producing a sustained tone; at mismatched frequencies, virtually no response occurs. By systematically scanning through a wide spectrum of frequencies and identifying sharp peaks in the atomic response, the team successfully mapped out the hidden energy levels.
When the researchers repeated the procedure across chains comprising up to 35 atoms, the empirical results aligned precisely with theoretical projections. The measured energy rungs adhered to the Ising conformal field theory, with the spectra collapsing onto a single universal curve once adjusted for the size of the system. Furthermore, by tuning the apparatus to a more complex parameter space known as the tricritical point, the team successfully measured the distinct, lower-level spectra predicted by tricritical Ising CFT.
Official Perspectives and Scientific Implications
The successful empirical validation of these complex theoretical models has elicited enthusiastic responses from the participating research teams, who view the milestone as a validation of decades of foundational physics.
"Physicists call this trait universality—the messy, microscopic details wash out and only a few essential features survive," remarks Jason Alicea, the William K. Davis Professor of Theoretical Physics at Caltech and a co-author of the study. "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."
The ability to control each atom individually granted the researchers an unprecedented degree of experimental precision. By classifying atomic excitations according to their inherent spatial symmetries, the team successfully exposed a secondary set of energy rungs that remained entirely hidden during initial, less-refined measurements. Moreover, by altering the quantum behavior of the atoms situated at the extreme ends of the chain, the researchers successfully reconfigured the energy ladder, generating alternative patterns that precisely mirrored theoretical forecasts.
Xiangkai Sun, a graduate student in the Endres lab and co-lead author of the research, emphasizes the instrumental shift represented by the project. "Our new tools borrow from quantum computing platforms," Sun notes. "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."
Manuel Endres, professor of physics at Caltech, highlights the broader analytical implications of deploying quantum simulators for basic science rather than standard computational tasks. "What excites me is that the technique doesn’t require knowing the answer in advance," Endres explains. "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."
Future Horizons: Expanding into Higher Dimensions
Following this initial success, the international collaboration is already turning its attention toward the next phase of experimental research. Moving forward, the team aims to scale their quantum simulation architectures beyond linear chains of atoms into complex two-dimensional grids.
This transition carries profound scientific weight. While one-dimensional conformal field theories are thoroughly mapped and understood within mathematical physics, two-dimensional CFTs remain significantly more complex and less analytically tractable. By constructing two-dimensional atomic arrays using optical tweezers, the researchers hope to probe quantum phases of matter that sit well beyond the computational capabilities of classical supercomputers.
If successful, this methodological leap could unlock deep insights into high-temperature superconductivity, quantum spin liquids, and other exotic phases of matter that have baffled theorists for generations. By transforming quantum simulators from speculative computing devices into precision measurement instruments, the scientific community has established a powerful new empirical lens through which to decode the fundamental architecture of the natural world.
Funding and institutional support for the published study, titled "Observation of conformal field theory spectra in a quantum simulator," were provided by a diverse coalition of major scientific agencies and foundations. These include the U.S. Department of Energy (operating through the Quantum Systems Accelerator and the Quantum Science Center), the National Science Foundation (via Caltech’s Institute for Quantum Information and Matter), 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.
Additional co-authors contributing to the research include Yuan Le, Stephen Naus, Richard Bing-Shiun Tsai, and Lewis Picard of Caltech; Sara Murciano of Université Paris-Saclay; and Michael Knap of the Technical University of Munich and the Munich Center for Quantum Science and Technology.
