  Monolayer transition metal dichalcogenides are a promising platform to
investigate many-body interactions of excitonic complexes. In monolayer
tungsten diselenide, the ground-state exciton is dark (spin-indirect), and the
valley degeneracy allows low-energy dark momentum-indirect excitons to form.
Interactions between the dark exciton species and the optically accessible
bright exciton (X) are likely to play significant roles in determining the
optical properties of X at high power, as well as limiting the ultimate exciton
densities that can be achieved, yet so far little is known about these
interactions. Here, we demonstrate long-lived dense populations of
momentum-indirect intervalley ($X_K$) and spin-indirect intravalley (D) dark
excitons by time-resolved photoluminescence measurements (Tr-PL). Our results
uncover an efficient inter-state conversion between X to D excitons through the
spin-flip process and the one between D and $X_K$ excitons mediated by the
exchange interaction (D + D to $X_K$ + $X_K$). Moreover, we observe a
persistent redshift of the X exciton due to strong excitonic screening by $X_K$
exciton with a response time in the timescale of sub-ns, revealing a
non-trivial inter-state exciton-exciton interaction. Our results provide a new
insight into the interaction between bright and dark excitons, and point to a
possibility to employ dark excitons for investigating exciton condensation and
the valleytronics.
