We report a high-resolution spectroscopic study of molecular ions at millikelvin temperatures. We measured several rovibrational infrared transitions in HD+ molecular ions, stored in a radio-frequency trap and sympathetically cooled to approximate to 20 mK by laser-cooled 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 HD+ ions in the upper vibrational state. The method described here is expected to be generally applicable.
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