Three-body interactions with cold polar molecules

Fundamental interactions between particles, such as the Coulomb law, involve pairs of particles, and our understanding of the plethora of phenomena in condensed-matter physics rests on models involving effective two-body interactions. On the other hand, exotic quantum phases, such as topological phases or spin liquids, are often identified as ground states of hamiltonians with three- or more-body terms. Although the study of these phases and the properties of their excitations is currently one of the most exciting developments in theoretical condensed-matter physics, it is difficult to identify real physical systems exhibiting such properties. Here, we show that polar molecules in optical lattices driven by microwave fields naturally give rise to Hubbard models with strong nearest-neighbour three-body interactions, whereas the two-body terms can be tuned with external fields. This may open a new route for an experimental study of exotic quantum phases with quantum degenerate molecular gases.