  We study the dynamics of multiple coupled states under the influence of an
arbitrary time-dependent external field to investigate the femtosecond
laser-driven excitation and the spin-orbit mediated dissociation in the NaRb
dimer. In this process, the dimer is excited from the ground triplet state
$1^3\Sigma^+$ to the $1^3\Pi$ state using the femtosecond laser impulse and the
spin-orbit coupling between the $1^3\Pi$ and $2^1\Sigma^+$ states results in
the singlet-triplet transition. The laser impulse parameters are optimised to
obtain maximum yield in electronic states correlating with the first excited
atomic asymptote. We observe the detailed population statistics and power-law
decay of these states. Finally, the analysis of the population oscillations
allows us to determine the optimal time delay for dumping the molecule to its
absolute ground state.
