Optical absorption is one of fundamental light-matter interactions. In most materials, optical absorption is a weak perturbation to the light. In this regime, absorption and emission are irreversible, incoherent processes due to strong damping. Excitons in monolayer transition metal dichalcogenides, however, interact strongly with light, leading to optical absorption in the non-perturbative regime where coherent re-emission of the light has to be considered. Between the incoherent and coherent limits, we show that a robust critical coupling condition exists, leading to perfect optical absorption. Up to 99.6% absorption is measured in a sub-nanometer thick MoSe2 monolayer placed in front of a mirror. The perfect absorption is controlled by tuning the exciton-phonon, exciton-exciton, and exciton-photon interactions by temperature, pulsed laser excitation, and a movable mirror, respectively. Our work suggests unprecedented opportunities for engineering exciton-light interactions using two-dimensional atomically thin crystals, enabling novel photonic applications including ultrafast light modulators and sensitive optical sensing.

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