Experimental observation of conformal field theory spectra

TL;DR

This study experimentally observes the energy spectra of emergent conformal field theories at quantum phase transitions in Rydberg chains, revealing universal ratios and spectral features characteristic of Ising and tricritical Ising CFTs.

Contribution

Developed a modulation technique to resolve finite-size spectra and distinguish CFT spectra in Rydberg chains at quantum critical points, enabling direct experimental observation of CFT features.

Findings

Resolved finite-size spectra of Rydberg chains at criticality.

Identified universal energy ratios characteristic of Ising and tricritical Ising CFTs.

Demonstrated control over excitation parities and boundary conditions.

Abstract

Conformal field theories (CFTs) feature prominently in high-energy physics, statistical mechanics, and condensed matter. For example, 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 unobserved in experiment. Here we directly observe the energy excitation spectra of emergent CFTs at quantum phase transitions -- recovering universal energy ratios characteristic of the underlying field theories. Specifically, we develop and implement a modulation technique to resolve a Rydberg chain's finite-size spectra, variably tuned to quantum phase transitions described by either Ising or tricritical Ising CFTs. We also employ local control to distinguish parities of excitations under reflection and, in the tricritical Ising chain, to induce transitions between distinct CFT spectra associated with changing boundary conditions. By utilizing a variant of the modulation technique, we furthermore study the dynamical structure factor of the critical system, which is closely related to the correlation of an underlying Ising conformal field. Our work not only probes the emergence of CFT features in a quantum simulator, but also provides a technique for diagnosing a priori unknown universality classes in future experiments.