  The chemical potential of a superconductor is of critical importance since,
at equilibrium, it is the energy where electrons pair and form the
superconducting condensate. However, in non-equilibrium measurements, there may
be a difference between the chemical potential of the quasiparticles and that
of the pairs. Here we report a systematic time- and angle-resolved
photoemission study of the pump-induced change in the chemical potential of an
optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212) sample in both its
normal and superconducting states. The change in chemical potential can be
understood by separately considering the change in the valence band energy
relative to the vacuum, and the change in chemical potential relative to the
valence band energy. We attribute the former effect to a changing potential
barrier at the sample surface, and the latter effect to the conservation of
charge in an asymmetrical density of states. The results indicate that the pair
and quasiparticle chemical potentials follow each other even on picosecond
timescales.
