Predissociation dynamics of charged long-range Rydberg molecules

We investigate predissociation in homonuclear ($^{87}$Rb$^*$$^{87}$Rb$^+$) and heteronuclear ($^{87}$Rb$^*$$^{7}$Li$^+$) long-range Rydberg atom-ion molecules. Owing to their micron-scale bond lengths, these dissociate on time scales far removed from those of more tightly bound diatomic molecules. We employ the eigenchannel $R$-matrix method to compute predissociation rates for a broad range of principal quantum numbers $n$. The rates depend strongly on the mass, but more remarkably display a rapid and periodic variation as a function of $n$ as well as within a single vibrational ladder. A semiclassical Landau-Zener-St\"uckelberg analysis reveals that St\"uckelberg interference governs the decay process and produces the observed variation in the molecular lifetime. Although the heavy mass of the homonuclear Rb molecule constrains its predissociation rates to a sub-kHz level, the lighter molecule $^{87}$Rb$^*$$^{7}$Li$^+$ dissociates on time scales competitive with radiative and collisional decay. This can enable in situ study of non-adiabatic decay via ion microscopy.