Dipolar interactions between localized interlayer excitons in van der Waals heterostructures

While photons in free space barely interact, matter can mediate interactions between them resulting in optical nonlinearities. Such interactions at the single-quantum level result in an on-site photon repulsion, crucial for photon-based quantum information processing and for realizing strongly interacting many-body states of light. Here, we report repulsive dipole-dipole interactions between electric field tuneable, localized interlayer excitons in MoSe$_2$/WSe$_2$ heterobilayer. The presence of a single, localized exciton with an out-of-plane, non-oscillating dipole moment increases the energy of the second excitation by $\sim$ 2 meV -- an order of magnitude larger than the emission linewidth and corresponding to an inter-dipole distance of $\sim$ 5 nm. At higher excitation power, multi-exciton complexes appear at systematically higher energies. The magnetic field dependence of the emission polarization is consistent with spin-valley singlet nature of the dipolar molecular state. Our finding is an important step towards the creation of excitonic few- and many-body states such as dipolar crystals with spin-valley spinor in van der Waals (vdW) heterostructures.