“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 at Caltech, who has been instrumental in the theoretical underpinnings of this research. This universal behavior is often elegantly described by a powerful mathematical framework known as conformal field theory (CFT). CFT provides a language to articulate these shared behaviors across diverse physical phenomena, offering a glimpse into the deep, underlying connections in the universe.

In a groundbreaking study published in the prestigious journal Nature, a collaborative team of researchers has achieved a remarkable feat: the first experimental validation of two distinct conformal field theories using sophisticated quantum simulators. These specialized systems, far from being general-purpose quantum computers, are meticulously engineered to precisely replicate and study particular quantum behaviors, making them ideal probes for fundamental physics.

The success of this ambitious endeavor is a testament to interdisciplinary collaboration, bringing together the experimental prowess of Manuel Endres, professor of physics at Caltech, Alicea’s insightful theoretical group, and distinguished theorists from Université Paris-Saclay and the Technical University of Munich. This fusion of experimental ingenuity and theoretical depth was crucial in tackling a problem that had eluded direct measurement for so long.

Leveraging newly developed quantum simulator technology, the researchers have achieved the first direct measurements of energy levels within synthetic quantum matter that were predicted by the Ising and tricritical Ising conformal field theories. The Ising theory, named after physicist Ernst Ising who made seminal contributions to magnetism in the 1920s, and its tricritical counterpart, describe universal behavior that emerges when a quantum system, imbued with exotic properties like entanglement and superposition, approaches a critical point. This critical point represents a delicate balance between two distinct states, where one state is more ordered than the other.

A Quantum Tipping Point Near Absolute Zero: Beyond Thermal Transitions

Crucially, the transition observed in these experiments is not driven by temperature, unlike familiar phase transitions such as water turning into steam. Instead, this quantum tipping point is entirely governed by quantum mechanical effects, occurring at temperatures chillingly close to absolute zero. At this precise critical juncture, the system becomes exquisitely sensitive, and precisely tuned lasers can excite it into a discrete sequence of specific energy states. The researchers aptly compare these distinct energy levels to the rungs of a ladder, representing a quantized energy landscape.

“The energy levels predicted by these theories are important because they encode profound information about the theories themselves,” Alicea emphasizes, highlighting the fundamental significance of these measurements. For approximately four decades, physicists have relied on conformal field theories to theoretically predict the spacing and ratios between these energy rungs. While these predictions were widely accepted as accurate, they had remained elusive to direct experimental verification until this pivotal experiment.

“Our new tools borrow from quantum computing platforms,” states Xiangkai Sun, a co-lead author of the study and a graduate student in the Endres lab. “Over the past 10 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.” This statement underscores the rapid advancement in quantum control technologies, which have now matured to the point of enabling unprecedented investigations into fundamental physical principles.

Trapping Atoms with Lasers: Building the Quantum Playground

The experimental setup builds upon the cutting-edge technology that the Endres lab is also developing for future quantum computers. The system ingeniously utilizes arrays of neutral atoms, meticulously held in place by tightly focused lasers, often referred to as optical tweezers. These optical tweezers act as microscopic traps, allowing for the precise arrangement and manipulation of individual atoms. This builds on related advancements in neutral atom platforms, with one such system recently achieving the remarkable feat of trapping an astonishing 6,100 atoms in a single array.

While the primary motivation behind the development of optical tweezer arrays has often been quantum computing, the researchers here ingeniously repurposed this technology to address a fundamental question in physics. They arranged strontium atoms in a linear configuration using optical tweezers. Subsequently, additional lasers were employed to elevate these atoms into highly excited energy levels known as Rydberg states. In these Rydberg states, the atoms exhibit exceptionally strong interactions with their neighbors, leading to collective quantum behavior.

These strong interactions transformed the chain of individual atoms into a cohesive quantum entity, behaving as a unified system rather than a collection of disparate particles. The researchers then meticulously adjusted the lasers, carefully guiding the entire system towards the critical tipping point that was the focus of their investigation.

Measuring a Hidden Energy Ladder: Spectroscopy in the Quantum Realm

To precisely detect the predicted energy levels, the research team developed an innovative technique called many-body modulation spectroscopy. This method involves gently perturbing the entire atomic chain by subtly altering the laser frequencies at a specific rate. The researchers then meticulously measured the strength of the atoms’ response to these perturbations. By systematically scanning through a wide range of frequencies and identifying peaks in the response, they were able to discern and map out the distinct energy levels.

The underlying principle of this technique is analogous to the familiar phenomenon of resonance. Imagine running a wet finger around the rim of a wine glass. When the motion of your finger matches the glass’s natural resonant frequency, the glass vibrates and produces a distinct sound. At other frequencies, the response is minimal. Similarly, in their experiment, specific frequencies of laser perturbation elicited strong responses from the atomic system, indicating the presence of distinct energy states.

“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,” Sun proudly reports. “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 remarkable agreement between experimental measurements and theoretical predictions for both Ising and tricritical Ising theories provides compelling evidence for the validity of these fundamental concepts.

Hidden Patterns Emerge from Individual Atoms: Unveiling Deeper Structures

A key advantage of their quantum simulator approach was the ability to control each atom individually. This level of precision enabled them to perform measurements that would be exceedingly difficult, if not impossible, with conventional materials. By manipulating individual atoms, the team was able to classify the excitations based on their symmetry, revealing a second set of energy rungs that had been hidden within the initial broader spectral measurements.

Furthermore, the researchers demonstrated the system’s versatility by deliberately altering the behavior of the atoms at the ends of the atomic chain. This manipulation effectively rearranged the energy ladder, generating different spectral patterns that precisely matched the predictions of the tricritical Ising theory.

“Even though we believed these theories to be true, it’s important to have an experimental realization, something you can poke and prod,” Alicea states with evident satisfaction. “To see those predictions borne out is a beautiful thing.” This sentiment reflects the profound scientific satisfaction that comes from bridging the gap between abstract theory and tangible experimental observation.

Pushing Quantum Simulations into New Territory: The Future of Exploration

Emboldened by this success, the researchers are already planning to expand their experiments to larger and more complex quantum systems. Instead of confining atoms to a linear arrangement, they aspire to study them in two-dimensional grids.

“In two dimensions, the conformal field theories are not as well understood, so this is an exciting opportunity,” Sun remarks, pointing towards the vast uncharted territory of theoretical physics that can now be explored experimentally. Studying these 2D systems could unlock new insights into quantum phenomena that are currently beyond the reach of precise theoretical calculation, potentially including problems that are intractable for even the most powerful classical computers.

“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 explains. “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.” This forward-looking perspective highlights the transformative potential of quantum simulation as a tool for scientific discovery, enabling exploration into realms previously inaccessible.

The groundbreaking Nature study, titled "Observation of conformal field theory spectra in a quantum simulator," received crucial funding from a consortium of esteemed organizations, including the U.S. Department of Energy (through its Quantum Systems Accelerator and 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.

The collaborative effort involved several other talented individuals from Caltech, including Yuan Le, Stephen Naus, Richard Bing-Shiun Tsai, and Lewis Picard, who is now contributing to the Caltech-linked startup Oratomic. Additional authors on the paper include Sara Murciano from Université Paris-Saclay, who was previously a postdoctoral scholar at Caltech, and Michael Knap from the Technical University of Munich and the Munich Center for Quantum Science and Technology. This wide-ranging collaboration underscores the global nature of cutting-edge scientific research.