Molecular ions that are generated by chemical reactions with trapped atomic ions can serve as an accessible testbed for developing molecular quantum technologies. On the other hand, they are also a hindrance to scaling up quantum computers based on atomic ions as unavoidable reactions with background gas destroy the information carriers. Here, we investigate the single- and two-photon dissociation processes of single molecular ions co-trapped in ion crystals using a femtosecond laser system. We report the photodissociation cross section spectra of for single-photon processes at 245 - 275nm and for two-photon processes at 500 - 540nm. Measurements are interpreted with quantum-chemical calculations, which predict the photodissociation threshold for at 265nm. This result can serve as a basis for dissociation-based spectroscopy for studying the internal structure of . The result also gives a prescription for recycling ions in large-scale trapped quantum experiments from undesired ions formed in the presence of background water vapor.

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