Precision laser spectroscopy 1 of cold and trapped molecular ions is a powerful tool for fundamental physics, including the determination of fundamental constants 2 , the laboratory test for their possible variation 3,4 , and the search for a possible electric dipole moment of the electron 5 . While the complexity of molecular structure facilitates these applications, the absence of cycling transitions poses a challenge for direct laser cooling 6 , quantum state control [7][8][9][10][11] , and detection. Previously employed state detection techniques based on photodissociation 12 or chemical reactions 13 are destructive and therefore inefficient, restricting the achievable resolution in laser spectroscopy. Here we experimentally demonstrate nondestructive state detection of a single trapped molecular ion through its strong Coulomb coupling to a well-controlled co-trapped atomic ion. An algorithm based on a state-dependent optical dipole force 14 (ODF) changes the internal state of the atom conditioned on the internal state of the molecule. We show that individual quantum states in the molecular ion can be distinguished by their coupling strength to the ODF and observe black-body radiationinduced quantum jumps between rotational states of a single molecular ion. Using the detuning dependence of the state detection signal, we implement a variant of quantum logic spectroscopy 15,16 of a molecular resonance. The state detection technique we demonstrate is applicable to a wide range of molecular ions, enabling further applications in state-controlled quantum chemistry 17 and spectroscopic investigations of molecules serving as probes for interstellar clouds 18,19 .One of the salient features of trapped ion systems is that the universal Coulomb interaction allows strong coupling of diverse quantum objects, such as different species of atomic ions or atomic and molecular ions. Being able to perform quantum logic operations e.g. in the form of gates 14,20,21 between the quantum objects has proven a powerful tool for quantum information processing and quantum simulations in such systems. It also allows combining the advantages of different atomic species. Quantum logic spectroscopy is one such application in which the high degree of control achieved over selected atomic ions is extended to species over which such control is lacking 15,16 . Here, we demonstrate for the first time quantum logic operations between a single molecular ion and a co-trapped atomic ion, making a wide range of molecular ions accessible to this highlydeveloped toolbox. The presented technique allows the investigation of single molecules in a well isolated system avoiding disturbance from the environment, which is the limiting factor in other implementations of single molecule spectroscopy such as surface enhanced Raman spectroscopy (SERS) 22 Quantum logic operations between atoms are based on state dependent forces often induced by laser fields. The same approach is applicable to molecular ions. The coupling is now distributed over many ro-vibrat...

We demonstrate an efficient high-precision optical spectroscopy technique for single trapped ions with nonclosed transitions. In a double-shelving technique, the absorption of a single photon is first amplified to several phonons of a normal motional mode shared with a cotrapped cooling ion of a different species, before being further amplified to thousands of fluorescence photons emitted by the cooling ion using the standard electron shelving technique. We employ this extension of the photon recoil spectroscopy technique to perform the first high precision absolute frequency measurement of the 2 D 3=2 → 2 P 1=2 transition in calcium, resulting in a transition frequency of f ¼ 346 000 234 867ð96Þ kHz. Furthermore, we determine the isotope shift of this transition and the 2 S 1=2 → 2 P 1=2 transition for 42 Ca þ , 44 Ca þ , and 48 Ca þ ions relative to 40 Ca þ with an accuracy below 100 kHz. Improved field and mass shift constants of these transitions as well as changes in mean square nuclear charge radii are extracted from this high resolution data.

Precision spectroscopy of atomic and molecular ions offers a window to new physics, but is typically limited to species with a cycling transition for laser cooling and detection. Quantum logic spectroscopy has overcome this limitation for species with long-lived excited states. Here we extend quantum logic spectroscopy to fast, dipole-allowed transitions and apply it to perform an absolute frequency measurement. We detect the absorption of photons by the spectroscopically investigated ion through the photon recoil imparted on a co-trapped ion of a different species, on which we can perform efficient quantum logic detection techniques. This amplifies the recoil signal from a few absorbed photons to thousands of fluorescence photons. We resolve the line centre of a dipole-allowed transition in 40 Ca þ to 1/300 of its observed linewidth, rendering this measurement one of the most accurate of a broad transition. The simplicity and versatility of this approach enables spectroscopy of many previously inaccessible species. P recision optical spectroscopy of broad transitions provides information on the structure of molecules 1 , it allows tests of quantum electrodynamics 2 , and, through comparison with astrophysical data, probes for a possible variation of fundamental constants over cosmological scales 3,4 . Nuclear properties are revealed through isotope shift measurements 5-9 , or absolute frequency measurements 10,11 . Trapped ions are particularly well suited for such high precision experiments. The ions are stored in an almost field-free environment and can be laser-cooled to eliminate Doppler shifts. These features have enabled record accuracies in optical clocks [12][13][14][15] . For long-lived excited states such as in atoms with clock transitions, the electron-shelving technique amplifies the signal from a single absorbed photon by scattering many photons on a closed transition through selective optical coupling of one of the two spectroscopy states to a third electronic level 16 . The invention of quantum logic spectroscopy (QLS) 12,17 removed the need to detect the signal on the spectroscopically investigated ion (spectroscopy ion) by transferring the internal state information through a series of laser pulses to the co-trapped, so-called logic ion where the signal is observed via the electron-shelving technique. However, this original implementation of QLS requires long-lived spectroscopy states to implement the transfer sequence. For transitions with a short-lived excited state, spectroscopy of trapped ions is typically implemented through detection of scattered photons in laserinduced fluorescence 7,18-22 or detection of absorbed photons in laser absorption spectroscopy 23 . Neither of the two techniques reaches the fundamental quantum projection noise limit as in the electron-shelving technique 24 due to low light collection efficiency in laser-induced fluorescence and small atom-light coupling in laser absorption spectroscopy. In a variation of absorption spectroscopy, the detuning-dependent effect of...

Cold molecular ions are promising candidates in various fields ranging from precision spectroscopy and test of fundamental physics to ultracold chemistry. Control of internal and external degrees of freedom is a prerequisite for many of these applications. Motional-ground-state cooling represents the starting point for quantum logic-assisted internal state preparation, detection, and spectroscopy protocols. Robust and fast cooling is crucial to maximize the fraction of time available for the actual experiment. We optimize the cooling rate of ground-state cooling schemes for single 25Mg+ ions and sympathetic ground-state cooling of 24MgH+. In particular, we show that robust cooling is achieved by combining pulsed Raman sideband cooling with continuous quench cooling. Furthermore, we experimentally demonstrate an efficient strategy for ground-state cooling outside the Lamb-Dicke regime.

Protocols used in quantum information and precision spectroscopy rely on efficient internal quantum state discrimination. With a single ion in a linear Paul trap, we implement a novel detection method which utilizes correlations between two detection events with an intermediate spin-flip. The technique is experimentally characterized as more robust against fluctuations in detection laser power compared to conventionally implemented methods. Furthermore, systematic detection errors which limit the Rabi oscillation contrast in conventional methods are overcome.