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arXiv:2605.00096

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

Sakshi Bahamnia, Thomas Bilitewski

quant-phcond-mat.quant-gasSubmitted Apr 30, 2026• Announced May 4, 2026• 0 citations
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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 $ξ^{2}\propto N^{-2/3}$ ($ξ^{2}\propto N^{-0.5}$) 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 $ξ^{2}\propto N^{-0.7}$ 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.

Comments
5 pages (main) + 2 pages SI + 5 figures (main) + 2 Figures (SI): Comments Welcome

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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 ξ2∝N−2/3ξ^{2}\propto N^{-2/3}ξ2∝N−2/3 (ξ2∝N−0.5ξ^{2}\propto N^{-0.5}ξ2∝N−0.5) with system size for all-to-all (two-dimensional dipolar) couplings. In both cases the quantum Fisher information reaches FQ∝N2F_Q\propto N^{2}FQ​∝N2. For antisymmetric interactions supplemented by a microwave drive we find a distinct two-axis countertwisting mechanism. This results in squeezing ξ2∝N−0.7ξ^{2}\propto N^{-0.7}ξ2∝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.
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Scalable spin squeezing in two-dimensional arrays of dipolar large-SSS spins
Controlling the quantum many-body state of arrays of qudits, possessing a large local Hilbert space, opens the path to a broad range of possibilities for many-particle entanglement, interesting both for fundamental quantum science, as well as for potential metrological applications. In this work we theoretically show that the spin-spin interactions realized in two-dimensional Mott insulators of large-spin magnetic atoms (such as Cr, Er or Dy) lead to scalable spin squeezing along the non-equilibrium unitary evolution initialized in a coherent spin state. An experimentally relevant perturbation to the collective squeezing dynamics is offered by a quadratic Zeeman shift, which leads instead to squeezing of individual spins. Making use of a truncated cumulant expansion for the quantum fluctuations of the spin array, we show that, for sufficiently small quadratic shifts, the spin squeezing dynamics is akin to that produced by the paradigmatic one-axis-twisting (OAT) model -- as expected from an effective separation between collective spin and spin-wave variables. Spin squeezing with OAT-like scaling is shown to be protected by the robustness of long-range ferromagnetic order to quadratic shifts in the equilibrium phase diagram of the system, that we reconstruct via quantum Monte Carlo and mean-field theory.
Spin squeezing in collective atomic ensembles enables quantum-enhanced metrology by reducing noise below the standard quantum limit through nonlinear interactions. Extending the one-axis and two-axis twisting paradigms of Kitagawa and Ueda, we introduce a general class of three-axis spin squeezed states within the anisotropic Lipkin-Meshkov-Glick model. The model features direction-dependent quadratic couplings that interpolate between uniaxial and biaxial regimes and can be interpreted as an asymmetric quantum rotor. Using semiclassical dynamics, Majorana representations, and Husimi-Q distributions, we analyze the structure and metrological properties of the resulting states. The three-axis framework reproduces the known N^(-2/3) scaling of one-axis twisting and the Heisenberg-limited N^(-1) scaling of two-axis twisting, while allowing additional tunability and enhanced entanglement generation in low-spin systems. We further show that tuning the anisotropy parameters induces ground-state and excited-state quantum phase transitions, including a second-order transition associated with level clustering and critical dynamics. These results unify spin squeezing, quantum criticality, and rotor analogies, and suggest implementations in Rydberg arrays and cavity-QED platforms for precision sensing and quantum simulation.
Spin squeezed entanglement enables metrological precision beyond the classical limit. Understood through the lens of continuous symmetry breaking, dipolar spin systems exhibit the remarkable ability to generate spin squeezing via their intrinsic quench dynamics. To date, this understanding has primarily focused on lattice spin systems; in practice however, dipolar spin systems$\unicode{x2014}$ranging from ultracold molecules to nuclear spin ensembles and solid-state color centers$\unicode{x2014}$often exhibit significant amounts of positional disorder. Here, we develop a theory for scalable spin squeezing in a two-dimensional randomly diluted lattice of quantum dipoles, which naturally realize a dipolar XXZ model. Via extensive quantum Monte Carlo simulations, we map out the phase diagram for finite-temperature XY order, and by extension scalable spin squeezing, as a function of both disorder and Ising anisotropy. As the disorder increases, we find that scalable spin squeezing survives only near the Heisenberg point. We show that this behavior is due to the presence of rare tightly-coupled dimers, which effectively heat the system post-quench. In the case of strongly-interacting nitrogen-vacancy centers in diamond, we demonstrate that an experimentally feasible strategy to decouple the problematic dimers from the dynamics is sufficient to enable scalable spin squeezing.
Ultracold molecular systems have recently emerged as a versatile platform for quantum computation and simulation. Spin-exchange interactions arising from direct molecular dipolar interactions constitute the key mechanism for generating quantum entanglement and simulating quantum spin models. However, the relatively small electric dipole moments result in weak spin-exchange couplings, fundamentally limiting the speed of quantum information processing and interaction cycle of many-body dynamics. Here, we introduce a framework that employs Rydberg atoms with large electric dipole moments to mediate strong interactions between molecules in optical tweezer arrays that enables individually laser addressing both the Rydberg atom and molecules. Our result reveals that the mediated coupling can realize an effective molecular spin-exchange interaction with an intrinsic Dzyaloshinskii-Moriya character, with the Rydberg atoms dynamically decoupled from the molecular degrees of freedom, and the effective interaction strength enhanced by up to three orders of magnitude. We further demonstrate its versatility through rapid entanglement generation, high-fidelity two-qubit gate operations, and the realization of non-equilibrium symmetry-protected topological phase with long-lived edge coherence. Our work establishes a route toward strong molecular spin interactions and opens opportunities for fast, scalable quantum information processing and quantum simulation of long-time non-equilibrium quantum many-body physics in optical tweezer arrays of ultracold molecules.