These data files contain the data for the measured transition frequencies shown in Table I and the traces in Figure 3 of the publication "Frequency-comb spectroscopy on pure quantum states of a single molecular ion," accessible at https://arxiv.org/abs/1911.12808. In this publication we use generally applicable quantum-logic techniques to prepare a trapped molecular ion in a single quantum state, drive terahertz rotational transitions with an optical frequency comb, and read out the molecular state non-destructively, leaving the molecule ready for further manipulation.

One file contains data For Table 1. In the measurement of rotational transition frequencies, the intensities of the comb beams are varied to characterize the effect of AC Stark shift, while the intensity ratio between the sigma and pi polarized beams are kept at close to 2. The average intensity of the sigma-polarized comb beam is quantified by measuring the resultant Stark shift, fSS_sigma, on the 729 nm transition of the Ca+ ion, with the Ca+ ion where the CaH+ ion would be during rotational spectroscopy experiments.

The other file contains data for Figure 3, (a) Spectra for the J = 4 to 2 transition: 40CaH+ is prepared in J = 2, followed by a pulse train from the comb Raman beams probing the J = 2 to J = 4 transition. After the probe pulse train, projective measurements of both initial and final states are performed and the state occupation probability is determined. The probe time is ~1.6 ms. The frequency shows the offset of the Raman difference frequency from the resonant value. (b) Rabi flopping on the J = 4 to J = 2 transition: Starting in J = 4, with the comb Raman pulse detuning set to resonance, the state of the 40CaH+ ion is driven coherently to J = 2 by a pulse train of variable duration from the comb Raman beams. The center wavelength of the frequency comb was ~800 nm for these spectra and Rabi flopping traces. The error bars stand for ±1 standard deviation.