Quadrupolar Excitons in MoSe$_2$ Bilayers

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 superposition 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 the emergence of quadrupolar excitons in natural MoSe$_2$ homobilayers, whose energy shifts quadratically in electric field. In contrast to trilayer systems, MoSe$_2$ homobilayers have many advantages, which include a larger coupling between dipolar excitons. Our experimental observations are complemented by many-particle theory calculations offering microscopic insights in the formation of quadrupolar 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 quantum simulations.