The Robustness and Breakdown of Collective Physics in Cavity-coupled Rydberg Arrays

Abstract

Quantized optical cavities naturally mediate long-range and even all-toall interactions between atoms, offering a route towards quantum many-body regimes that are difficult to access in conventional condensed matter systems. Their initial response is typically collective, with the atoms coherently behaving as a macroscopic spin and exhibiting phenomena such as spin squeezing. However, recent work has shown that sufficiently strong cavity interactions can nevertheless drive these systems into highly entangled states with non-trivial local structure, including quantum spin liquids. How a state that initially responds collectively to an all-to-all interaction can evolve into one dominated by local quantum correlations, remains an important question. Focusing on Rydberg atom arrays coupled to a single-mode cavity, we first show that the collective regime is remarkably robust. Even with strong superextensive cavity couplings, finite-momentum correlations vanish in the thermodynamic limit leading to a purely collective description. We develop a nonlinear spin-wave theory that predicts how this collective regime can break down and local correlations build up, but only under an unusual rescaling of the cavity interaction. More broadly, this thesis also highlights the challenges of characterizing long-range interacting quantum systems with standard many-body approaches, such as perturbation theory. Developing new theoretical descriptions for these intrinsically non-local systems may open the way to discovering quantum phases and dynamics beyond those accessible in short-range systems.