Rovibrational spectroscopy of trapped molecular hydrogen ions at millikelvin temperatures

We report a high-resolution spectroscopic study of molecular ions at millikelvin temperatures. We measured several rovibrational infrared transitions in $\mathrm{H}{\mathrm{D}}^{+}$ molecular ions, stored in a radio-frequency trap and sympathetically cooled to $\approx 20\mathrm{mK}$ by laser-cooled ${\mathrm{Be}}^{+}$ ions. We observed hyperfine splitting of the lines, in good agreement with theoretical predictions. The transitions were detected by monitoring the decrease in ion number after selective photodissociation of $\mathrm{H}{\mathrm{D}}^{+}$ ions in the upper vibrational state. The method described here is expected to be generally applicable.