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arXiv:2507.07875 · Physical Review A

Preparing spin-squeezed states in Rydberg atom arrays via quantum optimal control

Edison S. Carrera, Harold Erbin, Grégoire Misguich

Published Nov 20, 2025• 3 citations
arXivHTMLPDF

Abstract

We present a quantum optimal control protocol to generate highly spin-squeezed states in Rydberg atom arrays coupled via Ising-type van der Waals interactions. Using gradient-based optimization techniques, we construct time-dependent pulse sequences that steer an initial product state toward highly entangled, spin-squeezed states with predefined magnetization and squeezing axes. We focus on the Wineland parameter ${\ensuremath{\xi}}_{W}^{2}$ to measure spin squeezing, and our approach achieves near-optimal spin squeezing in one-dimensional ring arrays of up to $N=8$ spins, significantly outperforming conventional quench dynamics for all system sizes studied. Remarkably, optimized pulse sequences can be directly scaled to larger arrays without additional optimization, achieving a squeezing parameter as low as ${\ensuremath{\xi}}_{W}^{2}=0.227$ in systems containing $N=50$ spins. This work demonstrates the potential of quantum optimal control methods for preparing highly spin-squeezed states, opening pathways to enhanced quantum metrology.

DOI
10.1103/wdqt-tpwz

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We present a quantum optimal control protocol to generate highly spin-squeezed states in Rydberg atom arrays coupled via Ising-type van der Waals interactions. Using gradient-based optimization techniques, we construct time-dependent pulse sequences that steer an initial product state toward highly entangled, spin-squeezed states with predefined magnetization and squeezing axes. We focus on the Wineland parameter \ensuremathξW2{\ensuremath{\xi}}_{W}^{2}\ensuremathξW2​ to measure spin squeezing, and our approach achieves near-optimal spin squeezing in one-dimensional ring arrays of up to N=8N=8N=8 spins, significantly outperforming conventional quench dynamics for all system sizes studied. Remarkably, optimized pulse sequences can be directly scaled to larger arrays without additional optimization, achieving a squeezing parameter as low as \ensuremathξW2=0.227{\ensuremath{\xi}}_{W}^{2}=0.227\ensuremathξW2​=0.227 in systems containing N=50N=50N=50 spins. This work demonstrates the potential of quantum optimal control methods for preparing highly spin-squeezed states, opening pathways to enhanced quantum metrology.
Programmable Rydberg atom arrays provide a versatile platform for generating, controlling, and measuring interacting many-body quantum states. This thesis investigates which states can be explored using global controls, whether selected states can be prepared efficiently, how robust their useful properties are to imperfections, and how these properties can be certified from finite experimental data. First, we study ensembles generated by random global pulse sequences and compare their statistical properties with those of Haar-random states within the dynamically accessible symmetry sector. Weak interactions generate correlations slowly, whereas strong Rydberg blockade confines the dynamics to a restricted set of configurations. At intermediate interaction strengths, the system develops Haar-like statistical signatures on experimentally relevant timescales, revealing a compromise between interaction-induced exploration and blockade-induced confinement. However, quantum optimal-control calculations show that highly entangled target states are systematically more difficult to prepare than weakly entangled ones, demonstrating that expressibility does not imply trainability. Second, we use gradient-based quantum optimal control to prepare spin-squeezed states. For small systems, the optimized protocols approach the finite-size lower bound of the Wineland parameter and produce substantially stronger squeezing than uncontrolled quantum-quench dynamics. Pulses optimized for N=10 can be transferred without re-optimization to larger arrays, reaching a Wineland parameter of 0.227 for N=50. The robustness analysis further shows that the states with the strongest squeezing under unitary dynamics are not necessarily the most resilient to dephasing: states with a larger mean-spin length can retain greater metrological usefulness in the presence of noise. Finally, we formulate spin-squeezing certification with finite statistics as a hypothesis-testing problem. We derive rigorous non-asymptotic bounds on the corresponding p-value, thereby controlling the probability that finite-sample fluctuations lead to a false certification of squeezing. Together, these results show that reliable quantum-state engineering requires not only broad state-space exploration, but also efficient preparation, robustness to imperfections, and statistically controlled certification.
