Discrete Interactions between a few Interlayer Excitons Trapped at a MoSe$_2$-WSe$_2$ Heterointerface

Interlayer excitons (IXs) in heterobilayers (HBLs) of transition metal dichalcogenides (TMDs) represent an exciting emergent class of long-lived dipolar composite bosons in an atomically thin, near-ideal two-dimensional (2D) system. The emergence of quantum correlations in finite 2D systems may open up tantalizing prospects of excitonic Bose-Einstein condensation and Wigner-crystal-like phases at sufficiently low temperatures and in confined geometries. Here, we trap a tunable number of dipolar IXs within a nanoscale confinement potential induced by placing a MoSe$_2$-WSe$_2$-HBL onto an array of SiO$_2$ nanopillars. We control the mean occupation of the IX trap via the optical excitation level and observe discrete sharp-line emission from different configurations of interacting IXs. The intensities of these features exhibit characteristic near linear, quadratic, cubic and quartic power dependencies, which allows us to identify them as different multiparticle configurations with $N_{IX}=1-4$. We directly measure the hierarchy of dipolar and exchange interactions as $N_{IX}$ increases. The interlayer biexciton is found to be an emission doublet that is blue-shifted from the single exciton by $\Delta E=(8.4\pm0.6)$ meV and split by $2J=(1.2\pm0.5)$ meV. The blueshift is even more pronounced for triexcitons ($(12.4\pm0.4) $ meV) and quadexcitons ($(17.0\pm0.5)$ meV). These values are shown to be mutually consistent with numerical modelling of dipolar excitons moving in a harmonic trapping potential having a confinement length scale in the range $l\approx3$ nm. Our results contribute to the understanding of interactions between IXs in TMD-HBLs at the discrete limit of only a few excitations and represent a key step towards exploring quantum correlations between IXs in TMD-HBLs.