Two-mode Squeezing in Floquet Engineered Power-law Interacting Spin Models

We study the non-equilibrium dynamics of a quantum spin 1/2 XXZ model confined in a two-dimensional bi-layer system, with couplings mediated by inverse power-law interactions, falling off with distance r as 1/r^, and spatio-temporal 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 powerlaw models. We further demonstrate that spatially-temporally engineered interactions allow 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 powerlaw spin models, and demonstrates the advantage of spatio-temporal control to maximize the generation of metrologically useful entanglement, with potential applications in quantum-enhanced sensing.