  We present a full quantal study on the dissociation of a weakly bound
molecular ion in the presence of an external time-dependent electric field. We
focus on the dissociation dynamics of a molecular ion in a Paul trap relevant
for atom-ion hybrid traps. Our results show that a weakly bound molecular ion
survives in a Paul trap giving a theoretical ground to previous experimental
findings [A. Kr\"ukow et al. Phys. Rev. Lett. 116, 193201 (2016) and A.
Mohammadi et al. Phys. Rev. Research 3, 013196 (2021)]. In particular, we find
that weakly bound molecular ions are more likely to survive in traps with large
RF frequency. Similarly, we show that applying an electric field ramp is an
efficient method to state-selectively detect weakly bound molecular ions,
analogous to the well-known selective field ionization technique applied in
Rydberg atoms, that it may also be used to detect these species in atom-ion
hybrid traps.
