Realizing topological states with polyatomic symmetric top molecules

We show how to use polyatomic symmetric top molecules, such as methyl fluoride, in an optical lattice to produce states with non-trivial topology via a self-consistent analog of the proximity effect in the internal state space of the molecule. The key ingredient is pairwise transitions between internal states of a molecule which are generated by the dipole-dipole interaction and made resonant by a combination of static and AC electric field dressing. These pairwise transitions endow the effective many-body Hamiltonian with a U(1)$\times$Z$_2$ symmetry leading to topologically nontrivial states. We will present results of matrix product state simulations demonstrating non-trivial topology, and also provide mappings of the many-body description to models of quantum spins with un-conserved magnetization as well as to systems with Majorana fermion excitations.