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The transparent and conductive properties of indium tin oxide (ITO) thin films, make them an attractive coating for optically integrated ion traps. However, the relatively low transmittance for wavelengths $<$ 400 nm, high scattering and high production temperature limits the usability in trapped-ion-based quantum technologies. Here we present ITO coatings and a combined ITO + anti-reflective (AR) coating system optimized for an ion trap applied using ion beam sputtering (IBS). The coatings feature a high transmittance for wavelengths $<$ 400 nm and additional wavelengths up to 1000 nm, low scattering and low production temperature $<$ 150 $^{\circ}$C. The transmission, reflection and absorption spectra are simulated and the resistance, transmittance and scattering at 370 nm are measured for different ITO coating thicknesses and the ITO + AR coating system. For the ITO + AR coating system a resistance of 115 $\pm$ 5 $\Omega/\Box$, transmittance of 80$\%$ and scattering of 0.012 $\pm$ 0.002$\%$ at 370 nm is achieved., Comment: 13 pages, 9 figures

The Standard Model of particle physics describes the properties of elementary particles and their interactions remarkably well, but in particular does not account for dark matter. Isotope-shift spectroscopy is a sensitive probe of fifth forces and new particles that illuminate the dark matter sector. This method sets bounds on new bosons that couple neutrons and electrons with masses in the keV/c2 to MeV/c2 range. With increasing spectroscopic precision, such searches are limited by uncertainties of isotope masses and the understanding of nuclear structure. Here, we report on high-precision mass-ratio and isotope-shift measurements of the ytterbium isotopes $^{168,170,172,174,176}$Yb that exceed previous measurements by up to two orders of magnitude. From these measurements, we extract higher-order changes in the nuclear charge distribution along the Yb isotope chain and use these to benchmark novel ab initio calculations. Our measurements set new bounds on the existence of the proposed boson.

The demand for efficient preparation methods for dual-species ion crystals is rapidly expanding across quantum technology and fundamental physics applications with trapped ions. We present a deterministic and efficient technique to produce such crystals, utilizing the segmented structure of a linear Paul trap. By precisely tailoring the trapping potentials, we can split, move, and discard parts of an ion chain. This process is automated in a sequence that converts a larger ion sample into the desired configuration. A critical component of our approach is the accurate identification of crystal constituents. This is achieved by matching the measured positions of fluorescing ions against theoretical expectations for larger crystals, thus facilitating the detection of non-fluorescing ions and enabling accurate ion counting. We demonstrate that our method reliably produces two-ion crystals within minutes. These results represent a significant advance in the production of two-species ion crystals with applications ranging from quantum logic spectroscopy and optical clocks to quantum computing and simulation with trapped ions.

Coulomb crystals of cold trapped ions are a leading platform for the realisation of quantum processors and quantum simulations and, in quantum metrology, for the construction of optical atomic clocks and for fundamental tests of the Standard Model. For these applications, it is not only essential to cool the ion crystal in all its degrees of freedom down to the quantum ground state, but also to be able to determine its temperature with a high accuracy. However, when a large ground-state cooled crystal is interrogated for thermometry, complex many-body interactions take place, making it challenging to accurately estimate the temperature with established techniques. In this work we present a new thermometry method tailored for ion crystals. The method is applicable to all normal modes of motion and does not suffer from a computational bottleneck when applied to large ion crystals. We test the temperature estimate with two experiments, namely with a 1D linear chain of 4 ions and a 2D crystal of 19 ions and verify the results, where possible, using other methods. The results show that the new method is an accurate and efficient tool for thermometry of ion crystals., Comment: 13+4 pages, 10+2 figures (new figure 1, updated figures 2 and 10)

