Molecules trapped on an optical lattice represent a unique, controllable many-body system which can be used to study dynamics of collective excitations in new regimes. I will discuss the rotational excitations of molecules on an optical lattice leading to rotational Frenkel excitons. Apart from solid hydrogen, there is no other natural system that exhibits rotational excitons. The rotational excitons have unique properties that can be exploited for tuning non-linear exciton interactions and exciton-impurity scattering by applying an external electric field. I will show that this can be used to explore the competing role of the dynamical and kinematic exciton-exciton interactions in excitonic energy transfer and to study quantum localization in a dynamically tunable disordered potential.
The rotational excitons can also be used as a basis for quantum simulation of condensed matter models that cannot be realized with ultracold atoms. In particular, I will discuss the possibility of engineering the Holstein, breathing-mode and Su-Schrieffer-Heeger polaron models with polar molecules on an optical lattice. I will discuss the phase diagram of a polaron model with mixed breathing-mode and Su-Schrieffer-Heeger couplings and show that it has two sharp transitions, in contrast to pure models which exhibit one (for Su-Schrieffer-Heeger coupling) or no (for breathing-mode coupling) transition. I will show that ultracold molecules trapped in optical lattices can be used to study precisely this mixed Hamiltonian, and that the relative contributions of the two couplings can be tuned with external electric fields, which brings the possibility of observing the polaron transitions within reach of up-coming experiments. Time permitting, I will also discuss dipole blockade of microwave excitations in ensembles of trapped molecules and how it can be used to create quantum phases of interacting spin-1/2 particles without crossing phase transitions.
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