Algebraic law of local correlations in a driven Rydberg atomic system

Understanding the mechanism behind the buildup of inner correlations is crucial for studying nonequilibrium dynamics in complex, strongly interacting many-body systems. Here we investigate both analytically and numerically the buildup of antiferromagnetic (AF) correlations in a dynamically tuned Ising model with various geometries, realized in a Rydberg atomic system. Through second-order Magnus expansion (ME), we demonstrate quantitative agreement with numerical simulations for diverse configurations including $2 \times n$ lattice and cyclic lattice with a star. We find that the AF correlation magnitude at fixed Manhattan distance obeys a universal superposition principle: It corresponds to the algebraic sum of contributions from all shortest paths. This superposition law remains robust against variations in path equivalence, lattice geometries, and quench protocols, establishing a new paradigm for correlation propagation in quantum simulators.

💡 Research Summary

In this work the authors investigate how antiferromagnetic (AF) correlations emerge and spread in a driven Rydberg‑atom quantum simulator that realizes a tunable Ising model with spatially inhomogeneous interactions. The physical platform consists of single‑atom optical tweezers loaded with ^87Rb atoms. Two‑photon excitation couples the hyperfine ground state |g⟩ to a high‑lying Rydberg state |r⟩ while a far‑detuned intermediate level |e⟩ is adiabatically eliminated, yielding an effective two‑level system with controllable Rabi frequency Ω(t) and two‑photon detuning δ(t). The atoms interact via van‑der‑Waals forces U_{ij}∝1/r_{ij}^6, which generate a blockade radius R_b that prevents simultaneous excitation of nearby atoms. The resulting Hamiltonian is that of a transverse‑field Ising model with a longitudinal field: H(t)=Ω(t)∑i σ_i^x−δ(t)∑i n_i+∑{⟨ij⟩}U{ij} n_i n_j, where n_i=(σ_i^z+1)/2.

To describe the non‑equilibrium dynamics during a finite‑time quench, the authors employ the Magnus expansion (ME). Under the convergence condition ∫_0^T‖H(t)‖dt<π, the time‑evolution operator can be written as U(T)=exp