  Interlayer excitons (IXs) in hetero-bilayers 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 long-range interactions that arise from the spatial separation of
electrons and holes can give rise to novel quantum, as well as classical
multi-particle correlation effects. In order to acquire a detailed
understanding of the possible many-body effects, the fundamental interactions
between individual IXs have to be studied. Here, we trap a tunable number of
dipolar within a nanoscale confinement potential induced by placing a
MoSe$_2$-WSe$_2$ hetero-bilayer (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. We identify these features as different multiparticle states
with $N_{IX}\sim1-5$ via their power dependencies and directly measure the
hierarchy of dipolar and exchange interactions as $N_{IX}$ increases. The
interlayer biexciton ($N_{IX}=2$) 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), quadexcitons ($(15.5\pm0.6)$ meV) and quintexcitons
($(18.2\pm0.8)$ meV). These values are shown to be mutually consistent with
numerical modelling of dipolar excitons confined to a harmonic trapping
potential having a confinement lengthscale in the range $\ell\approx 3$ 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 them.
