Experimental observation of conformal field theory spectra

Conformal field theories (CFTs) govern emergent universal properties of systems tuned to quantum phase transitions, including their entanglement, correlations, and low-energy excitation spectra. Much of the rich structure predicted by CFTs nevertheless remains unexplored in experiment. In this talk, I will present direct observations of the excitation-energy spectra in programmable Rydberg atom arrays and their theoretical interpretation in terms of emergent CFTs. The experiment specifically utilizes a newly developed modulation spectroscopy technique to resolve the finite-size excitation spectrum for Rydberg chains tuned to quantum phase transitions in both Ising and tricritical Ising universality classes. The measured energy spectra are consistent with universal ratios predicted by the underlying CFTs; moreover, for tricritical chains local control enables inducing a transition between distinct CFT spectra associated with different fixed-point boundary conditions. This work not only probes detailed emergent CFT features in an analog quantum simulator, but also provides a technique for diagnosing a priori unknown universality classes in future experiments.