  Monolayer transition metal dichalcogenides, a new class of atomically thin
semiconductors, possess optically coupled 2D valley excitons. The nature of
exciton relaxation in these systems is currently poorly understood. Here, we
investigate exciton relaxation in monolayer MoSe2 using polarization-resolved
coherent nonlinear optical spectroscopy with high spectral resolution. We
report strikingly narrow population pulsation resonances with two different
characteristic linewidths of 1 {\mu}eV and <0.2 {\mu}eV at low-temperature.
These linewidths are more than three orders of magnitude narrower than the
photoluminescence and absorption linewidth, and indicate that a component of
the exciton relaxation dynamics occurs on timescales longer than 1 ns. The
ultra-narrow resonance (<0.2 {\mu}eV) emerges with increasing excitation
intensity, and implies the existence of a long-lived state whose lifetime
exceeds 6 ns.
