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We present a method of sensing AC magnetic fields. The method is based on the construction of a robust qubit by the application of continuous driving fields. Specifically, magnetic noise and power fluctuations of the driving fields do not operate within the robust qubit subspace, and hence, robustness to both external and controller noise is achieved. We consider trapped-ion based implementation via the dipole transitions, which is relevant for several types of ions, such as the $^{40}{\rm{Ca}}^{+}$, $^{88}{\rm{Sr}}^{+}$, and the $^{138}{\rm{Ba}}^{+}$ ions. Taking experimental errors into account, we conclude that the coherence time of the robust qubit can be improved by up to $\sim 4$ orders of magnitude compared to the coherence time of the bare states. We show how the robust qubit can be utilized for the task of sensing AC magnetic fields, leading to an improvement of $\sim 2$ orders of magnitude of the sensitivity. In addition, we present a microwave based sensing scheme that is suitable for ions with a hyperfine structure, such as the $^{9}{\rm{Be}}^{+}$,$^{25}{\rm{Mg}}^{+}$,$^{43}{\rm{Ca}}^{+}$,$^{87}{\rm{Sr}}^{+}$,$^{137}{\rm{Ba}}^{+}$,$^{111}{\rm{Cd}}^{+}$,$^{171}{\rm{Yb}}^{+}$, and the $^{199}{\rm{Hg}}^{+}$ ions. This scheme enables the enhanced sensing of high frequency fields at the GHz level.

A general method for rotational microwave spectroscopy and control of polar molecular ions via direct microwave addressing is considered. Our method makes use of spatially varying AC Stark shifts, induced by far off-resonant, focused laser beams to achieve an effective coupling between the rotational state of a molecular ion and the electronic state of an atomic ion. In this setting, the atomic ion is used for read-out of the molecular ion state, in a manner analogous to quantum logic spectroscopy based on Raman transitions. In addition to high-precision spectroscopy, this setting allows for rotational ground state cooling, and can be considered as a candidate for the quantum information processing with polar molecular ions. All elements of our proposal can be realized with currently available technology.

We present a new robust decoupling scheme suitable for levels with either half integer or integer angular momentum states. Through continuous dynamical decoupling techniques, we create a protected qubit subspace, utilizing a multi-state qubit construction. Remarkably, the multi-state system can also be comprised of multiple sub-states within a single level. Our scheme can be realized with state-of-the-art experimental setups and thus has immediate applications for quantum information science. While the scheme is general and relevant for a multitude of solid state and atomic systems, we analyze its performance for the case composed of trapped ions. Explicitly, we show how single qubit gates and an ensemble coupling to a cavity mode can be implemented efficiently. The scheme predicts a coherence time of ~1 second, as compared to typically a few milliseconds for the bare states.

We present a method to measure the decay rate of the first excited vibrational state of simple polar molecular ions being part of a Coulomb crystal in a cryogenic linear Paul trap. Specifically, we have monitored the decay of the $|\nu$=$1,J$=$1 \rangle_X$ towards the $|\nu$=$0,J$=$0 \rangle_X$ level in MgH$^+$ by saturated laser excitation of the $|\nu$=$0,J$=$2 \rangle_X$-$|\nu$=$1,J$=$1 \rangle_X$ transition followed by state selective resonance enhanced two-photon dissociation out of the $|\nu$=$0,J$=$2 \rangle_X$ level. The technique enables the determination of decay rates, and thus absorption strengths, with an accuracy at the few percent level., Comment: 5 pages, 4 figures

We examine the time-dependent dynamics of ion crystals in radiofrequency traps. The problem of stable trapping of general three-dimensional crystals is considered and the validity of the pseudopotential approximation is discussed. We derive analytically the micromotion amplitude of the ions, rigorously proving well-known experimental observations. We use a method of infinite determinants to find the modes which diagonalize the linearized time-dependent dynamical problem. This allows obtaining explicitly the ('Floquet-Lyapunov') transformation to coordinates of decoupled linear oscillators. We demonstrate the utility of the method by analyzing the modes of a small `peculiar' crystal in a linear Paul trap. The calculations can be readily generalized to multispecies ion crystals in general multipole traps, and time-dependent quantum wavefunctions of ion oscillations in such traps can be obtained., Comment: 24 pages, 3 figures, v2 adds citations and small corrections

We expand the solutions of linearly coupled Mathieu equations in terms of infinite-continued matrix inversions, and use it to find the modes which diagonalize the dynamical problem. This allows obtaining explicitly the ('Floquet-Lyapunov') transformation to coordinates in which the motion is that of decoupled linear oscillators. We use this transformation to solve the Heisenberg equations of the corresponding quantum-mechanical problem, and find the quantum wavefunctions for stable oscillations, expressed in configuration-space. The obtained transformation and quantum solutions can be applied to more general linear systems with periodic coefficients (coupled Hill equations, periodically driven parametric oscillators), and to nonlinear systems as a starting point for convenient perturbative treatment of the nonlinearity., Comment: 25 pages, v2 adds citations and small corrections