Photoexcitation of trapped ions by Hermite-Gaussian (HG) modes from guided beam structures is proposed and investigated theoretically. In particular, simple analytical expressions for the Rabi frequencies of induced atomic transitions are derived that depend both on the parameters of HG beams and on the geometry of an experiment. By using these general expressions, we investigate the $^{2}S_{1/2} \to \; ^{2}F_{7/2}$ electric octupole (E3) transition in an Yb$^{+}$ ion, localized in the low--intensity center of the HG$_{10}$ and HG$_{01}$ beams. We show how the corresponding Rabi frequency can be enhanced by properly choosing the polarization of incident light and the orientation of an external magnetic field, which defines the quantization axis of a target ion. The calculations, performed for experimentally feasible beam parameters, indicate that the achieved Rabi frequencies can be comparable or even higher than those observed for the conventional Laguerre-Gaussian (LG) modes. Since HG-like modes can be relatively straightforwardly generated with high purity and stability from integrated photonics, our results suggest that they may form a novel tool for investigating highly-forbidden atomic transitions., Comment: 9 pages, 4 figures

In attempts to unify the four known fundamental forces in a single quantum-consistent theory, it is suggested that Lorentz symmetry may be broken at the Planck scale. Here we search for Lorentz violation at the low-energy limit by comparing orthogonally oriented atomic orbitals in a Michelson-Morley-type experiment. We apply a robust radiofrequency composite pulse sequence in the $^2F_{7/2}$ manifold of an Yb$^+$ ion, extending the coherence time from 200 $\mu$s to more than 1 s. In this manner, we fully exploit the high intrinsic susceptibility of the $^2F_{7/2}$ state and take advantage of its exceptionally long lifetime. We match the stability of the previous best Lorentz symmetry test nearly an order of magnitude faster and improve the constraints on the symmetry breaking coefficients to the 10$^{-21}$ level. These results represent the most stringent test of this type of Lorentz violation. The demonstrated method can be further extended to ion Coulomb crystals.

We investigate the normal mode spectrum of a trapped ion chain at the symmetry-breaking linear to zigzag transition and at finite temperatures. For this purpose we modulate the amplitude of the Doppler cooling laser in order to excite and measure mode oscillations. The expected mode softening at the critical point, a signature of the second-order transition, is not observed. Numerical simulations show that this is mainly due to the finite temperature of the chain. Inspection of the trajectories suggest that the thermal shifts of the normal-mode spectrum can be understood by the ions collectively jumping between the two ground state configurations of the symmetry broken phase. We develop an effective analytical model, which allows us to reproduce the low-frequency spectrum as a function of the temperature and close to the transition point. In this model the frequency shift of the soft mode is due to the anharmonic coupling with the high frequency modes of the spectrum, acting as an averaged effective thermal environment. Our study could prove important for implementing ground-state laser cooling close to the critical point., Comment: 17 pages, 10 figures

We report on the first coherent excitation of the highly forbidden $^2S_{1/2}\rightarrow{}^2F_{7/2}$ electric octupole (E3) transition in a single trapped ${}^{172}$Yb$^+$ ion, an isotope without nuclear spin. Using the transition in ${}^{171}$Yb$^+$ as a reference, we determine the transition frequency to be $642\,116\,784\,950\,887.6(2.4)\,$Hz. We map out the magnetic field environment using the forbidden $^2S_{1/2} \rightarrow{}^2D_{5/2}$ electric quadrupole (E2) transition and determine its frequency to be $729\,476\,867\,027\,206.8(4.4)\,$Hz. Our results are a factor of $1\times10^5$ ($3\times10^{5}$) more accurate for the E2 (E3) transition compared to previous measurements. The results open up the way to search for new physics via precise isotope shift measurements and improved tests of local Lorentz invariance using the metastable $^2F_{7/2}$ state of Yb$^+$., Comment: 6 pages, 5 figures

