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 ${\xi }_W^2$ 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 ${\xi }_W^2=0.227$ 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.

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• Entanglement detection
• Open quantum systems & decoherence
• Quantum control
• Quantum entanglement
• Quantum metrology
• Quantum sensing
• Rydberg gases
• Trapped atoms
• Ising model
• Many-body techniques