Ultranarrow, electric-dipole forbidden transitions between rovibrational states in molecules and molecular ions with expected natural linewidths on the Hz level present intriguing opportunities for the development of highly precise mid-infrared frequency standards and for the exploration of fundamental physical problems such as possible time variations of fundamental constants [1]. The molecular nitrogen ion N₂⁺ has been proposed as an attractive system for precision molecular spectroscopy because, as an apolar diatomic ion, it features small systematic shifts and transitions with low sensitivity to magnetic fields in its electronic ground state [2,3]. However, the experimental detection of pure rovibrational transitions in systems like N₂⁺ [4] and their precision spectroscopy is challenging on several levels. Besides the weak line strengths, which require highly sensitive detection methods, the positions of the lines are usually known only with substantial uncertainties based on spectroscopic constants determined through indirect methods. Moreover, theoretical predictions of the line strengths are also affected by significant uncertainties.

Here, we report the first observation of electric-quadrupole rovibrational transitions in single molecular ions using a highly sensitive quantum-logic detection protocol [5]. We studied individual hyperfine-Zeeman components of the |v=1, N=2>←|v=0, N=0> rovibrational transition in the X²Σ_g⁺ electronic ground state of single N₂⁺ ions confined in a radiofrequency ion trap with a co-trapped Ca⁺ ion used for sympathetic laser cooling and quantum-logic state detection. The transitions were directly driven by rapid adiabatic passage using a frequency-chirped laser pulse from a mid-infrared quantum cascade laser. This approach enabled the effective, fully reversible transfer of the rovibrational populations even without precise knowledge of the transition frequencies and at the same time allowed the recycling of the same single molecule in sequential spectroscopic experiments. Thus, line positions could be detected with a 2 MHz uncertainty limited by the frequency sweep of the laser pulse. The present approach represents a powerful methodology for coherently manipulating single molecules on ultranarrow spectroscopic transitions for precision measurements and quantum technologies applications. It can readily be adapted for other diatomic and polyatomic species, provided suitable laser sources for excitation and quantum-logic detection of transitions are available.

[1] M. S. Safronova, D. Budker, D. DeMille, D. F. J. Kimball, A. Derevianko, and C. W. Clark. Rev. Mod. Phys., 2018, 90, 025008.

[2] M. Kajita,  Phys. Rev. A, 2015, 92, 043423.

[3] K. Najafian, Z. Meir, and S. Willitsch. Phys. Chem. Chem. Phys., 2020, 22, 23083-23098.

[4] M. Germann, X. Tong, and S. Willitsch. Nat. Phys., 2014, 10, 820-824.

[5] M. Sinhal, Z. Meir, K. Najafian, G. Hegi, and S. Willitsch. Science, 2020, 367, 1213-1218.