  Using a nonequilibrium implementation of the Lanczos-based exact
diagonalisation technique we study the possibility of the light-induced
superconducting phase coherence in a solid state system after an ultrafast
optical excitation. In particular, we investigate the buildup of
superconducting correlations by calculating an exact time-dependent wave
function reflecting the properties of the system in non-equilibrium and the
corresponding transient response functions. Within our picture we identify a
possible transient Meissner effect after dynamical quenching of the
non-superconducting wavefunction and extract a characteristic superfluid
density that we compare to experimental data. Finally, we find that the
stability of the induced superconducting state depends crucially on the nature
of the excitation quench: namely, a pure interaction quench induces a
long-lived superconducting state, whereas a phase quench leads to a short-lived
transient superconductor.
