  The importance of multi-electron dynamics during the tunnel ionization of a
correlated quantum system is investigated. By comparison of the solution of the
time-dependent Schr\"odinger equation (TDSE) with the time-dependent
configuration interaction singles approach (TDCIS), we demonstrate the
importance of a multi-electron description of the tunnel ionization process
especially for weakly confined quantum systems. Within this context, we observe
that adiabatic driving by an intense light field can even enhance the
correlations between still trapped electrons.
