Caltech Quantum Simulator Confirms 40-Year-Old Prediction

For four decades, physicists could calculate the exact spacing between certain energy levels in quantum matter but couldn’t measure them. Now, a Caltech team has finally done so, and their findings align perfectly with theoretical predictions.

The results, published in Nature in a peer-reviewed paper titled “Observation of conformal field theory spectra in a quantum simulator,” are a collaborative effort from Manuel Endres’s experimental group and Jason Alicea’s theory group, with contributions from Université Paris-Saclay and the Technical University of Munich. This achievement was realized through a real hardware experiment using trapped atoms.

Universality: When diverse systems behave identically

Consider heating water past its boiling point into steam, or a magnet past a critical temperature causing it to lose its magnetic pull. Despite the different materials and underlying physics, these tipping points exhibit identical mathematical behavior.

Physicists refer to this phenomenon as universality. At these critical junctures, microscopic complexities recede, leaving only a few defining characteristics. The framework that describes these persistent features is called conformal field theory. In this experiment, the specific versions explored are the Ising model and its more complex relative, the tricritical Ising model. The Ising model is named after Ernst Ising, who developed an early model of magnetism in the 1920s.

The experimental system operates at a quantum tipping point, driven by quantum effects near absolute zero. At this point, lasers can elevate the system through a series of distinct energy levels, much like rungs on a ladder. Conformal field theory accurately predicts the precise ratios between these energy rungs, which are predictions that remained untested for 40 years.

The wine glass trick, applied to atoms

The team measured these energy rungs by trapping strontium atoms in a line using optical tweezers, which are lasers that grasp and hold individual atoms in place. They then subjected the atoms to additional light, pushing them into Rydberg states. These are high-energy states that induce strong interactions between neighboring atoms and cause the chain to transition from a collection of separate particles to a single, interconnected entity.

To measure the energy rungs, they employed a novel technique called many-body modulation spectroscopy. They gently vibrated the entire chain by wobbling the lasers at a chosen frequency, then observed the atoms’ response strength. By sweeping across various frequencies and noting where the response spiked, the energy rungs became apparent.

Co-lead author Xiangkai Sun clearly articulated the significance of their findings:

“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.”

This process is analogous to running a wet finger around the rim of a wine glass: apply the correct speed, and the glass resonates; the wrong speed yields nothing. Similarly, the atoms resonate, and the pitches at which they resonate correspond to the energy rungs. This platform is related to the neutral-atom arrays developed in Endres’s lab for quantum computing, the same hardware family that recently set records for the number of atoms held in a single array.

Advantages of individual atom control over bulk materials

The ability to individually address each atom in the array provides a level of control unattainable with ordinary bulk materials.

By sorting excitations based on their symmetry, the team uncovered a second family of rungs that were initially hidden. They then precisely adjusted only the two atoms at the ends of the chain. Each adjustment produced a unique rung pattern, and each pattern consistently matched the predictions of the tricritical Ising theory for those specific boundary conditions. Such precise manipulation of a magnet’s endpoints is impossible, but here, the theory consistently held true.

This demonstrates the value of quantum simulation. A quantum simulator is a specialized quantum machine designed to address specific types of questions. This particular simulator answered a question about the fundamental structure of quantum phases, a domain where classical methods struggle to scale.

What this represents (and what it doesn’t yet)

This research unequivocally confirms established theory. The team meticulously compared their measurements with exact predictions, and the predictions proved accurate. No new physics was discovered here; physicists already believed these results, and now they have been experimentally observed.

The demonstrated scale involves one-dimensional chains of up to 35 atoms. The stated next step, according to Sun and Endres, is to extend this to two-dimensional grids, where conformal field theories are far less understood. Endres directly expressed the ambition: to apply this technique to systems “where nobody knows the response of the system quantitatively, including regimes that classical computers can’t reach.” This remains a future objective. The achievement of surpassing classical computational capabilities hasn’t yet occurred.

Related work on how simulators can surpass classical machines occupies this same frontier of ongoing research.

In summary: A clear experimental confirmation of previously unmeasured theory has been achieved using hardware developed for quantum computing. The aspiration for extending this beyond current limitations remains a future goal.