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 [1, 2], crucial for photon-based quantum information processing and for realizing strongly interacting many-body states of light [3][4][5][6][7]. 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 ∼ 2 meV -an order of magnitude larger than the emission linewidth and corresponding to an inter-dipole distance of ∼ 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.Optical response in atomically thin layered semiconductors is determined by excitons and other excitonic complexes such as trions and biexcitons which are strongly bound due to increased Coulomb interactions in truly 2D limit [5,9]. In addition, due to the type-II band alignment in heterobilayer of MoSe 2 /WSe 2 , an interlayer exciton comprising of an electron in the MoSe 2 layer and hole in the WSe 2 layer is found to be stable and long-lived [4,10,11,13]. As shown in Fig. 1a, due to the spatial separation of electron and hole, the interlayer exciton carries a static, out-of-plane electric dipole moment which allows for the tuning of its energy by an external electric field (E). The orientation of this dipole is fixed by the ordering of MoSe 2 and WSe 2 layers and hence leads to a repulsive interaction between interlayer excitons. arXiv:1910.08139v1 [cond-mat.mes-hall] 17 Oct 2019 10 µm WSe2 MoSe2 a b c U d-d on-site E x E x -+ Mo W Se ℎ + − Electric field Figure 1: Interlayer exciton dipoles in WSe 2 /MoSe 2 heterostructure. a, A schematic showing the interlayer exciton in WSe 2 -MoSe 2 heterobilayer under an external electric field E. Due to the type-II band alignment, electron and hole are separated in MoSe 2 and WSe 2 , respectively, forming a permanent out-ofplane dipole. The dipole energy red-shifts (blue-shifts) when E is parallel (anti-parallel) to the direction of dipole. b, Energy diagram of localized interlayer exciton and biexciton in a potential well. The energy of biexciton is raised up by on-site dipole-dipole interaction U on−site dd . c, An optical image of WSe 2 /MoSe 2 heterobilayer with graphite bottom gate. Monolayer WSe 2 (MoSe 2 ) is depicted in orange (yellow) dashed line. The final device has graphite bottom and top gates with h-BN as dielectric on both sides.This dipolar interaction is potentially interesting for inducing e...