  Rubidium dimers residing on the surface of He nanodroplets are doubly ionized
by an intense fs laser pulse leading to fragmentation into a pair of
$\mathrm{Rb^+}$ ions. We show that the kinetic energy of the $\mathrm{Rb^+}$
fragment ions can be used to identify dimers formed in either the X
$^1\Sigma_{\mathrm{g}}^+$ ground state or in the lowest-lying triplet state, a
$^3\Sigma_{\mathrm{u}}^+$. From the experiment, we estimate the abundance ratio
of dimers in the a and X states as a function of the mean droplet size and find
values between 4:1 and 5:1. Our technique applies generally to dimers and
trimers of alkali atoms, here also demonstrated for $\mathrm{Li_2}$,
$\mathrm{Na_2}$, and $\mathrm{K_2}$, and will enable fs time-resolved
measurements of their rotational and vibrational dynamics, possibly with atomic
structural resolution.
