  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.
