Dipolar interactions between field-tuneable, localized emitters 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.