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

We study the non-equilibrium dynamics of dipoles confined in multiple stacked two-dimensional layers realising a long-range interacting quantum spin 1/2 XXZ model. We demonstrate that strong in-plane XXX interactions can protect a manifold of collective layer dynamics. This then allows us to map the many-body spin dynamics to bosonic models.