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Spectroscopy is a powerful tool for studying molecules and is commonlyperformed on large thermal molecular ensembles that are perturbed by motionalshifts and interactions with the environment and one another, resulting inconvoluted spectra and limited resolution. Here, we use generally applicablequantum-logic techniques to prepare a trapped molecular ion in a single quantumstate, drive terahertz rotational transitions with an optical frequency comb,and read out the final state non-destructively, leaving the molecule ready forfurther manipulation. We resolve rotational transitions to 11 significantdigits and derive the rotational constant of CaH+ to be B_R = 142501777.9(1.7)kHz. Our approach suits a wide range of molecular ions, including polyatomicsand species relevant for tests of fundamental physics, chemistry, andastrophysics.

Precision frequency-comb terahertz spectroscopy on pure quantum states of a single molecular ion