Bose-Einstein condensation and many-body localization of rotational excitations of polar molecules following a microwave pulse

We study theoretically the collective dynamics of rotational excitations of polar molecules loaded into an optical lattice in two dimensions. We explore the collective many-body phases that form following a microwave pulse. We show that, owing to the long-range interactions between molecules and energy conservation in this isolated system, the rotational excitations can form a Bose-Einstein condensate with long-range order, even for the natural (undressed) dipole interactions. This manifests itself as a divergent T-2 coherence time of the rotational transition even in the presence of inhomogeneous broadening. The dynamical evolution of a dense gas of rotational excitations shows regimes of nonergodicity, characteristic of many-body localization and localization protected quantum order.