There has been tremendous progress in the performance of optical frequency standards since the first proposals to carry out precision spectroscopy on trapped, single ions in the 1970s. The estimated fractional frequency uncertainty of today's leading optical standards is currently in the $10^{-18}$ range, approximately two orders of magnitude better than that of the best caesium primary frequency standards. This exceptional accuracy and stability is resulting in a growing number of research groups developing optical clocks. While good review papers covering the topic already exist, more practical guidelines are needed as a complement. The purpose of this document is therefore to provide technical guidance for researchers starting in the field of optical clocks. The target audience includes national metrology institutes (NMIs) wanting to set up optical clocks (or subsystems thereof) and PhD students and postdocs entering the field. Another potential audience is academic groups with experience in atomic physics and atom or ion trapping, but with less experience of time and frequency metrology and optical clock requirements. These guidelines have arisen from the scope of the EMPIR project "Optical clocks with $1 \times 10^{-18}$ uncertainty" (OC18). Therefore, the examples are from European laboratories even though similar work is carried out all over the world. The goal of OC18 was to push the development of optical clocks by improving each of the necessary subsystems: ultrastable lasers, neutral-atom and single-ion traps, and interrogation techniques. This document shares the knowledge acquired by the OC18 project consortium and gives practical guidance on each of these aspects., Comment: 130 pages, Table 5.3 corrected in v2

We study nanofriction in an ion Coulomb crystal under the presence of topological defects. We observe signatures of the pinning to sliding transition, namely the transverse vibrational soft mode signaling the transition and the symmetry breaking of the crystal configuration. We present details on experimental measurements and numerical simulations of this system, including the gaps in the hull function and the spectroscopy of the localized defect mode. We also investigate how external forces, such as those due to anharmonic potentials or differential light pressure, break the intrinsic crystal symmetry, thereby reducing mode softening near the sliding transition. We find that the local structure and position of the topological defect is essential for the presence of the soft mode and illustrate how the defect changes its properties, when it moves through the crystal., Comment: 17 pages, 12 figures

We study the non-equilibrium dynamics of second-order phase transitions in a simplified Ginzburg-Landau model using the Fokker-Planck formalism. In particular, we focus on deriving the Kibble-Zurek scaling laws that dictate the dependence of spatial correlations on the quench rate. In the limiting cases of overdamped and underdamped dynamics, the Fokker-Planck method confirms the theoretical predictions of the Kibble-Zurek scaling theory. The developed framework is computationally efficient, enables the prediction of finite-size scaling functions and is applicable to microscopic models as well as their hydrodynamic approximations. We demonstrate this extended range of applicability by analyzing the non-equilibrium linear to zigzag structural phase transition in ion Coulomb crystals confined in a trap with periodic boundary conditions., Comment: 11 pages, 10 figures

In many of the high-precision optical frequency standards with trapped atoms or ions that are under development to date, the AC Stark shift induced by thermal radiation leads to a major contribution to the systematic uncertainty. We present an analysis of the inhomogeneous thermal environment experienced by ions in various types of ion traps. Finite element models which allow the determination of the temperature of the trap structure and the temperature of the radiation were developed for 5 ion trap designs, including operational traps at PTB and NPL and further optimized designs. Models were refined based on comparison with infrared camera measurement until an agreement of better than 10% of the measured temperature rise at critical test points was reached. The effective temperature rises of the radiation seen by the ion range from 0.8 K to 2.1 K at standard working conditions. The corresponding fractional frequency shift uncertainties resulting from the uncertainty in temperature are in the 10-18 range for optical clocks based on the Sr+ and Yb+ E2 transitions, and even lower for Yb+ E3, In+ and Al+. Issues critical for heating of the trap structure and its predictability were identified and design recommendations developed., Comment: 16 pages, submitted to Metrologia

We use laser-cooled ion Coulomb crystals in the well-controlled environment of a harmonic radiofrequency ion trap to investigate phase transitions and defect formation. Topological defects in ion Coulomb crystals (kinks) have been recently proposed for studies of nonlinear physics with solitons and as carriers of quantum information. Defects form when a symmetry breaking phase transition is crossed nonadiabatically. For a second order phase transition, the Kibble-Zurek mechanism predicts that the formation of these defects follows a power law scaling in the rate of the transition. We demonstrate a scaling of defect density and describe kink dynamics and stability. We further discuss the implementation of mass defects and electric fields as first steps toward controlled kink preparation and manipulation., Comment: ECRYS-2014 Proceedings. 7 pages, 6 figures

