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...

The quantum noise of the vacuum limits the achievable sensitivity of quantum sensors. In non-classical measurement schemes the noise can be reduced to overcome this limitation. However, schemes based on squeezed or Schrödinger cat states require alignment of the relative phase between the measured interaction and the non-classical quantum state. Here we present two measurement schemes on a trapped ion prepared in a motional Fock state for displacement and frequency metrology that are insensitive to this phase. The achieved statistical uncertainty is below the standard quantum limit set by quantum vacuum fluctuations, enabling applications in spectroscopy and mass measurements.

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.

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.

Nuclear magnetic resonance (NMR) spectra of 23Na (I = 32) and 93Nb (I = 92) from a powdered sample of NaNbO3 have been studied. At room temperature the 23Na spectrum shows the presence of two distinct sites, one having axial symmetry with a coupling constant of 21.5 ± 0.2 MHz and the other having an asymmetry parameter lying between 0.80 and 1.0 with a coupling constant of 1.0 ± 0.1 MHz. The niobium spectrum arises from a single site with a coupling constant of 19.7 ± 0.5 MHz and an asymmetry parameter of 0.82 ± 0.02. The (12 ↔ − 12) transition in the 93Nb spectrum exhibits some unusual features which were confirmed by computer-simulated powder patterns. The temperature dependence of one 23Na site indicated a rather linear decrease in the coupling constant, from 2.6–1.6 MHz, and the asymmetry parameter was approximately zero as the temperature increased from − 170–280°C. The 93Nb quadrupole interaction showed a linear decrease not only in the coupling constant, from 19.7–10 MHz, but also in the asymmetry parameter, from 0.82–0.64, as the temperature rose from room temperature to 270°C. Electric-field-gradient calculations for 93Nb produced coupling constants lower than the measured value by about an order of magnitude while yielding values of the asymmetry parameter comparable to that observed. Similar calculations for 23Na gave relatively high values of the asymmetry parameter, and the coupling constants were of the same order of magnitude as those determined experimentally. Third-order corrections to the NMR frequencies perturbed by the quadrupole interactions for the case of the asymmetry parameter unequal to zero were calculated. These proved to be negligible except for the case of niobium at low frequencies.