Highly non-linear interlayer exciton-polaritons in bilayer MoS$_2$.

Realizing nonlinear optical response in the low photon density limit in solid state systems has been a long-standing challenge. Semiconductor microcavities in the strong coupling regime hosting light-matter quasiparticles called exciton-polaritons have emerged as an attractive candidate in this context. However, the weak interaction between these quasiparticles has been a hurdle in this quest. Two-dimensional transition metal dichalcogenides (TMDCs) owing to their inherently large oscillator strength and the wide array of excitonic complexes they host present an opportunity to address this challenge. Among the different excitations supported by TMDCs, a prime candidate is the interlayer excitons that form in heterostructures of TMDCs. Due to the spatial separation of the electron and holes in different layers, they have a permanent dipole moment making them interact stronger. This advantage is often diminished by their poor oscillator strength making them unsuitable for realizing polaritons. The recent discovery of interlayer excitons in naturally occurring homobilayer MoS$_2$ alleviates this issue owing to their hybrid characteristics arising from the interlayer charge transfer state and intralayer B exciton. Here we demonstrate the strong coupling of interlayer excitons in bilayer MoS$_2$ with cavity photons resulting in unprecedented nonlinear interaction strengths. A ten-fold increase in nonlinearity is observed for the interlayer excitons compared to the conventional A excitons which have been used extensively for strong coupling studies. The measured interaction strength in the weak pump limit is $\sim(100\pm 2)$ \textmu eV \textmu m$^{2}$. The observed nonlinear response is attributed to a combination of both exciton-exciton interaction and saturation due to phase space-filling.