Direct tests of conformal symmetry with Rydberg atoms: assessment and proposals

Abstract

We propose a direct test of conformal symmetry using Rydberg-atom arrays. By arranging the atoms on a circle and measuring equal-time two-point correlation functions, the characteristic functional form predicted by conformal field theory can be tested directly. We estimate the number of experimental snapshots required to resolve this behavior with sufficient statistical precision. We further optimize the time-dependent ramp profile of the Rabi frequency~$Ω$ and detuning~$Δ$ used to prepare the target critical state adiabatically. The optimized profile achieves higher fidelity over much shorter evolution times than those employed in previous experiments. Taken together, these results suggest that a direct experimental test of conformal symmetry is feasible with current Rydberg-atom technology.

The paper asks whether current Rydberg-atom arrays can directly test emergent conformal symmetry through the spatial form of critical correlators, rather than through critical exponents alone. For a periodic Ising-critical chain, the proposed observable is the equal-time correlator $\langle s_i s_j\rangle\propto[2\sin(\pi|i-j|/N)]^{-1/4}$. Its finite-size dependence tests conformal constraints beyond an infinite-system power law. The paper also discusses boundary one-point functions and state–operator correspondence, including existing experimental tests. Numerical analysis focuses on $N=24$ atoms at two points on the Ising critical line: a near-blockade point used in previous experiments and a point with onsite $\mathbb Z_2$ symmetry. Exact diagonalization finds ground-state correlators matching the CFT shape, after normalization, within approximately $4\%$ and $1\%$, respectively, even at nearest-neighbor separation. Born-rule sampling with translation averaging gives statistical errors below $2.5\%$ from $2{,}000$ snapshots. Ramp schedules are optimized in a moving 20-state low-energy subspace and validated by full symmetry-reduced Schrödinger evolution. Near blockade, a $2.5\,\mu\mathrm{s}$ ramp achieves $99.18\%$ fidelity, compared with $99.04\%$ for a previous $7\,\mu\mathrm{s}$ schedule. At the symmetric point, $1.2\,\mu\mathrm{s}$ achieves $99.90\%$. Correlator errors from imperfect preparation are approximately $4\%$ or less for the reported optimized ramps. These fidelities assume coherent dynamics. Detailed decoherence simulations are not performed; reduced atomic motion and decay are inferred from shorter durations. Detection reliability away from blockade remains unresolved, and the quantitative demonstrations are restricted to the 24-site system.