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This AI image shows a chain of strontium atoms (orange), each held in an optical tweezer (blue cones). The chain sits within a modulated laser field. The evenly spaced lines above represent the ladder of excitation energies predicted by conformal field theory, whose rungs the team measured.
Image Credit: AI-generated artwork by Stephan Naus
Scientific Frontline: Extended "At a Glance" Summary: Conformal Field Theories in Quantum Matter
The Core Concept: Researchers have successfully used quantum simulators to directly measure the specific energy levels in synthetic quantum matter, confirming decades-old predictions of universal mathematical patterns described by conformal field theories.
Key Distinction/Mechanism: Unlike typical phase transitions driven by temperature (like water boiling), this study focused on quantum phase transitions occurring near absolute zero. By trapping strontium atoms with optical tweezers, researchers created a chain of interacting atoms that behaved as a single entity. They then used a new technique, "many-body modulation spectroscopy," to gently vibrate this atomic chain, effectively mapping its precise, ladder-like energy states.
Origin/History: The underlying mathematical frameworks have been used by theoretical physicists for over forty years to calculate these exact energy ratios, but this marks the first time they have been directly measured and confirmed in a physical experiment. The foundation of this work relates to the Ising model, developed in the 1920s to describe magnetism.
Major Frameworks/Components:
- Conformal Field Theory: The broad mathematical framework used to describe "universality," where different materials transitioning between phases behave identically, losing their unique microscopic details.
- Ising and Tricritical Ising Conformal Field Theories: Specific models of conformal field theory whose predicted energy spectra were tested and confirmed in this study.
- Quantum Simulators: Simplified quantum computers designed for specific tasks, in this case, utilizing arrays of neutral strontium atoms trapped by optical tweezers.
- Rydberg States: High-energy atomic states used to force strong interactions between the neighboring atoms in the chain.
- Many-Body Modulation Spectroscopy: The novel measurement technique developed to read out the energy levels by modulating the lasers and measuring the atoms' collective response.
Branch of Science: Quantum Physics, Condensed Matter Physics, Theoretical Physics.
Future Application: The techniques developed can be applied to larger, two-dimensional atomic grids where conformal field theories are not yet fully understood. Ultimately, this approach will allow scientists to probe complex quantum systems whose behavior is unknown and beyond the computational limits of classical computers.
Why It Matters: This research provides the first direct experimental verification of fundamental theories that have governed theoretical physics for decades. It demonstrates that quantum simulators, originally developed for computing, are now sophisticated enough to act as powerful tools for discovering and testing fundamental physics.
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| Stephen Naus explains the theory behind the experiment. Photo Credit: Caltech/Gyohei Nomura |
When different materials transition from one phase to another, such as water coming to a boil or a magnet losing its ability to attract metals, something remarkable can happen: they begin to behave identically, following the same mathematical rules. "Physicists call this trait universality—the messy, microscopic details wash out, and only a few essential features survive," explains Jason Alicea, William K. Davis Professor of Theoretical Physics. The math underlying these universal traits is commonly described by a theoretical framework called conformal field theory.
Reporting in the journal Nature, a collaboration between the experimental group of Caltech's Manuel Endres, professor of physics, and Alicea's theory group, together with theorists at Université Paris-Saclay and the Technical University of Munich, performed first-of-their-kind experiments on two different conformal field theories using quantum simulators, which are simplified versions of quantum computers tailored for specific tasks.
Using new technology developed for these quantum simulators, the team reports the first direct measurement of energy levels in synthetic quantum matter as predicted by the Ising and tricritical Ising conformal field theories. (Ising refers to Ernst Ising, a physicist who, in the 1920s, solved an early model of magnetism.) Both theories describe universal behavior that emerges when a quantum system—exhibiting exotic traits such as entanglement and superposition—is placed at a tipping point between two states, one of which is more ordered than the other.
Unlike transitions familiar from everyday life, such as water turning into steam, this one is driven not by temperature but by quantum effects alone that happen to take place at temperatures near absolute zero. Once at that tipping point, the system can be excited by lasers to reach a series of specific energies, like the rungs of a ladder. "The energy levels predicted by these theories are important because they encode profound information about the theories themselves," Alicea says.
For four decades, researchers used conformal field theories to calculate the spacings between those rungs, which come in precise ratios, but nobody had measured them in an experiment until now.
"Our new tools borrow from quantum computing platforms," says Xiangkai Sun, a co-lead author of the new study and a graduate student working in the Endres lab. "Over the past ten years, people have been learning to control these systems, and now we are at the point where we can use them to do fundamental physics research."
The quantum system in the study is based on platforms the Endres lab uses to build quantum computers: arrays of neutral atoms trapped by lasers called optical tweezers. A related neutral-atom platform in the lab recently set a milestone by trapping 6,100 atoms in a single array. Though the tweezer technology behind these arrays was developed largely with quantum computing in mind, in the new study, the team turned it toward a question in fundamental physics.
For the experiment, the researchers used optical tweezers to trap strontium atoms in a line. They used other lasers to excite the atoms into high-energy states called Rydberg states, a process that causes neighboring atoms to interact strongly. The chain of atoms then behaved as a single entity rather than as independent particles. Next, the researchers tuned the lasers in a way that placed the chain at the tipping point.
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| Left to right: Yuan Le, Xiangkai Sun, Jason Alicea, Manuel Endres, Stephen Naus, and Richard Bing-Shiun Tsai in the Endres lab at Caltech. Photo Credit: Caltech/Gyohei Nomura |
To read out the energy ladder, the team applied a new tool developed for these studies called many-body modulation spectroscopy. In this approach, the researchers gently shook the entire chain by modulating the lasers at a chosen frequency and then measured how strongly the atoms responded. By sweeping through frequencies and noting where the response spiked, the team was able to map out the rungs of the ladder. The method is similar to running a wet finger around the rim of a wineglass: at the right speed, the glass resonates with sound, and at the wrong speed, nothing happens.
"We repeated the experiment on chains of up to thirty-five 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," Sun says. "We then tuned to the tricritical point and measured the lowest levels of its distinct spectrum, which came out in the different ratios the theory predicts."
Because every atom in the array can be addressed individually, the team could also do things that are far harder using traditional materials. They sorted the excitations according to their symmetry, revealing a second family of rungs hidden from the first measurement. And by adjusting the atoms at the two ends of the chain, they changed how the ladder was arranged—each setting produced a different pattern that the tricritical Ising theory predicts.
"Even though we believed these theories to be true, it's important to have an experimental realization, something you can poke and prod," Alicea says. "To see those predictions borne out is a beautiful thing."
In the future, the team plans to use an even larger quantum system to study conformal field theories using not just atoms in a line but also atoms in a grid. "In two dimensions, the conformal field theories are not as well understood, so this is an exciting opportunity," Sun says.
"What excites me is that the technique doesn't require knowing the answer in advance. Here, we could check our measurements against exact predictions," Endres says. "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."
Funding: by the US Department of Energy, including its Quantum Systems Accelerator and its Quantum Science Center; the National Science Foundation, including the Institute for Quantum Information and Matter at Caltech (IQIM); 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.
Published in journal: Nature
Title: Observation of conformal field theory spectra in a quantum simulator
Authors: Xiangkai Sun (孙向恺), Yuan Le (乐媛), Stephen Naus, Richard Bing-Shiun Tsai, Lewis R. B. Picard, Sara Murciano, Michael Knap, Jason Alicea, and Manuel Endres
Source/Credit: California Institute of Technology | Whitney Clavin
Edited by: Scientific Frontline
Reference Number: qs081926_01
