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Trapped atoms and ions are among the best controlled quantum systems whichfind widespread applications in quantum information, sensing and metrology. Formolecules, however, a similar degree of control is currently lacking owing totheir complex energy-level structure. Quantum-logic protocols in which atomicions serve as probes for molecular ions are a promising route for achievingthis level of control, especially with homonuclear molecules that decouple fromblack-body radiation. Here, a quantum-non-demolition protocol on single trappedN$_2^+$ molecules is demonstrated. The spin-rovibronic state of the molecule isdetected with more than 99% fidelity and the position and strength of aspectroscopic transition in the molecule are determined, both withoutdestroying the molecular quantum state. The present method lays the foundationsfor new approaches to molecular precision spectroscopy, for state-to-statechemistry on the single-molecule level and for the implementation of molecularqubits.

Quantum non-demolition state detection and spectroscopy of single trapped molecules