The strong light-matter interaction and the valley selective optical selection rules make monolayer (ML) MoS_{2} an exciting 2D material for fundamental physics and optoelectronics applications. But, so far, optical transition linewidths even at low temperature are typically as large as a few tens of meV and contain homogeneous and inhomogeneous contributions. This prevented in-depth studies, in contrast to the better-characterized ML materials MoSe_{2} and WSe_{2}. In this work, we show that encapsulation of ML MoS_{2} in hexagonal boron nitride can efficiently suppress the inhomogeneous contribution to the exciton linewidth, as we measure in photoluminescence and reflectivity a FWHM down to 2 meV at T=4 K. Narrow optical transition linewidths are also observed in encapsulated WS_{2}, WSe_{2}, and MoSe_{2} MLs. This indicates that surface protection and substrate flatness are key ingredients for obtaining stable, high-quality samples. Among the new possibilities offered by the well-defined optical transitions, we measure the homogeneous broadening induced by the interaction with phonons in temperature-dependent experiments. We uncover new information on spin and valley physics and present the rotation of valley coherence in applied magnetic fields perpendicular to the ML.
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