Researchers at Caltech have conducted the first experimental measurements of energy levels in quantum systems described by conformal field theory, confirming predictions made approximately four decades earlier. The study, published in Nature, represents a collaboration between Caltech’s experimental and theoretical physics groups alongside international partners at Université Paris-Saclay and the Technical University of Munich.
The research focused on two specific conformal field theories: the Ising and tricritical Ising models, which describe universal behaviors that emerge when quantum systems reach critical transition points between different states. Unlike conventional phase transitions driven by temperature changes, these quantum transitions occur at temperatures near absolute zero and are generated entirely by quantum mechanical effects such as entanglement and superposition. At these critical points, the energy levels available to the system form what researchers describe as a ladder structure with rungs positioned at specific, predictable intervals.
To conduct their measurements, the team employed quantum simulators—specialized devices designed to reproduce particular quantum behaviors more simply than general-purpose quantum computers. The experimental setup utilized arrays of neutral strontium atoms trapped and manipulated using optical tweezers, focused laser beams that can hold individual atoms in place. The researchers excited these atoms to highly energetic states known as Rydberg states, where neighboring atoms interact very strongly and cause the entire chain to behave as a collective system rather than individual particles.
The team developed a technique called many-body modulation spectroscopy to detect the hidden energy levels. By gently disturbing the atomic chains at various frequencies and measuring the strength of the system’s response, researchers identified the distinct energy rungs predicted by theory. Testing on chains of up to thirty-five atoms confirmed that the measured energy ratios matched theoretical predictions precisely, with the results collapsing onto a universal curve when adjusted for size. The researchers also validated measurements for the tricritical Ising theory by observing its predicted energy ratios at different transition points.
Looking forward, the research team plans to expand their investigations to two-dimensional arrays of atoms rather than single chains. This expansion could enable study of quantum systems whose behavior cannot yet be calculated with precision using conventional mathematical methods, potentially addressing problems beyond the capabilities of classical computers.
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