  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.
