“Physicists call this property universality: the messy, minute details are washed away, and only a few important features survive,” explains Jason Alicia, the William K. Davis Professor of Theoretical Physics.

Physicists often use a mathematical framework known as conformal field theory to describe this universal behavior. Now, researchers have used a quantum simulator to directly measure energy levels predicted by two different conformal field theories: Ising and tricritical Ising theory.

Quantum simulator tests fundamental physics

In a study published in Nature, researchers conducted the first experiments of their kind on two conformal field theories. These specialized quantum systems are simpler than general-purpose quantum computers and are designed to reproduce specific types of quantum behavior.

The collaboration brought together the experimental group of physics professor Manuel Endres at the California Institute of Technology, Alicia’s theoretical group, and theorists from the Universities Paris-Saclay and the Technical University of Munich.

Using newly developed quantum simulator technology, the researchers directly measured the energy levels of synthetic quantum materials predicted by Ising and tricritical Ising conformal field theory. The name Ising refers to physicist Ernst Ising, who developed an early model of magnetism in the 1920s.

Both theories describe universal behavior that emerges when a quantum system with unusual properties, such as entanglement or superposition, reaches a critical point between two states—one more ordered than the other.

A quantum tipping point near absolute zero

Unlike ordinary phase transitions, such as water changing into vapor, this transition is not caused by temperature. Instead, it arises entirely from quantum effects at temperatures close to absolute zero.

At the critical point, a laser can excite the system into a set of specific energy states. Researchers compare these energy levels to rungs on a ladder.

“The energy levels predicted by these theories are important because they encode deep information about the theory itself,” Alicia says.

For about 40 years, physicists have used conformal field theory to calculate the spacing between these energy levels. The levels are expected to appear in precise proportions, but those predictions had never been directly measured before this experiment.

“Our new tool borrows from quantum computing platforms,” says Xiangkai Sun, co-lead author of the study and a graduate student working in the Endres laboratory. “Over the past decade, people have learned how to control these systems and are now at a point where they can be used to conduct fundamental physics research.”

Trapping atoms with laser light

The experiment used technology that the Endres laboratory also applies to quantum computing. The system relies on an array of neutral atoms held in place by tightly focused lasers known as optical tweezers.

A related neutral-atom platform in the laboratory recently reached a milestone by trapping 6,100 atoms in a single array.

Although optical-tweezer arrays were developed primarily for quantum computing, researchers are also using the technology to investigate fundamental questions in physics.

The researchers used optical tweezers to align strontium atoms. An additional laser then pushed the atoms into highly excited energy levels known as Rydberg states, in which neighboring atoms interact very strongly.

These interactions caused the chains of atoms to behave collectively rather than as individual particles. The researchers then tuned the laser until the entire system reached the critical point they wanted to study.

Measuring the hidden quantum energy ladder

To detect the predicted energy levels, the researchers developed a technique called multibody modulation spectroscopy.

They gently disturbed the entire atomic chain by changing the laser at a specific frequency and measured how strongly the atoms responded. By scanning many frequencies and looking for peaks in the response, the researchers identified different energy levels.

The basic idea is similar to running a wet finger along the rim of a wine glass. When the movement matches the glass’s natural frequency, the glass resonates and produces sound. At most other frequencies, it does not.

“When we repeated the experiment with chains of up to 35 atoms, we obtained horizontal lines as predicted by Ising conformal field theory. When we rescaled the size, the spectra fit into a single universal curve,” Sun says. “We then tuned to the tricritical point and measured the lowest levels of its characteristic spectrum, which appeared in different proportions as predicted by theory.”

Hidden patterns emerge from individual atoms

Because scientists can control each atom individually, they can perform measurements that would be much more difficult with traditional materials.

The researchers classified the excitations according to their symmetry, revealing a second set of energy rungs that had been hidden in the initial measurements.

They also changed the behavior of the atoms at each end of the chain. This rearranged the energy ladder and produced different patterns consistent with predictions from tricritical Ising theory.

“We believed these theories were true, but it’s important to have experimental awareness—something you can poke and prod at,” Alicia says. “It’s great to see these predictions come true.”

Expanding quantum simulation into new territory

The researchers now plan to expand their experiments to larger quantum systems. Instead of arranging atoms only in a row, they also want to study grids of atoms.

“This is an interesting opportunity because in two dimensions, conformal field theory is poorly understood,” Sun says.

These experiments could help scientists investigate quantum systems whose behavior cannot yet be calculated precisely, including problems that may be too difficult for classical computers.

“What excites me is that with this technology you don’t need to know the answer in advance; here you can check measurements against accurate predictions,” Endres says. “The next step is to direct this toward systems where no one knows quantitatively the response of the system—systems that include areas that classical computers cannot reach.”

Study details and authors

The study, “Observing conformal field theory spectra in quantum simulators,” was published in Nature. It received funding from the U.S. Department of Energy, including the Quantum Systems Accelerator and the Center for Quantum Science; the National Science Foundation, including the Institute for Quantum Information and Materials (IQIM) at the California Institute of Technology; 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 German Compulsory Educational Institution.

Other Caltech authors include Yuan Le, Stephen Naus, Richard Bing-Shiun Tsai, and Lewis Picard, who currently works at Caltech-affiliated startup Oratomic. Additional authors are Sara Murciano of the University of Paris-Saclay, formerly a postdoctoral fellow at the California Institute of Technology, and Michael Knapp of the Technical University of Munich and the Munich Center for Quantum Science and Technology.