  Quantifying and controlling the coherent dynamics and couplings of optically
active excitations in solids is of paramount importance in fundamental research
in condensed matter optics and for their prospective optoelectronic
applications in quantum technologies. Here, we perform ultrafast coherent
nonlinear spectroscopy of a charge-tunable MoSe$_2$ monolayer. The experiments
show that the homogeneous and inhomogeneous line width and the population decay
of exciton complexes hosted by this material can be directly tuned by an
applied gate bias, which governs the Fermi level and therefore the free carrier
density. By performing two-dimensional spectroscopy, we also show that the same
bias-tuning approach permits us to control the coherent coupling strength
between charged and neutral exciton complexes.