We present the design and realization of two reference cavities for ultra-stable lasers addressing narrow transitions in mixed-species (In+ / Yb+) Coulomb crystals. With a simple setup, we achieve a fractional frequency instability close to the thermal noise limit of a 12 cm long cavity, reaching 4.7 * 10^{-16} at 10 s with a linear drift of 53 mHz/s. We discuss the individual instability contributions and show that in a setup with a lower thermal noise floor and vibration sensitivity, an instability of 1 * 10^{-16} can be reached. To achieve this, we implement a vibration insensitive design for a 30 cm long cavity mounted horizontally and conduct first tests that show a sensitivity of 1.8 * 10^{-11} / ms^{-2} to vertical accelerations. This is about a factor of 20 less than the value observed for the short cavity. Mechanical tolerances and ways to further reduce the sensitivity are discussed., Comment: 8 pages, 8 figures

We study experimentally and theoretically the properties of structural defects (kink solitons) in two-dimensional ion Coulomb crystals. We show how different types of kink solitons with different physical properties can be realized, and transformed from one type into another by varying the aspect ratio of the trap confinement. Further, we discuss how impurities in ion Coulomb crystals, such as mass defects, can modify the dynamics of kink creation and their stability. For both pure and impure crystals, the experimentally observed kink dynamics are analyzed in detail and explained theoretically by numerical simulations and calculations of the Peierls-Nabarro potential. Finally, we show that static electric fields provide a handle to vary the influence of mass defects on kinks in a controlled way and allow for deterministic manipulation and creation of kinks., Comment: 21 pages, 8 figures

Symmetry breaking phase transitions play an important role in nature. When a system traverses such a transition at a finite rate, its causally disconnected regions choose the new broken symmetry state independently. Where such local choices are incompatible, defects will form with densities predicted to follow a power law scaling in the rate of the transition. The importance of this Kibble-Zurek mechanism (KZM) ranges from cosmology to condensed matter [1-4]. In previous tests in homogeneous systems, defect formation was seen, but weak dependence on the transition rate and limited control of external parameters so far prevented tests of KZM scaling. As recently predicted [5-9], in inhomogeneous systems propagation of the critical front enhances the role of causality and steepens scaling of defect density with the transition rate. We use ion Coulomb crystals in a harmonic trap to demonstrate, for the first time, scaling of the number of topological defects with the transition rate - the central prediction of KZM - in a well-controlled environment.

We present an experiment to characterize our new linear ion trap designed for the operation of a many-ion optical clock using 115-In^+ as clock ions. For the characterization of the trap as well as the sympathetic cooling of the clock ions we use 172-Yb^+. The trap design has been derived from finite element method (FEM) calculations and a first prototype based on glass-reinforced thermoset laminates was built. This paper details on the trap manufacturing process and micromotion measurement. Excess micromotion is measured using photon-correlation spectroscopy with a resolution of 1.1nm in motional amplitude, and residual axial rf fields in this trap are compared to FEM calculations. With this method, we demonstrate a sensitivity to systematic clock shifts due to excess micromotion of |({\Delta}{\nu}/{\nu})| = 8.5x10^-20. Based on the measurement of axial rf fields of our trap, we estimate a number of twelve ions that can be stored per trapping segment and used as an optical frequency standard with a fractional inaccuracy of \leq 1x10^-18 due to micromotion., Comment: 19 pages with 14 pictures

We report on the design of a segmented linear Paul trap for optical clock applications using trapped ion Coulomb crystals. For an optical clock with an improved short-term stability and a fractional frequency uncertainty of 10^-18, we propose 115In+ ions sympathetically cooled by 172Yb+. We discuss the systematic frequency shifts of such a frequency standard. In particular, we elaborate on high precision calculations of the electric radiofrequency field of the ion trap using the finite element method. These calculations are used to find a scalable design with minimized excess micromotion of the ions at a level at which the corresponding second- order Doppler shift contributes less than 10^-18 to the relative uncertainty of the frequency standard.