Caltech physicists experimentally confirm 40-year-old quantum energy predictions

For four decades, physicists have calculated what should happen at the edge of a quantum phase transition—the precise spacing between energy levels, the ratios that govern how a system behaves when it tips from one state into another. They built these predictions using conformal field theory, a mathematical framework that describes universal patterns emerging from the quantum world. But calculation and observation are not the same thing. Until now, no one had actually measured those energy levels directly and confirmed the theory was right.

A team at Caltech has done exactly that. Using a quantum simulator made from laser-trapped strontium atoms, they recreated two different quantum tipping points and watched the atoms settle into energy states that matched the theoretical predictions with striking precision. The work, published in Nature, represents the first direct experimental confirmation of these 40-year-old calculations and opens a new way to investigate quantum systems where the answer is not already known.

The key insight underlying the whole enterprise is something physicists call universality. When a quantum system reaches a critical point—a moment of transition between two different states—the messy details of how individual atoms behave wash away. What remains are a few essential features that follow universal rules, the same rules that would apply to many different physical systems. Conformal field theory provides the mathematical language to describe these universal patterns. Jason Alicea, a theoretical physicist at Caltech, explains that the energy levels predicted by these theories encode profound information about the theories themselves. For 40 years, physicists calculated how far apart those energy rungs should be, expecting them to appear in precise ratios. But the predictions had never been directly measured in an experiment.

The Caltech team, led by Manuel Endres, built their quantum simulator using optical tweezers—tightly focused laser beams that can trap individual atoms in place. They arranged strontium atoms in a line and then used additional lasers to push them into highly excited energy states called Rydberg states, where neighboring atoms interact very strongly. These interactions caused the chain of atoms to behave as a collective system rather than as separate particles. By adjusting the lasers, the researchers tuned the entire system to reach the critical tipping point they wanted to study. Unlike ordinary phase transitions like water turning to steam, this transition happens at temperatures close to absolute zero and arises entirely from quantum effects, not from heat.

To measure the hidden energy levels, the team developed a technique called many body modulation spectroscopy. They gently disturbed the atomic chain by changing the lasers at particular frequencies and measured how strongly the atoms responded. By scanning through many frequencies and looking for peaks in the response, they could identify the different energy levels—like running a wet finger around the rim of a wine glass to find the frequencies that make it ring. When they repeated the experiment on chains of up to 35 atoms, the energy rungs came out exactly as predicted by the Ising conformal field theory. The spectra collapsed onto a single universal curve once rescaled for size. They then tuned to a different critical point, the tricritical Ising theory, and measured its lowest energy levels, which appeared in the different ratios that theory predicts.

What made this measurement possible was the ability to control each atom separately. Because the researchers could manipulate individual atoms and measure their behavior with precision, they could perform experiments that would be far more difficult with conventional materials. They classified the excitations by their symmetry and exposed a second set of energy rungs that had been hidden in the initial measurement. They also changed the behavior of atoms at either end of the chain, which rearranged the energy ladder and produced different patterns that matched predictions from the tricritical Ising theory.

The implications extend beyond confirming old predictions. The technique does not require knowing the answer in advance. Here, the researchers could check their measurements against exact theoretical predictions. But the next step is to point this tool at quantum systems where nobody yet knows the response—regimes that classical computers cannot reach. The team plans to expand the experiments to larger systems, arranging atoms not just in lines but in two-dimensional grids. In two dimensions, conformal field theories are not as well understood, making this an exciting opportunity to investigate quantum behavior that cannot yet be calculated precisely. Manuel Endres notes that what excites him is the prospect of studying systems where the quantitative response is unknown, potentially unlocking physics that lies beyond the reach of classical computation.