  Using the adaptive time-dependent density-matrix renormalization group method
for the 1D Hubbard model, the splitting of local perturbations into separate
wave packets carrying charge and spin is observed in real-time. We show the
robustness of this separation beyond the low-energy Luttinger liquid theory by
studying the time-evolution of single particle excitations and density wave
packets. A striking signature of spin-charge separation is found in 1D cold
Fermi gases in a harmonic trap at the boundary between liquid and
Mott-insulating phases. We give quantitative estimates for an experimental
observation of spin-charge separation in an array of atomic wires.
