Trapped atoms and ions are among the best controlled quantum systems which find widespread applications in quantum information, sensing and metrology. For molecules, however, a similar degree of control is currently lacking owing to their complex energy-level structure. Quantum-logic protocols in which atomic ions serve as probes for molecular ions are a promising route for achieving this level of control, especially with homonuclear molecules that decouple from black-body radiation. Here, a quantum-non-demolition protocol on single trapped N + 2 molecules is demonstrated. The spin-rovibronic state of the molecule is detected with more than 99% fidelity and the position and strength of a spectroscopic transition in the molecule are determined, both without destroying the molecular quantum state. The present method lays the foundations for new approaches to molecular precision spectroscopy, for state-to-state chemistry on the single-molecule level and for the implementation of molecular qubits.The impressive advances achieved in the control of ultracold trapped atoms and ions on the quantum level are now increasingly being transferred to molecular systems. Cold, trapped molecules have been created by, e.g., binding ultracold atoms via Feshbach resonances [1] and photoassociation [2, 3], molecular-beam slowing [4], direct laser cooling [5,6] and sympathetic cooling [7,8]. The trapping of the cold molecules enables experiments with long interaction times and thus paves the way for new applications such as studies of ultracold chemistry [9] and precision spectroscopic measurements which aim, e.g., at a precise determination of fundamental physical constants [10] and their possible time variation [11,12] as well as tests of fundamental theories which reach beyond the standard model [13,14].The complex energy level structure and the absence of optical cycling transitions in most molecular systems constitute a major challenge in the state preparation, laser cooling, state detection and coherent manipulation of molecules. Molecular ions trapped in radiofrequency ion traps which are sympathetically cooled by simultaneously trapped atomic ions [7,8] have proven a promising route for overcoming these obstacles. Recently, their rotational cooling and state preparation has been achieved [15][16][17][18], precision measurements of quantum electrodynamics and fundamental constants have been performed [10,19], the first studies of dipole-forbidden spectroscopic transitions in the mid-infrared spectral domain have been reported [20] and state-and energy-controlled collisions with cold atoms have been realized [21,22]. However, in order to reach the same exquisite level of control on the quantum level for a single molecule which can be achieved with trapped atoms [23], new methodological developments are required. In this context, the most promising route for achieving ultimate quantum control of molecular ions in trap experiments is constituted by quantum-logic protocols [24] in which a cotrapped atomic ion acts as a probe for th...

We present theoretical and experimental progress towards a new approach for the precision spectroscopy, coherent manipulation and state-to-state chemistry of single isolated molecular ions in the gas phase. Our method consists of a molecular beam for creating packets of rotationally cold neutrals from which a single molecule is state-selectively ionized and trapped inside a radiofrequency ion trap. In addition to the molecular ion, a single co-trapped atomic ion is used to cool the molecular external degrees of freedom to the ground state of the trap and to detect the molecular state using state-selective coherent motional excitation from a modulated optical-dipole force acting on the molecule. We present a detailed discussion and theoretical characterization of the present approach. We simulate the molecular signal experimentally using a single atomic ion indicating that different rovibronic molecular states can be resolved and individually detected with our method. The present approach for the coherent control and non-destructive detection of the quantum state of a single molecular ion opens up new perspectives for precision spectroscopies relevant for, e.g., tests of fundamental physical theories and the development of new types of clocks based on molecular vibrational transitions. It will also enable the observation and control of chemical reactions of single particles on the quantum level. While focusing on N + 2 as a prototypical example in the present work, our method is applicable to a wide range of diatomic and polyatomic molecules.

Quantum-logic techniques used to manipulate quantum systems are now increasingly being applied to molecules. Previous experiments on single trapped diatomic species have enabled state detection with excellent fidelities and highly precise spectroscopic measurements. However, for complex molecules with a dense energy-level structure improved methods are necessary. Here, we demonstrate an enhanced quantum protocol for molecular state detection using state-dependent forces. Our approach is based on interfering a reference and a signal force applied to a single atomic and molecular ion. By changing the relative phase of the forces, we identify states embedded in a dense molecular energy-level structure and monitor state-to-state inelastic scattering processes. This method can also be used to exclude a large number of states in a single measurement when the initial state preparation is imperfect and information on the molecular properties is incomplete. While the present experiments focus on N$${}_{2}^{+}$$ 2 + , the method is general and is expected to be of particular benefit for polyatomic systems.

We report a precise determination of the lifetime of the (4p) 2 P 3/2 state of 40 Ca + , τP 3/2 = 6.639(42) ns, using a combination of measurements of the induced light shift and scattering rate on a single trapped ion. Good agreement with the result of a recent high-level theoretical calculation, 6.69 (6) ns [Safronova et al., PRA 83, 012503 (2011)], but a 6-σ discrepancy with the most precise previous experimental value, 6.924(19) ns [Jin et al., PRL 70, 3213 (1993)] is found. To corroborate the consistency and accuracy of the new measurements, relativistically corrected ratios of reduceddipole-matrix elements are used to directly compare our result with a recent result for the P 1/2 state, yielding a good agreement. The application of the present method to precise determinations of radiative quantities of molecular systems is discussed.

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