Physicists at Caltech have performed the first direct experimental measurement of energy levels predicted by two conformal field theories, the Ising and tricritical Ising models, using a quantum simulator built from neutral atoms. The work, published in Nature, was a collaboration between the experimental group of Manuel Endres, professor of physics, the theory group of Jason Alicea, William K. Davis Professor of Theoretical Physics, and theorists at Université Paris-Saclay and the Technical University of Munich.
Conformal field theories describe universal behavior that emerges when a quantum system sits at a critical point between two phases, such as the transition between ordered and disordered magnetic states. Unlike thermal phase transitions like boiling water, these quantum transitions are driven by quantum effects at temperatures near absolute zero. For four decades, theorists have calculated the precise ratios between the discrete energy levels, or "rungs," that appear at these critical points, but experimental verification had remained out of reach.
The quantum simulator consisted of a one-dimensional chain of up to 35 strontium atoms trapped by optical tweezers—focused laser beams that hold individual atoms in place. The researchers excited the atoms into high-energy Rydberg states, causing strong interactions that made the chain behave as a single quantum entity. By tuning laser parameters, they positioned the system at the critical points described by the Ising and tricritical Ising theories.
To measure the energy ladder, the team developed a technique called many-body modulation spectroscopy. They gently modulated the trapping lasers at varying frequencies, effectively shaking the atomic chain, and measured the system's response. Sharp spikes in the response revealed the discrete energy levels, analogous to finding the resonant frequencies of a wine glass by running a wet finger along its rim.
The measured spectra for chains of different lengths collapsed onto a single universal curve when rescaled, matching the Ising conformal field theory predictions. At the tricritical point, the team observed the lowest energy levels in the distinct ratios predicted by the tricritical Ising theory. Because each atom in the array can be individually controlled, the researchers could also sort excitations by symmetry, revealing a second family of energy levels hidden in the initial measurement, and modify boundary conditions to produce different spectral patterns also predicted by the theory.
The experiment demonstrates that quantum simulators originally developed for quantum computing can now address fundamental questions in physics. The Endres lab recently achieved a milestone of trapping 6,100 atoms in a single array, and the team plans to extend their studies to two-dimensional arrays where conformal field theories are less understood. "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 said.
The study was funded by the U.S. Department of Energy, the National Science Foundation, 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.
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