The unique excited-state properties of the overlapped (diabatic) optically-allowed 1B(u)(+) and the optically-forbidden 1B(u)(-) or 3A(g)(-) vibronic levels close to conical intersection ('the diabatic pair') are summarized: Pump-probe spectroscopy after selective excitation with similar to 100 fs pulses of all-trans carotenoids (Cars) in nonpolar solvent identified a symmetry selection rule in the diabatic electronic mixing and diabatic internal conversion, i.e., '1B(u)(+)-to-1B(u)(-) is allowed but 1B(u)(+)-to-3A(g)(-) is forbidden'. On the other hand, pump-probe spectroscopy after coherent excitation with similar to 30 fs of all-trans Cars in THF generated stimulated emission with quantum beat, consisting of the long-lived coherent diabatic cross term and a pair of short-lived incoherent terms.