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We study the non-equilibrium dynamics of dipoles confined in multiple stackedtwo-dimensional layers realising a long-range interacting quantum spin 1/2 XXZmodel. We demonstrate that strong in-plane XXX interactions can protect amanifold of collective layer dynamics. This then allows us to map the many-bodyspin dynamics to bosonic models. In a bilayer configuration we show how toengineer the paradigmatic two-mode squeezing Hamiltonian known from quantumoptics, resulting in exponential production of entangled pairs and generationof metrologically useful entanglement from initially prepared product states.In multi-layer configurations we engineer a bosonic variant of the Kitaev modeldisplaying chiral propagation along the layer direction. Our study illustrateshow the control over interactions, lattice geometry and state preparation ininteracting dipolar systems uniquely afforded by AMO platforms such as Rydbergand magnetic atoms, polar molecules or trapped ions allow for the control overthe temporal and spatial propagation of correlations for applications inquantum sensing and quantum simulation.

Manipulating growth and propagation of correlations in dipolar multilayers: From pair production to bosonic Kitaev models