Scientists have directly measured, for the first time, the energy levels of quantum matter predicted by two conformal field theories. The experiment confirmed universal patterns that describe the behavior of quantum systems at a critical point — a state of transition between two phases.
The study was conducted by an international team of physicists from the California Institute of Technology (Caltech), Université Paris-Saclay, and the Technical University of Munich.
The scientists used a quantum simulator based on strontium atoms held in optical tweezers by lasers.
In ordinary phase transitions, such as the boiling of water or the demagnetization of a material, different materials can begin to follow the same mathematical laws. This property is known as universality: the details of a system’s microscopic structure cease to be decisive, while its behavior is determined by a small number of key parameters.
Conformal field theory is used to describe this type of universality in quantum systems.
In the new experiment, the researchers tested the predictions of two versions of this theory — the Ising theory and the tricritical Ising theory.
To do this, the scientists arranged a chain of strontium atoms and used lasers to transfer them into high-energy Rydberg states. In this state, neighboring atoms interact very strongly, causing the entire chain to behave as a single quantum system.
The researchers then adjusted the parameters of the laser field so that the system reached a critical point.
Unlike conventional phase transitions, this transition is determined not by temperature but by quantum effects and occurs at temperatures close to absolute zero.
At the critical point, the system can be excited by laser irradiation, transferring it to specific energy levels. Conformal field theory predicts precise relationships between these levels, but they had not previously been measured directly in an experiment.
For the measurements, the team used a new technique called many-body modulation spectroscopy.
The researchers periodically varied the parameters of the laser field at a specific frequency and measured the response of the entire chain of atoms. When the frequency of the applied modulation matched one of the system’s natural frequencies, its response became stronger.
By systematically varying the frequency, the researchers were able to reconstruct the structure of the energy levels.
The experiments were performed using chains containing up to 35 atoms. After scaling the results to account for the size of the system, the measured spectra matched a single universal curve predicted by the conformal field theory of the Ising model.
The researchers then moved the system to a tricritical point and measured its lowest energy levels. The relationships between these levels matched the predictions of the tricritical Ising theory.
The capabilities of the quantum simulator allowed the researchers to conduct additional measurements. Because individual atoms can be controlled independently, the scientists were able to separate excitations according to their symmetry and identify an additional group of energy levels.
By changing the state of the atoms at the ends of the chain, they also altered the structure of the spectrum and obtained different configurations predicted by the tricritical Ising theory.
In the future, the researchers plan to move from one-dimensional chains to two-dimensional arrays of atoms. Conformal field theory in two dimensions is much less thoroughly understood, so such experiments could make it possible to investigate quantum systems for which precise theoretical predictions are not yet available.