Time- and angle-resolved extreme ultraviolet photoemission spectroscopy is used to study the electronic structure dynamics in BaFe$_2$As$_2$ around the high-symmetry points $Gamma$ and $M$. A global oscillation of the Fermi level at the frequency of
the $A_{1g}$(As) phonon mode is observed. It is argued that this behavior reflects a modulation of the effective chemical potential in the photoexcited surface region that arises from the high sensitivity of the band structure near the Fermi level to the $A_{1g}$ phonon mode combined with a low electron diffusivity perpendicular to the layers. The results establish a novel way to tune the electronic properties of iron pnictides: coherent control of the effective chemical potential. The results further suggest that the equilibration time for the effective chemical potential needs to be considered in the ultrafast electronic structure dynamics of materials with weak interlayer coupling.
