The (PXP)$^2$ model: long-range quantum scars in optical cavities

TL;DR

The paper introduces a minimal, scalable (PXP)^2 model for Rydberg atoms in an optical cavity by projecting to the strong Rydberg blockade subspace and adiabatically eliminating the cavity field. It reveals three equilibrium phases—paramagnetic, Néel, and a blockaded ferromagnetic/superradiant phase—and demonstrates long-range quantum many-body scars with logarithmic entanglement growth, bridging PXP scar physics and Dicke-type long-range interactions. The authors develop a soft-spin field theory to capture low-energy excitations and provide numerical analysis of ground-state properties, excitations, and non-equilibrium dynamics, including scar-induced slow thermalization and resonance-driven entanglement peaks. They also discuss experimental feasibility with realistic Rydberg-dressing and cavity-coupling parameters, outlining directions for higher-dimensional implementations and robust observations of non-thermal dynamics in cavity–Rydberg platforms.

Abstract

Rydberg-cavity systems are emerging as promising platforms for quantum simulation and quantum information processing. These hybrid architectures combine two complementary interaction mechanisms: cavity photons mediate collective long-range couplings, while Rydberg excitations generate strong short-range interactions. Together, they offer a setting for engineering many-body phases characterized by a hierarchy of interactions across widely different length scales. In this work, we introduce a minimal and scalable model for such systems. Focusing on the strong Rydberg blockade regime, we restrict the Hilbert space to the subspace enforced by the blockade, yielding a kinetically constrained long-range model in one spatial dimension. This approach both captures the physics of Rydberg-cavity experiments in the regime of strong Rydberg interactions and provides a conceptually transparent framework for studying the interplay of long-range and short-range interactions. At equilibrium, in addition to paramagnetic and Néel-ordered phases, the system supports a blockaded ferromagnetic/superradiant phase, distinct from the conventional superradiant phase. Out of equilibrium, we identify long-range quantum many-body scars, which are atypical nonthermal eigenstates that evade the eigenstate thermalization hypothesis, and giving rise to slow entanglement growth. In contrast to the linear-in-time entanglement growth characteristic of short-range scarred models, these long-range scars exhibit logarithmic entanglement dynamics. Our results establish a minimal yet versatile framework for Rydberg-cavity systems, and provide a stepping stone for future theoretical and experimental studies of this frontier platform in quantum many-body physics.

Figures (7)

• Figure 1: Schematics of the model. A chain of two-level atoms is placed inside an optical cavity and suspended by optical tweezers (yellow shades). The cavity mode (red shade) mediates long-range interactions that generate hybridization between atomic ground and excited states across the chain (red wavy line). In addition, atoms experience short-range Rydberg interactions that energetically penalize configurations with simultaneously excited nearest neighbors (blockade). The interplay of short-range and long-range interactions leads to distinct physics, both in and out-out equilibrium.
• Figure 2: Ground state behavior of the (PXP)$^2$ model. (a) Ground state half-cut entanglement entropy, in the absence (blue) and presence (orange) of small symmetry breaking fields. The peaks in the latter show phase transition points. (b) Staggered magnetization (black) and uniform magnetization (red), showing three different phases depending on the value of the field $\Delta$. Dashes show the maximum magnetization possible for a classical state in presence of blockade. Data have been obtained for a chain of 20 spins.
• Figure 3: Spectrum of the low-energy excitations for different values of $\Delta$, for a chain of 24 spins. The discontinuity at $k=0$ is due to the long-range cavity-induced interaction, with a vanishing gap at $\Delta \approx 0.8$, signaling a second-order transition to a FM ground state. The $k=\pi$ mode becomes gapless at $\Delta\approx -0.6$, where the ground state transforms to a Néel ordered state.
• Figure 4: Dispersion of excitations in the paramagnetic phase and close to the FM transition, obtained from the soft-spin approximation for a chain of 24 spins.
• Figure 5: (a) and (b), the overlap between the Néel state and the eigenstates of the Hamiltonian for $\Delta=0$ and $\Delta=-0.2$, showing the presence of scars in the spectrum. (c) Energy level statistics in the zero-momentum and inversion-symmetric subspace, compared to Poisson, Wigner-Dyson, and semi-Poisson distributions. (d) Correlation dynamics for $\ket{\psi_0}=\ket{Z_2}$. The long-time persistence of staggered magnetization for $\Delta=0$ is due to the overlap of the initial state with scars. $L=30$ for (a)-(c) and $28$ for (d).