Scalable spin-nematic squeezing in multi-level dipole-interacting Rydberg atom arrays

TL;DR

This paper demonstrates scalable spin-nematic squeezing and entanglement generation in three-level Rydberg atom arrays with dipolar interactions, advancing beyond qubit systems towards qudit entanglement.

Contribution

It introduces a theoretical framework for generating scalable entanglement in spin-1 systems with dipolar interactions, including new squeezing mechanisms and scaling laws.

Findings

Squeezing scales as N^{-2/3} for all-to-all interactions.

Quantum Fisher information scales as N^{2} in both interaction types.

Two-axis countertwisting yields enhanced squeezing in certain regimes.

Abstract

We study the generation of metrologically useful entanglement in a three-level (spin-1) system naturally realized in arrays of dipole-interacting Rydberg atoms confined in optical tweezers. In the spin-quadrupolar operator basis, the interaction Hamiltonian decomposes into effective SU(2) subspaces, within which quench dynamics from product initial states generate scalable spin-nematic squeezing. For symmetric interactions, we identify a mapping to effective one-axis twisting within bright and dark manifolds and demonstrate that the squeezing parameter scales as $\xi^{2}\propto N^{-2/3}$ ($\xi^{2}\propto N^{-0.5}$) with system size for all-to-all (two-dimensional dipolar) couplings. In both cases the quantum Fisher information reaches $F_Q\propto N^{2}$. For antisymmetric interactions supplemented by a microwave drive we find a distinct two-axis countertwisting mechanism. This results in squeezing $\xi^{2}\propto N^{-0.7}$ for all-to-all interactions and moderate squeezing for dipolar interactions in 2D. Our results constitute a first theoretical step beyond the well-studied qubit setting toward scalable entanglement generation in qudit systems with dipolar interactions, directly relevant to current Rydberg tweezer experiments.