Journal Of The American Statistical Association V-27

Hybrid systems of laser-cooled trapped ions and ultracold atoms combined in a single experimental setup have recently emerged as a new platform for fundamental research in quantum physics. This paper reviews the theoretical and experimental progress in research on cold hybrid ion-atom systems which aim to combine the best features of the two well-established fields. A broad overview is provided of the theoretical description of ion-atom mixtures and their applications, and a report is given on advances in experiments with ions trapped in Paul or dipole traps overlapped with a cloud of cold atoms, and with ions directly produced in a Bose-Einstein condensate. This review begins with microscopic models describing the electronic structure, interactions, and collisional physics of ion-atom systems at low and ultralow temperatures, including radiative and nonradiative charge-transfer processes and their control with magnetically tunable Feshbach resonances. Then the relevant experimental techniques and the intrinsic properties of hybrid systems are described. In particular, the impact is discussed of the micromotion of ions in Paul traps on ion-atom hybrid systems. Next, a review of recent proposals is given for using ions immersed in ultracold gases for studying cold collisions, chemistry, many-body physics, quantum simulation, and quantum computation and their experimental realizations. The last part focuses on the formation of molecular ions via spontaneous radiative association, photoassociation, magnetoassociation, and sympathetic cooling. Applications and prospects are discussed of cold molecular ions for cold controlled chemistry and precision spectroscopy.

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Cold hybrid ion-atom systems

We demonstrate single-shot imaging and narrow-line cooling of individual alkaline earth atoms in optical tweezers; specifically, strontium-88 atoms trapped in $515.2~\text{nm}$ light. We achieve high-fidelity single-atom-resolved imaging by detecting photons from the broad singlet transition while cooling on the narrow intercombination line, and extend this technique to highly uniform two-dimensional arrays of $121$ tweezers. Cooling during imaging is based on a previously unobserved narrow-line Sisyphus mechanism, which we predict to be applicable in a wide variety of experimental situations. Further, we demonstrate optically resolved sideband cooling of a single atom close to the motional ground state of a tweezer. Precise determination of losses during imaging indicate that the branching ratio from $^1$P$_1$ to $^1$D$_2$ is more than a factor of two larger than commonly quoted, a discrepancy also predicted by our ab initio calculations. We also measure the differential polarizability of the intercombination line in a $515.2~\text{nm}$ tweezer and achieve a magic-trapping configuration by tuning the tweezer polarization from linear to elliptical. We present calculations, in agreement with our results, which predict a magic crossing for linear polarization at $520(2)~\text{nm}$ and a crossing independent of polarization at 500.65(50)nm. Our results pave the way for a wide range of novel experimental avenues based on individually controlled alkaline earth atoms in tweezers -- from fundamental experiments in atomic physics to quantum computing, simulation, and metrology implementations.

Alkaline earth atoms in optical tweezers

Multipole radiofrequency ion traps are a highly versatile tool to study molecular ions and their interactions in a well-controllable environment. In particular the cryogenic 22-pole ion trap configuration is used to study ion–molecule reactions and complex molecular spectroscopy at temperatures between a few kelvin and room temperatures. This paper presents a tutorial on radiofrequency ion trapping in multipole electrode configurations. Stable trapping conditions and buffer gas cooling, as well as important heating mechanisms, are discussed. In addition, selected experimental studies on cation and anion–molecule reactions and on spectroscopy of trapped ions are reviewed. Starting from these studies an outlook on the future of multipole ion trap research is given.

https://iopscience.iop.org/article/10.1088/0953-4075/42/15/154001/pdf

Radiofrequency multipole traps: tools for spectroscopy and dynamics of cold molecular ions

Ions confined using a Paul trap require a stable, high voltage and low noise radio frequency (RF) potential. We present a guide for the design and construction of a helical coil resonator for a desired frequency that maximises the quality factor for a set of experimental constraints. We provide an in-depth analysis of the system formed from a shielded helical coil and an ion trap by treating the system as a lumped element model. This allows us to predict the resonant frequency and quality factor in terms of the physical parameters of the resonator and the properties of the ion trap. We also compare theoretical predictions with experimental data for different resonators, and predict the voltage applied to the ion trap as a function of the Q-factor, input power and the properties of the resonant circuit.

