Nanoplasmonic systems combined with optically-active two-dimensional materials provide intriguing opportunities to explore and control light-matter interactions at extreme sub-wavelength lengthscales approaching the exciton Bohr radius. Here, we present room- and cryogenic-temperature investigations of light-matter interactions between an MoSe$_2$ monolayer and individual lithographically defined gold dipole nanoantennas having sub-10 nm feed gaps. By progressively tuning the nanoantenna size, their dipolar resonance is tuned relative to the A-exciton transition in a proximal MoSe$_2$ monolayer achieving a total tuning of $sim 130;mathrm{meV}$. Differential reflectance measurements performed on $> 100$ structures reveal an apparent avoided crossing between exciton and dipolar mode and an exciton-plasmon coupling constant of $g= 55;mathrm{meV}$, representing $g/(hbaromega_X)geq3%$ of the transition energy. This places our hybrid system in the intermediate-coupling regime where spectra exhibit a characteristic Fano-like shape, indicative of the interplay between pronounced light-matter coupling and significant damping. We also demonstrate active control of the optical response by varying the polarization of the excitation light to programmably suppress coupling to the dipole mode. We further study the emerging optical signatures of the monolayer localized at dipole nanoantennas at $10;mathrm{K}$. Our findings represent a key step towards realizing non-linear photonic devices based on 2D materials with potential for low-energy and ultrafast performance.
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