Extended Bose-Hubbard model with dipolar excitons.

The Hubbard model constitutes one of the most celebrated theoretical frameworks of condensed-matter physics. It describes strongly correlated phases of interacting quantum particles confined in lattice potentials 1,2 . For bosons, the Hubbard Hamiltonian has been deeply scrutinized for short-range on-site interactions 3-6 . However, accessing longer-range couplings has remained elusive experimentally 7 . This marks the frontier towards the extended Bose-Hubbard Hamiltonian, which enables insulating ordered phases at fractional lattice fillings 8-12 . Here we implement this Hamiltonian by confining semiconductor dipolar excitons in an artificial two-dimensional square lattice. Strong dipolar repulsions between nearest-neighbour lattice sites then stabilize an insulating state at half filling. This characteristic feature of the extended Bose-Hubbard model exhibits the signatures theoretically expected for a chequerboard spatial order. Our work thus highlights that dipolar excitons enable controlled implementations of boson-like arrays with strong off-site interactions, in lattices with programmable geometries and more than 100 sites.