  Electric dipole radiation can be controlled by coherent optical feedback, as
has previously been studied by modulating the photonic environment for point
dipoles placed both in optical cavities and near metal mirrors. In experiments
involving fluorescent molecules, trapped ions and quantum dots the point nature
of the dipole, its sub-unity quantum efficiency, and decoherence rate conspire
to severely limit any change in total linewidth. Here we show that the
transverse coherence of exciton emission in the monolayer two-dimensional (2D)
material MoSe${}_2$ removes many of the fundamental physical limitations
present in previous experiments. The coherent interaction between excitons and
a photonic mode localized between the MoSe${}_2$ and a nearby planar mirror
depends interferometrically on mirror position, enabling full control over the
radiative coupling rate from near-zero to 1.8 meV and a corresponding change in
exciton total linewidth from 0.9 to 2.3 meV. The highly radiatively broadened
exciton resonance (a ratio of up to $3:1$ in our samples) necessary to observe
this modulation is made possible by recent advances in 2D materials sample
fabrication. Our method of mirror translation is free of any coupling to strain
or DC electric field in the monolayer, which allows a fundamental study of this
photonic effect. The weak coherent driving field in our experiments yields a
mean excitation occupation number of ${\sim} 10^{-3}$ such that our experiments
correspond to probing radiative reaction in the regime of perturbative quantum
electrodynamics. This system will serve as a testbed for exploring new
excitonic physics and quantum nonlinear optical effects.
