  The valley pseudospin in monolayer transition metal dichalcogenides (TMDs)
has been proposed as a new way to manipulate information in various
optoelectronic devices. This relies on a large valley polarization that remains
stable over long timescales (hundreds of ns). However, time resolved
measurements report valley lifetimes of only a few ps. This has been attributed
to mechanisms such as phonon-mediated inter-valley scattering and a precession
of the valley psedospin through electron-hole exchange. Here we use transient
spin grating to directly measure the valley depolarization lifetime in
monolayer MoSe$_{2}$. We find a fast valley decay rate that scales linearly
with the excitation density at different temperatures. This establishes the
presence of strong exciton-exciton Coulomb exchange interactions enhancing the
valley depolarization. Our work highlights the microscopic processes inhibiting
the efficient use of the exciton valley pseudospin in monolayer TMDs.
