  We study the thermalization of a strongly coupled quantum field theory in the
presence of a chemical potential. More precisely, using the holographic
prescription, we calculate non- local operators such as two point function,
Wilson loop and entanglement entropy in a time- dependent background that
interpolates between AdSd+1 and AdSd+1 -Reissner-Nordstr\"om for d = 3, 4. We
find that it is the entanglement entropy that thermalizes the latest and thus
sets a time-scale for equilibration in the field theory. We study the
dependence of the thermalization time on the probe length and the chemical
potential. We find an interesting non-monotonic behavior. For a fixed small
value of T l and small values of \mu/T the thermalization time decreases as we
increase \mu/T, thus the plasma thermalizes faster. For large values of \mu/T
the dependence changes and the thermalization time increases with increasing
\mu/T . On the other hand, if we increase the value of T l this non-monotonic
behavior becomes less pronounced and eventually disappears indicating two
different regimes for the physics of thermalization: non-monotonic dependence
of the thermalization time on the chemical potential for T l << 1 and monotonic
for T l >> 1.
