In crystals, energy band extrema in momentum space can be identified by a valley index. The internal quantum degree of freedom associated with valley pseudospin indices can act as a useful information carrier, analogous to electronic charge or spin [1][2][3][4] . Interest in valleytronics has been revived in recent years following the discovery of atomically thin materials such as graphene and transition metal dichalcogenides [5][6][7] . However, the valley coherence time-a crucial quantity for valley pseudospin manipulation-is di cult to directly probe. In this work, we use two-dimensional coherent spectroscopy to resonantly generate and detect valley coherence of excitons (Coulomb-bound electron-hole pairs) in monolayer WSe 2 (refs 8,9). The imposed valley coherence persists for approximately one hundred femtoseconds. We propose that the electron-hole exchange interaction provides an important decoherence mechanism in addition to exciton population recombination. This work provides critical insight into the requirements and strategies for optical manipulation of the valley pseudospin for future valleytronics applications.Group-VI transition metal dichalcogenides (TMDs) with 2H structure (for example, MX 2 , M = Mo, W; X = S, Se) are a particularly intriguing class of semiconductors when thinned down to monolayers 6,7 . The valence and conduction band extrema are located at both K and K points at the corners of the hexagonal Brillouin zone, as illustrated in Fig. 1a. The degenerate K and K points are related to each other by time reversal symmetry and give rise to the valley degree of freedom (DoF) of the band-edge electrons and holes. Strong Coulomb interactions lead to the formation of excitons with remarkably large binding energies due to the heavy effective mass and reduced dielectric screening in monolayer TMDs (refs 10-12). An exciton as a bound electron-hole pair inherits the valley DoF. Because of valley-dependent optical selection rules, they can be excited only by σ + (σ − ) circularly polarized light at the K(K ) valley. Owing to its close analogy to spin 4 , the valley DoF can be considered as a pseudospin represented by a vector S on the Bloch sphere (Fig. 1b). The out-of-plane component S z and in-plane component S x,y describe the valley polarization and the coherent superposition of exciton valley states, respectively. After optical initialization, valley depolarization and decoherence are manifested by a reduction in the magnitudes of S z and S x,y , respectively.The ability to coherently manipulate spins and pseudospins is at the heart of spintronics and valleytronics; however, previous investigations have focused mainly on the creation and relaxation of valley polarization using non-resonant photoluminescence (PL) or pump/probe spectroscopy techniques [13][14][15][16][17][18][19] . Optical excitation close to the lowest energy exciton resonance leads to nearly 100% valley polarization in monolayer TMDs such as MoS 2 (refs 13,15,20). Time-resolved PL spectroscopy has revealed a fewpicosecon...

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. Here, we implement polarization-resolved two-dimensional coherent spectroscopy (2DCS) to unravel the complex optical response of monolayer MoSe2 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 and ∼5 meV binding energies—similar to recent calculations using variational and Monte Carlo methods. A theoretical model considering the valley-dependent optical selection rules reveals the quantum pathways that give rise to these states. Inter-valley biexcitons identified here, comprising of neutral and charged excitons from different valleys, offer new opportunities for developing ultrathin biexciton lasers and polarization-entangled photon sources.

The optical properties of semiconducting transition metal dichalcogenides are dominated by both neutral excitons (electron-hole pairs) and charged excitons (trions) that are stable even at room temperature. While trions directly influence charge transport properties in optoelectronic devices, excitons may be relevant through exciton-trion coupling and conversion phenomena. In this work, we reveal the coherent and incoherent nature of exciton-trion coupling and the relevant timescales in monolayer MoSe2 using optical two-dimensional coherent spectroscopy. Coherent interaction between excitons and trions is definitively identified as quantum beating of cross peaks in the spectra that persists for a few hundred femtoseconds. For longer times up to 10 ps, surprisingly, the relative intensity of the cross peaks increases, which is attributed to incoherent energy transfer likely due to phonon-assisted up-conversion and down-conversion processes that are efficient even at cryogenic temperature.