Direct Frequency-Comb-Driven Raman Transitions in the Terahertz Range.

We demonstrate the use of a femtosecond frequency comb to coherently drive stimulated Raman transitions between terahertz-spaced atomic energy levels. More specifically, we address the 3d ^{2}D_{3/2} and 3d ^{2}D_{5/2} fine structure levels of a single trapped ^{40}Ca^{+} ion and spectroscopically resolve the transition frequency to be ν_{D}=1,819,599,021,534±8 Hz. The achieved accuracy is nearly a factor of five better than the previous best Raman spectroscopy, and is currently limited by the stability of our atomic clock reference. Furthermore, the population dynamics of frequency-comb-driven Raman transitions can be fully predicted from the spectral properties of the frequency comb, and Rabi oscillations with a contrast of 99.3(6)% and millisecond coherence time have been achieved. Importantly, the technique can be easily generalized to transitions in the sub-kHz to tens of THz range and should be applicable for driving, e.g., spin-resolved rovibrational transitions in molecules and hyperfine transitions in highly charged ions.

Coulomb crystallization of highly charged ions.

Control over the motional degrees of freedom of atoms, ions, and molecules in a field-free environment enables unrivalled measurement accuracies but has yet to be applied to highly charged ions (HCIs), which are of particular interest to future atomic clock designs and searches for physics beyond the Standard Model. Here, we report on the Coulomb crystallization of HCIs (specifically (40)Ar(13+)) produced in an electron beam ion trap and retrapped in a cryogenic linear radiofrequency trap by means of sympathetic motional cooling through Coulomb interaction with a directly laser-cooled ensemble of Be(+) ions. We also demonstrate cooling of a single Ar(13+) ion by a single Be(+) ion-the prerequisite for quantum logic spectroscopy with a potential 10(-19) accuracy level. Achieving a seven-orders-of-magnitude decrease in HCI temperature starting at megakelvin down to the millikelvin range removes the major obstacle for HCI investigation with high-precision laser spectroscopy.

Efficient rotational cooling of Coulomb-crystallized molecular ions by a helium buffer gas.

The preparation of cold molecules is of great importance in many contexts, such as fundamental physics investigations, high-resolution spectroscopy of complex molecules, cold chemistry and astrochemistry. One versatile and widely applied method to cool molecules is helium buffer-gas cooling in either a supersonic beam expansion or a cryogenic trap environment. Another more recent method applicable to trapped molecular ions relies on sympathetic translational cooling, through collisional interactions with co-trapped, laser-cooled atomic ions, into spatially ordered structures called Coulomb crystals, combined with laser-controlled internal-state preparation. Here we present experimental results on helium buffer-gas cooling of the rotational degrees of freedom of MgH(+) molecular ions, which have been trapped and sympathetically cooled in a cryogenic linear radio-frequency quadrupole trap. With helium collision rates of only about ten per second--that is, four to five orders of magnitude lower than in typical buffer-gas cooling settings--we have cooled a single molecular ion to a rotational temperature of 7.5(+0.9)(-0.7) kelvin, the lowest such temperature so far measured. In addition, by varying the shape of, or the number of atomic and molecular ions in, larger Coulomb crystals, or both, we have tuned the effective rotational temperature from about 7 kelvin to about 60 kelvin by changing the translational micromotion energy of the ions. The extremely low helium collision rate may allow for sympathetic sideband cooling of single molecular ions, and eventually make quantum-logic spectroscopy of buffer-gas-cooled molecular ions feasible. Furthermore, application of the present cooling scheme to complex molecular ions should enable single- or few-state manipulations of individual molecules of biological interest.

Decay rate measurement of the first vibrationally excited state of MgH+ in a cryogenic Paul trap.