We demonstrate resolved sideband laser cooling of a single 40Ca+ ion in a macroscopic linear radio frequency trap with a radial diagonal electrode spacing of 7 mm and an rf drive frequency of just 3.7 MHz. For an oscillation frequency of 585 kHz along the rf-field-free axis, a ground state population of 99+-1% has been achieved, corresponding to a temperature of only 6 microkelvin. For several oscillation frequencies in the range 285 - 585 kHz, heating rates below one motional quantum per second have been measured at room temperature. The lowest measured heating power is about an order of magnitude lower than reported previously in room temperature, as well as cryogenically cooled traps., Comment: 4 figures

A detailed description and theoretical analysis of experiments achieving coherent coupling between an ion Coulomb crystal and an optical cavity field are presented. The various methods used to measure the coherent coupling rate between large ion Coulomb crystals in a linear quadrupole radiofrequency ion trap and a single field mode of a moderately high-finesse cavity are described in detail. Theoretical models based on a semiclassical approach are applied in assessment of the experimental results of [P. F. Herskind et al., Nature Phys. 5, 494 (2009)] and of complementary new measurements. Generally, a very good agreement between theory and experiments is obtained., Comment: 15 pages, 15 figures

We report on a novel non-invasive method to determine the normal mode frequencies of ion Coulomb crystals in traps based on the resonance enhanced collective coupling between the electronic states of the ions and an optical cavity field at the single photon level. Excitations of the normal modes are observed through a Doppler broadening of the resonance. An excellent agreement with the predictions of a zero-temperature uniformly charged liquid plasma model is found. The technique opens up for investigations of the heating and damping of cold plasma modes, as well as the coupling between them., Comment: 4 pages, 4 figures

We present an investigation of the coherent coupling of various transverse field modes of an optical cavity to ion Coulomb crystals. The obtained experimental results, which include the demonstration of identical collective coupling rates for different transverse modes of a cavity field to ions in the same large Coulomb crystal, are in excellent agreement with theoretical predictions. The results furthermore suggest that Coulomb crystals in the future may serve as near-ideal media for highfidelity multi-mode quantum information processing and communication purposes, including the generation and storage of single photon qubits encoded in different transverse modes., Comment: 4 pages, 5 figures

We demonstrate a general technique to achieve a precise radial displacement of the nodal line of the radiofrequency (rf) field in a linear Paul trap. The technique relies on selective adjustment of the load capacitance of the trap electrodes, achieved through the addition of capacitors to the basic resonant rf-circuit used to drive the trap. Displacements of up to 100 micrometer with micrometer precision are measured using a combination of fluorescence images of ion Coulomb crystals and coherent coupling of such crystals to a mode of an optical cavity. The displacements are made without measurable distortion of the shape or structure of the Coulomb crystals, as well as without introducing excess heating commonly associated with the radial displacement of crystals by adjustment through static potentials. We expect this technique to be of importance for future developments of microtrap architectures and ion-based cavity QED.

We demonstrate the implementation of a spin qubit with a single Ca ion in a micro ion trap. The qubit is encoded in the Zeeman ground state levels mJ=+1/2 and mJ=-1/2 of the S1/2 state of the ion. We show sideband cooling close to the vibrational ground state and demonstrate the initialization and readout of the qubit levels with 99.5% efficiency. We employ a Raman transition close to the S1/2 - P1/2 resonance for coherent manipulation of the qubit. We observe single qubit rotations with 96% fidelity and gate times below 5mus. Rabi oscillations on the blue motional sideband are used to extract the phonon number distribution. The dynamics of this distribution is analyzed to deduce the trap-induced heating rate of 0.3(1) phonons/ms.

We report on the loading of large ion Coulomb crystals into a linear Paul trap incorporating a high-Finesse optical cavity (F~3200). We show that, even though the 3-mm diameter dielectric cavity mirrors are placed between the trap electrodes and separated by only 12 mm, it is possible to produce in situ ion Coulomb crystals containing more than 100.000 calcium ions of various isotopes and with lengths of up to several millimeters along the cavity axis. We show that the number of ions inside the cavity mode is in principle high enough to achieve strong collective coupling between the ion Coulomb crystal and the cavity field. The results thus represent an important step towards ion trap based Cavity Quantum ElectroDynamics (CQED) experiments using cold ion Coulomb crystals.

