We study the nonequilibrium dynamics of a quantum spin-1/2 $XXZ$ model confined in a two-dimensional bilayer system, with couplings mediated by inverse power-law interactions, falling off with distance $r$ as $1/r^{\alpha }$, with spatiotemporal control of the spins enabled via local fields. An initial state of spins with opposite magnetization in the two layers is dynamically unstable resulting in exponential generation of correlated pairs of excitations. We find that scalable generation of entanglement in the form of two-mode squeezing between the layers can generically be achieved in power-law models. We further demonstrate that spatially temporally engineered interactions allow one to significantly increase the generated entanglement and in fact achieve Heisenberg limited scaling. This work is relevant to a wide variety of experimental atomic, molecular, and optical platforms, which realize power-law spin models, and demonstrates the advantage of spatiotemporal control to maximize the generation of metrologically useful entanglement, with potential applications in quantum-enhanced sensing.

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• Cold gases in optical lattices
• Dipolar gases
• Entanglement in quantum gases
• Entanglement production
• Long-range interactions
• Rydberg gases
• Floquet systems
• Trapped ions