We report on the creation of an array of spin-squeezed ensembles of cesium atoms via Rydberg dressing, a technique that offers optical control over local interactions between neutral atoms. We optimize the coherence of the interactions by a stroboscopic dressing sequence that suppresses super-Poissonian loss. We thereby prepare squeezed states of N=200 atoms with a metrological squeezing parameter ξ^{2}=0.77(9) quantifying the reduction in phase variance below the standard quantum limit. We realize metrological gain across three spatially separated ensembles in parallel, with the strength of squeezing controlled by the local intensity of the dressing light. Our method can be applied to enhance the precision of tests of fundamental physics based on arrays of atomic clocks and to enable quantum-enhanced imaging of electromagnetic fields.
Spin squeezing is both a fundamental witness of quantum entanglement and a key resource for quantum-enhanced metrology. While all-to-all interactions provide a paradigmatic route to generate spin squeezing, many programmable quantum simulators naturally realize finite-range interactions that induce coupling between collective spin dynamics and finite-momentum spin-wave modes, thereby degrading the achievable squeezing. Here we develop an optimization-based global-control strategy for enhancing spin squeezing in a two-dimensional XX model with dipolar interactions. By combining rotor-spin-wave theory with an extension to open boundary conditions, we enable efficient optimization of control protocols for large finite-range interacting systems. We show that a single collective transverse field generates squeezing beyond the conventional two-axis-twisting benchmark across system sizes accessible to numerical benchmarking. The optimized dynamics exploits squeezing-axis reorientation while suppressing spin-wave excitations, thereby stabilizing strong squeezing over extended times. We further implement the optimized protocol in a two-dimensional Rydberg-atom array and experimentally observe enhanced, long-lived spin squeezing in good agreement with theory.
Entangled atomic states, such as spin-squeezed states, represent a promising resource for a new generation of quantum sensors and atomic clocks. We demonstrate that optimal control techniques can be used to substantially enhance the degree of spin squeezing in strongly interacting many-body systems, even in the presence of noise and imperfections. Specifically, we present a protocol that is robust to noise and outperforms conventional methods. Potential experimental implementations are discussed.
WWW- and Dicke-state engineering using optimal global control in nearest-neighbor coupled ring-shaped qubit arrays
Motivated by a compelling need for time-efficient and robust schemes for quantum-state engineering in systems of neutral atoms in optical tweezers, we consider a ring-shaped array of qubits with nearest-neighbor Ising-type (zzzzzz) coupling and transverse (xxx and yyy) global control fields. This system to a large extent mimics -- outside of the Rydberg-blockade regime -- a circular array of neutral atoms interacting through van-der-Waals type interaction. We investigate the preparation of WWW and Dicke states in this system starting from the default initial state ∣00…0⟩|00\ldots 0\rangle∣00…0⟩ using two different optimal-control approaches: (i) NMR-like pulse sequence, which consists of instantaneous (delta-shaped) control- and Ising-interaction pulses, and (ii) time-dependent control scheme, which entails shaped control pulses in the presence of always-on Ising interaction between adjacent qubits. By making use of the underlying dihedral symmetry of this system -- which allows one to use a symmetry-adapted computational basis with O(2N/N)\mathcal{O}(2^N / N)O(2N/N) states in an NNN-qubit system -- and utilizing advanced global-optimization methods, we find optimal sequences of pulses for realizing WWW and Dicke states within both approaches. In addition, we demonstrate robustness of these sequences against unavoidable control errors. Finally, using typical values of parameters in realistic Rydberg-atom systems, we show that our control schemes enable the preparation of the desired multiqubit states on time scales much shorter than the relevant coherence times of those systems.
Arrays of atoms trapped in optical tweezers combine features of programmable analog quantum simulators with atomic quantum sensors. Here we propose variational quantum algorithms, tailored for tweezer arrays as programmable quantum sensors, capable of generating entangled states on demand for precision metrology. The scheme is designed to generate metrological enhancement by optimizing it in a feedback loop on the quantum device itself, thus preparing the best entangled states given the available quantum resources. We apply our ideas to the generation of spin-squeezed states on Sr atom tweezer arrays, where finite-range interactions are generated through Rydberg dressing. The complexity of experimental variational optimization of our quantum circuits is expected to scale favorably with system size. We numerically show our approach to be robust to noise, and surpassing known protocols.