We present a method to measure the decay rate of the first excited vibrational state of polar molecular ions that are part of a Coulomb crystal in a cryogenic linear Paul trap. Specifically, we have monitored the decay of the |ν = 1, J = 1)(X) towards the |ν = 0, J = 0)(X) level in MgH+ by saturated laser excitation of the |ν = 0, J = 2)(X)-|ν = 1, J = 1)(X) transition followed by state selective resonance enhanced two-photon dissociation out of the |ν = 0, J=2)(X) level. The experimentally observed rate of 6.32(0.69) s(-1) is in excellent agreement with the theory value of 6.13(0.03) s(-1) (this Letter). The technique enables the determination of decay rates, and thus absorption strengths, with an accuracy at the few percent level.

General scheme for the construction of a protected qubit subspace.

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 multistate qubit construction. Remarkably, the multistate system can also be composed of multiple substates 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 s, as compared to typically a few milliseconds for the bare states.

Cryogenic linear Paul trap for cold highly charged ion experiments.

Storage and cooling of highly charged ions require ultra-high vacuum levels obtainable by means of cryogenic methods. We have developed a linear Paul trap operating at 4 K capable of very long ion storage times of about 30 h. A conservative upper bound of the H(2) partial pressure of about 10(-15) mbar (at 4 K) is obtained from this. External ion injection is possible and optimized optical access for lasers is provided, while exposure to black body radiation is minimized. First results of its operation with atomic and molecular ions are presented. An all-solid state laser system at 313 nm has been set up to provide cold Be(+) ions for sympathetic cooling of highly charged ions.

Noninvasive vibrational mode spectroscopy of ion Coulomb crystals through resonant collective coupling to an optical cavity field.

We report on a novel noninvasive 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.

Observation of three-dimensional long-range order in small ion coulomb crystals in an rf trap.

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 approximately 1,000 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 approximately 50,000 ions or more.

Nondestructive identification of cold and extremely localized single molecular ions.

We demonstrate a simple and nondestructive method for identification of a single molecular ion sympathetically cooled by a single laser cooled atomic ion in a linear Paul trap. The technique is based on a precise nondestructive 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 molecular ion mass doublets can potentially be distinguished from each other. The obtained results represent an important step towards single molecule gas phase chemical physics.

Coulomb bicrystals of species with identical charge-to-mass ratios.

Structures of cold bicomponent Coulomb systems of particles with identical charge-to-mass ratios and common oscillation frequency in a spherical harmonic potential are studied by molecular dynamics simulations with up to 10(6) particles. For most initial conditions and cooling rates, the final state becomes a completely mixed core surrounded by a set of nearly degenerated double shells of separate species. For an equal amount of the two species, it is found that the ground state for larger systems consists of a simple cubic structured core surrounded by outer double-shell structures.

Blackbody-radiation-assisted laser cooling of molecular ions.

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.

Structural properties of two-component coulomb crystals in linear paul traps.

We report on structural properties of two-component Coulomb crystals in a linear Paul trap. The crystals consist of two laser cooled ion species, 24Mg+ and 40Ca+. The lighter 24Mg+ ions form an inner cylindrical crystal structure surprisingly similar to that of an infinitely long single component crystal, while the outermost shell of the surrounding 40Ca+ ions have a spheroidal shape, which is highly insensitive to the presence of the 24Mg+ ions. Observed changes in the radial separation of the two ion species with the radius of the inner cylindrical crystal is explained by a simple model.

From the cover: temperature, ordering, and equilibrium with time-dependent confining forces.

The concepts of temperature and equilibrium are not well defined in systems of particles with time-varying external forces. An example is a radio frequency ion trap, with the ions laser cooled into an ordered solid, characteristic of sub-mK temperatures, whereas the kinetic energies associated with the fast coherent motion in the trap are up to 7 orders of magnitude higher. Simulations with 1,000 ions reach equilibrium between the degrees of freedom when only aperiodic displacements (secular motion) are considered. The coupling of the periodic driven motion associated with the confinement to the nonperiodic random motion of the ions is very small at low temperatures and increases quadratically with temperature.