Non-local state-swapping of polar molecules in bilayers

The observation of significant dipolar effects in gases of ultra-cold polar molecules typically demands a strong external electric field to polarize the molecules. We show that even in the absence of a significant polarization, dipolar effects may play a crucial role in the physics of polar molecules in bilayers, provided that the molecules in each layer are initially prepared in a different rotational state. Then, inter-layer dipolar interactions result in a non-local swap of the rotational state between molecules in different layers, even for weak applied electric fields. The inter-layer scattering due to the dipole-dipole interaction leads to a non-trivial dependence of the swapping rate on density, temperature, inter-layer spacing, and population imbalance. For reactive molecules like KRb, chemical recombination immediately follows a non-local swap and dominates the losses even for temperatures well above quantum degeneracy, and could be hence observed under current experimental conditions.