On August 19, 2026, a team led by Caltech published results in Nature reporting the first direct measurement of finite-size energy excitation spectra predicted by two-dimensional conformal field theories (CFTs). The experiment used a neutral-atom quantum simulator: chains of up to 35 strontium atoms held in optical tweezers and driven into strongly interacting Rydberg states.
The work combines the experimental group of Manuel Endres and the theory group of Jason Alicea at Caltech with theorists at Université Paris-Saclay and the Technical University of Munich. Caltech's announcement is the source for the framing below. The underlying measurements appear in the peer-reviewed paper.
What conformal field theory predicts
CFTs describe the universal behavior of systems at quantum critical points, where microscopic details drop away and low-energy excitations follow fixed scaling laws. John Cardy developed much of the modern framework for these finite-size spectra roughly 40 years ago. The Ising CFT and the tricritical Ising CFT are textbook examples. They predict precise ratios between the energy levels, or rungs, of the low-lying excitation ladder.
Testing those ratios in a real quantum system is hard. You need to place the system exactly at a quantum phase transition, probe it without destroying the state, and resolve the discrete energy levels. Classical numerical methods struggle as the system grows, which is where a programmable quantum simulator becomes useful.
The measurement technique
The Caltech team trapped strontium atoms in one-dimensional chains using optical tweezers and tuned laser Rabi frequencies and detunings to sit at quantum critical points. They then applied many-body modulation spectroscopy: a weak periodic modulation of the global laser drive swept through a range of frequencies, and the researchers measured the collective response. Peaks in the response correspond to transitions between quantized energy levels.
The method resolved low-energy level ratios consistent with Ising and tricritical Ising CFT predictions. The team also used individual atom addressing to sort excitations by reflection parity and applied site-dependent boundary detunings. By changing the boundary conditions, they shifted the observed spectrum in the way the CFT predicts for different fixed-point boundary states.
Why the result matters
The experiment is a direct test of universal predictions from statistical mechanics and high-energy physics in a engineered quantum system. It also gives physicists a new diagnostic tool. Modulation spectroscopy lets them characterize unknown quantum phase transitions by matching measured spectra to CFT predictions, even in regimes where classical simulation is impractical.
The result is a physics milestone, not a computing benchmark. It does not advance qubit counts, gate fidelities, or commercial applications. It does show that a neutral-atom simulator produces data precise enough to confront theoretical predictions from CFTs, a step that matters for both quantum simulation as a field and for the use of quantum hardware to study strongly correlated matter.
The paper is available open access in Nature, and Caltech published its own summary. For context on how quantum simulators compare with programmable gate-model computers, see our quantum simulators comparison and our hardware overview.