Neutral and Charged Inter-Valley Biexcitons in Monolayer MoSe$_2$

In atomically thin transition metal dichalcogenides (TMDs), reduced dielectric screening of the Coulomb interaction leads to strongly correlated many-body states, including excitons and trions, that dominate the optical properties. Higher-order states, such as bound biexcitons, are possible but are difficult to identify unambiguously using linear optical spectroscopy methods alone. Here, we implement polarization-resolved two-dimensional coherent spectroscopy to unravel the complex optical response of monolayer MoSe$_2$ and identify multiple higher-order correlated states. Decisive signatures of neutral and charged inter-valley biexcitons appear in cross-polarized two-dimensional spectra as distinct resonances with respective ~20 meV and ~5 meV binding energies--similar to recent calculations using variational and Monte Carlo methods. A theoretical model taking into account the valley-dependent optical selection rules reveals the specific quantum pathways that give rise to these states. Inter-valley biexcitons identified here, comprised of neutral and charged excitons from different valleys, offer new opportunities for creating exotic exciton-polariton condensates and for developing ultrathin biexciton lasers and polarization-entangled photon sources.