  The quest for platforms to generate and control exotic excitonic states has
greatly benefited from the advent of transition metal dichalcogenide (TMD)
monolayers and their heterostructures. Among the unconventional excitonic
states, quadrupolar excitons - a hybridized combination of two dipolar excitons
with anti-aligned dipole moments - are of great interest for applications in
quantum simulations and for the investigation of many-body physics. Here, we
unambiguously demonstrate for the first time in natural MoSe$_2$ homobilayers
the emergence of quadrupolar excitons, whose energy shifts quadratically in
electric field. In contrast to, so far reported trilayer systems hosting
quadrupolar excitons, MoSe$_2$ homobilayers have many advantages, a stronger
interlayer hybridization, cleaner potential landscapes and inherent stability
with respect to moir\'e potentials or post-stacking reconstruction. Our
experimental observations are complemented by many-particle theory calculations
offering microscopic insights in the formation of quadrupole excitons. Our
results suggest TMD homobilayers as ideal platform for the engineering of
excitonic states and their interaction with light and thus candidate for
carrying out on-chip simulations.
