Layered materials can be assembled vertically to fabricate a new class of van der Waals (VDW) heterostructures a few atomic layers thick, compatible with a wide range of substrates and optoelectronic device geometries, enabling new strategies for control of light-matter coupling. Here, we incorporate molybdenum diselenide/boron nitride (MoSe$_2$/hBN) quantum wells (QWs) in a tunable optical microcavity. Part-light-part-matter polariton eigenstates are observed as a result of the strong coupling between MoSe$_2$ excitons and cavity photons, evidenced from a clear anticrossing between the neutral exciton and the cavity modes with a splitting of 20 meV for a single MoSe$_2$ monolayer QW, enhanced to 29 meV in MoSe$_2$/hBN/MoSe$_2$ double-QWs. The splitting at resonance provides an estimate of the exciton radiative lifetime of 0.4 ps. Our results pave the way for room temperature polaritonic devices based on multiple-QW VDW heterostructures, where polariton condensation and electrical polariton injection through the incorporation of graphene contacts may be realised.
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