Doppler cooling of calcium ions has been experimentally demonstrated using the S1/2 to D5/2 dipole-forbidden transition. Scattering forces and fluorescence levels a factor of 5 smaller than for usual Doppler cooling on the dipole allowed S1/2 to P1/2 transition have been achieved. Since the light scattered from the ions can be monitored at (violet) wavelengths that are very different from the excitation wavelengths, single ions can be detected with an essentially zero background level. This, as well as other features of the cooling scheme, can be extremely valuable for ion trap based quantum information processing., Comment: 4 pages, 4 figures, minor changes to commentary and references

An experimental demonstration of a novel all-optical technique for loading ion traps, that has particular application to microtrap architectures, is presented. The technique is based on photo-ionisation of an atomic beam created by pulsed laser ablation of a calcium target, and provides improved temporal control compared to traditional trap loading methods. Ion loading rates as high as 125 ions per second have so far been observed. Also described are observations of trap loading where Rydberg state atoms are photo-ionised by the ion Doppler cooling laser., Comment: 8 pages, 9 figures

We report on the observations of three-dimensional long-range ordered structures in the central $^{40}$Ca$^+$ ion component of $^{40}$Ca$^+$--$^{44}$Ca$^+$ two-species ion Coulomb crystals in a linear Paul trap. In contrast to long-range ordering previously observed in single species crystals, the structures observed are strikingly persistent and always of one specific type in one particular orientation. Molecular dynamics simulations strongly indicate that these characteristics are a hitherto unpredicted consequence of the co-axial cylindrical symmetry of the central ion component of the Coulomb crystal and the radio frequency quadrupole trapping field., Comment: Abstract and conclusion changed. Fig. 4 corrected

Three-dimensional long-range ordered structures in smaller and near-spherically symmetric Coulomb crystals of ^{40}Ca^+ ions confined in a linear rf Paul trap have been observed when the number of ions exceeds ~1000 ions. This result is unexpected from ground state molecular dynamics (MD) simulations, but found to be in agreement with MD simulations of metastable ion configurations. Previously, three-dimensional long-range ordered structures have only been reported in Penning traps in systems of ~50,000 ions or more., Comment: 5 pages; 4 figures; to appear in Phys. Rev. Lett.; changed contents

We show how to prepare a single molecular ion in a specific internal quantum state in a situation where the molecule is trapped and sympathetically cooled by an atomic ion and where its internal degrees of freedom are initially in thermal equilibrium with the surroundings. The scheme is based on conditional creation of correlation between the internal state of the molecule and the translational state of the collective motion of the two ions, followed by a projection measurement of this collective mode by atomic ion shelving techniques. State preparation in a large number of internal states is possible., Comment: 4 pages, 2 figures, 2 tables

The translational motion of molecular ions can be effectively cooled sympathetically to translational temperatures below 100 mK in ion traps through Coulomb interactions with laser-cooled atomic ions. The ro-vibrational degrees of freedom, however, are expected to be largely unaffected during translational cooling. We have previously proposed schemes for cooling of the internal degrees of freedom of such translationally cold but internally hot heteronuclear diatomic ions in the simplest case of ^1-Sigma electronic ground state molecules. Here we present a significant simplification of these schemes and make a generalization to the most frequently encountered electronic ground states of heteronuclear molecular ions: ^1-Sigma, ^2-Sigma, ^3-Sigma and ^2-Pi. The schemes are relying on one or two laser driven transitions with the possible inclusion of a tailored incoherent far infrared radiation field., Comment: 16 pages, 13 figures

A simple and non-destructive method for identification of a single molecular ion sympathetically cooled by a single laser cooled atomic ion in a linear Paul trap is demonstrated. The technique is based on a precise determination of the molecular ion mass through a measurement of the eigenfrequency of a common motional mode of the two ions. The demonstrated mass resolution is sufficiently high that a particular molecular ion species can be distinguished from other equally charged atomic or molecular ions having the same total number of nucleons.

We investigate theoretically the application of tailored incoherent far-infrared fields in combination with laser excitation of a single rovibrational transition for rotational cooling of translationally cold polar diatomic molecules. The cooling schemes are effective on a timescale shorter than typical unperturbed trapping times in ion traps and comparable to obtainable confinement times of neutral molecules., Comment: 5 pages, 2 figures

Using a technique based on production of ion Coulomb crystals, the isotope shifts of the 4s2 1S0 -> 4s5p 1P1 transition for all naturally occurring isotopes of calcium as well as the hyperfine splitting of the 4s5p 1P1 state in Ca-43 have been measured. The field shift and specific mass shift coefficients as well as the hyperfine structure constants for Ca-43 have been derived from the data., Comment: 6 pages,6 figures, to be published in Phys. Rev. A

The translational motion of molecular ions can be effectively cooled sympathetically to temperatures below 100 mK in ion traps through Coulomb interactions with laser-cooled atomic ions. The distribution of internal rovibrational states, however, gets in thermal equilibrium with the typically much higher temperature of the environment within tens of seconds. We consider a concept for rotational cooling of such internally hot, but translationally cold heteronuclear diatomic molecular ions. The scheme relies on a combination of optical pumping from a few specific rotational levels into a ``dark state'' with redistribution of rotational populations mediated by blackbody radiation., Comment: 4 pages, 5 figures