On the application of radio frequency voltages to ion traps via helical resonators

Long trapping times, as well as low heating and decoherence rates, essentially isolating individual particles from the environment, are crucial ingredients for controlling these particles on the quantum level
 1
 . Here, we demonstrate that optical trapping and isolation of ions can be performed on a level comparable to neutral atoms, boosting their lifetime by three orders of magnitude compared to previous work
 2,3
 , and measure an upper bound of the total heating rate. The achieved isolation from the environment opens a path to a novel regime of ultracold interactions of ions and atoms at previously inaccessible collision energies
 4–6
 and may permit a novel class of experimental quantum simulations with ions and atoms in a variety of versatile optical trapping geometries
 7
 , for example, bichromatic traps or higher-dimensional optical lattices
 8,9
 . Optical trapping of ions with a high level of isolation from the environment is achieved, opening a path to performing ultracold interactions of ions and atoms at previously inaccessible collision energies.

Long lifetimes and effective isolation of ions in optical and electrostatic traps

A single laser ion trap confines six ions without additional confinement fields, paving the way for studies of the dynamics within Coulomb crystals that are masked by traditional trapping techniques.

https://link.aps.org/pdf/10.1103/PhysRevX.8.021028

Optical Trapping of Ion Coulomb Crystals

The electronic and motional degrees of freedom of trapped ions can be controlled and coherently coupled on the level of individual quanta. Assembling complex quantum systems ion by ion while keeping this unique level of control remains a challenging task. For many applications, linear chains of ions in conventional traps are ideally suited to address this problem. However, driven motion due to the magnetic or radio-frequency electric trapping fields sometimes limits the performance in one dimension and severely affects the extension to higher dimensional systems. Here, we report on the trapping of multiple Barium ions in a single-beam optical dipole trap without radio-frequency or additional magnetic fields. We study the persistence of order in ensembles of up to six ions within the optical trap, measure their temperature and conclude that the ions form a linear chain, commonly called a one-dimensional Coulomb crystal. As a proof-of-concept demonstration, we access the collective motion and perform spectrometry of the normal modes in the optical trap. Our system provides a platform which is free of driven motion and combines advantages of optical trapping, such as state-dependent confinement and nano-scale potentials, with the desirable properties of crystals of trapped ions, such as long-range interactions featuring collective motion. Starting with small numbers of ions, it has been proposed that these properties would allow the experimental study of many-body physics and the onset of structural quantum phase transitions between one- and two-dimensional crystals.

Optical trapping of ion Coulomb crystals

We report on single Barium ions confined in a near-infrared optical dipole trap for up to three seconds in absence of any radio-frequency fields. Additionally, the lifetime in a visible optical dipole trap is increased by two orders of magnitude as compared to the state-of-the-art using an efficient repumping method. We characterize the state-dependent potentials and measure an upper bound for the heating rate in the near-infrared trap. These findings are beneficial for entering the regime of ultracold interaction in atom-ion ensembles exploiting bichromatic optical dipole traps. Long lifetimes and low scattering rates are essential to reach long coherence times for quantum simulations in optical lattices employing many ions, or ions and atoms.

Long lifetimes in optical ion traps

The efficient suppression of autoionizing collisions is a stringent requirement to achieve quantum degeneracy in metastable rare gases. Here, we report on the suppression of Penning ionization in collisions between metastable He and laser-excited Li atoms. Our results show that the suppression is achieved by the conservation of both the total electron spin and $\mathrm{\ensuremath{\Lambda}}$, i.e., the projection of the total molecular orbital angular momentum along the internuclear axis. Our findings suggest that $\mathrm{\ensuremath{\Lambda}}$ conservation can be used as a more general means of reaction control, in particular, to improve schemes for the simultaneous laser cooling and trapping of metastable He and alkali-metal atoms.

Suppression of Penning ionization by orbital angular momentum conservation

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