Investigating phonon-mediated interactions with polar molecules

We show that an ensemble of polar molecules in an optical lattice realizes the Peierls polaron model for hard-core particles/pseudospins. We analyze the quasiparticle spectrum in the one-particle subspace, the two-particle subspace and at finite concentrations. We derive an effective model that describes the low-energy behavior of the system. We show that the Hamiltonian includes phonon-mediated repulsions and phonon-mediated ``pair-hopping" terms which move the particle pair as a whole. We show that microwave excitations of the system exhibit signatures of these interactions. These results pave the way for the experimental observation of phonon-mediated repulsion.