We show that an ensemble of polar molecules trapped in an optical lattice can be considered as a controllable open quantum system. The coupling between collective rotational excitations and the motion of the molecules in the lattice potential can be controlled by varying the strength and orientation of an external dc electric field as well as the intensity of the trapping laser. The system can be described by a generalized Holstein Hamiltonian with tunable parameters and can be used as a quantum simulator of excitation energy transfer and polaron phenomena. We show that the character of excitation energy transfer can be modified by tuning experimental parameters.
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
T2 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.