Pair creation, correlations and entanglement dynamics in dipolar multi-layers*

We study the temporal growth and spatial propagation of quantum correlations in two-dimensional bi- and multi-layers realising spin 1/2 quantum XXZ models with couplings mediated by long range and anisotropic dipolar interactions.

Starting with an initial state consisting of spins with opposite magnetization in each of the layers we find exponentially fast creation of correlated pairs of excitations.

In the collective regime which is realised at the Heisenberg point this allows us to engineer the paradigmatic two-mode squeezing Hamiltonian, resulting in exponential generation of metrologically useful entanglement from initially prepared product states. At the XX point we predict the emergence of a momentum-dependent dynamic instability observable in the spin structure factor. The characteristic momentum distribution of the pair creation process can be tuned by controlling the dipolar orientation and the separation between the bilayers.

The predicted behavior remains observable at very low filling fractions making it accessible to state-of-the-art Rydberg atom, magnetic atom and polar molecule arrays.