  Temperature-dependent reflectivity measurements in the frequency range 85 -
7000 cm$^{-1}$ were performed on BaFe$_2$As$_2$ single crystals under pressure
up to $\sim$5 GPa. The corresponding pressure- and temperature-dependent
optical conductivity was analyzed with the Drude-Lorentz model to extract the
coherent and incoherent contributions. The gradual suppression of the
spin-density wave (SDW) state with increasing pressure and the appearance of
the superconducting phase coexisting with the SDW phase at 3.6~GPa were
observed. At 3.6~GPa, the reflectivity reaches unity below $\sim$95~cm$^{-1}$
indicating the opening of the superconducting gap and shows a full gap tendency
at 6 K.
