  Moir\'e patterns with a superlattice potential can be formed by vertically
stacking two layered materials with a relative twist or lattice constant
mismatch. The moir\'e superlattice can generate flat bands that result in new
correlated insulating, superconducting, and topological states. Strong electron
correlations, tunable by the fractional filling, have been observed in both
graphene and transition metal dichalcogenide (TMD) based systems. In addition,
in TMD based systems, the moir\'e potential landscape can trap interlayer
excitons (IX) at specific atomic registries. Here we report that spatially
isolated trapped IX in a molybdenum diselenide/tungsten diselenide
heterobilayer device provide a sensitive optical probe of carrier filling in
their immediate environment. By mapping the spatial positions of individual
trapped IX, we are able to spectrally track the emitters as the moir\'e lattice
is filled with excess carriers. Upon initial doping of the heterobilayer,
neutral trapped IX form charged IX (IX trions) uniformly with a binding energy
of ~7 meV. Upon further doping, the empty superlattice sites sequentially fill,
creating a Coulomb staircase: stepwise changes in the IX trion emission energy
due to Coulomb interactions with carriers at nearest neighbour moir\'e sites.
This non-invasive, highly local technique can complement transport and
non-local optical sensing techniques to characterise Coulomb interaction
energies, visualise charge correlated states, or probe local disorder in a
moir\'e superlattice.
