# Publications

## Articles, Theses, and Preprints

### 2016

Sympathetic cooling of trapped ions through collisions with neutral buffer gases is critical to a variety of modern scientific fields, including fundamental chemistry, mass spectrometry, nuclear and particle physics, and atomic and molecular physics. Despite its widespread use over four decades, there remain open questions regarding its fundamental limitations. To probe these limits, here we examine the steady-state evolution of up to 10 barium ions immersed in a gas of three-million laser-cooled calcium atoms. We observe and explain the emergence of nonequilibrium behaviour as evidenced by bifurcations in the ion steady-state temperature, parameterized by ion number. We show that this behaviour leads to the limitations in creating and maintaining translationally cold samples of trapped ions using neutral-gas sympathetic cooling. These results may provide a route to studying non-equilibrium thermodynamics at the atomic level.

Abstract Recently, we reported an ion trap experiment with an integrated time-of-flight mass spectrometer (TOFMS) [1] focusing on the improvement of mass resolution and detection limit due to sample preparation at millikelvin temperatures. The system utilizes a radio-frequency (RF) ion trap with asymmetric drive for storing and manipulating laser-cooled ions and features radial extraction into a compact 275 mm long TOF drift tube. The mass resolution exceeds m/Δm = 500, which provides isotopic resolution over the whole mass range of interest in current experiments and constitutes an improvement of almost an order of magnitude over other implementations. In this article, we discuss the experimental implementation in detail, which is comprised of newly developed drive electronics for generating the required voltages to operate RF trap and TOFMS, as well as control electronics for regulating RF outputs and synchronizing the TOFMS extraction.

### 2015

We estimate the range of the radiative lifetime and energy of the anomalous, low-energy $3/2^+(7.8 \pm 0.5$~eV) state in the $^{229}$Th nucleus. Our phenomenological calculations are based on the available experimental data for the intensities of $M1$ and $E2$ transitions between excited levels of the $^{229}$Th nucleus in the $K^{\pi}[Nn_Z\Lambda]=5/2^+[633]$ and $3/2^+[631]$ rotational bands. We also discuss the influence of certain branching coefficients, which affect the currently accepted measured energy of the isomeric state. From this work, we establish a favored region, $0.66\times10^6~{\text{s~eV}}^3/\omega^3 \leq\tau\leq 2.2\times10^6~{\text{s~eV}}^3/\omega^3$, where the transition lifetime $\tau$ as a function of transition energy $\omega$ should lie at roughly the 95\% confidence level. Together with the result of [Beck et al.: LLNL-PROC-415170 (2009)], we establish a favored area where transition lifetime and energy should lie at roughly the 90\% confidence level. We also suggest new nuclear physics measurements, which would significantly reduce the ambiguity in the present data.

We report the results of a direct search for the $^{229}$Th ($I^\pi = 3/2^+\leftarrow 5/2^+$) nuclear isomeric transition, performed by exposing $^{229}$Th-doped LiSrAlF$_6$ crystals to tunable vacuum-ultraviolet synchrotron radiation and observing any resulting fluorescence. We also use existing nuclear physics data to establish a range of possible transition strengths for the isomeric transition. We find no evidence for the thorium nuclear transition between $7.3 \mbox{eV}$ and $8.8 \mbox{eV}$ with transition lifetime $(1-2)\mbox{s} \lesssim \tau \lesssim (2000-5600)\mbox{s}$. This measurement excludes roughly half of the favored transition search area and can be used to direct future searches.

### 2014

Mass spectrometry is used in a wide range of scientific disciplines including proteomics, pharmaceutics, forensics, and fundamental physics and chemistry. Given this ubiquity, there is a worldwide effort to improve the efficiency and resolution of mass spectrometers. However, the performance of all techniques is ultimately limited by the initial phase-space distribution of the molecules being analyzed. Here, we dramatically reduce the width of this initial phase-space distribution by sympathetically cooling the input molecules with laser-cooled, cotrapped atomic ions, improving both the mass resolution and detection efficiency of a time-of-flight mass spectrometer by over an order of magnitude. Detailed molecular-dynamics simulations verify the technique and aid with evaluating its effectiveness. This technique appears to be applicable to other types of mass spectrometers.

### 2012

We report on three-dimensional optical trapping of single ions in a one-dimensional optical lattice formed by two counterpropagating laser beams. We characterize the trapping parameters of the standing-wave using the ion as a sensor stored in a hybrid trap consisting of a radio-frequency (rf), a dc, and the optical potential. When loading ions directly from the rf into the standing-wave trap, we observe a dominant heating rate. Monte Carlo simulations confirm rf-induced parametric excitations within the deep optical lattice as the main source. We demonstrate a way around this effect by an alternative transfer protocol which involves an intermediate step of optical confinement in a single-beam trap avoiding the temporal overlap of the standing-wave and the rf field. Implications arise for hybrid (rf-optical) and pure optical traps as platforms for ultracold chemistry experiments exploring atom-ion collisions or quantum simulation experiments with ions, or combinations of ions and atoms.

We examine the prospects of discrete quantum walks (QWs) with trapped ions. In particular, we analyze in detail the limitations of the protocol of Travaglione and Milburn (2002 Phys. Rev. A 65 032310) that has been implemented by several experimental groups in recent years. Based on the first realization in our group (Schmitz et al 2009 Phys. Rev. Lett. 103 090504), we investigate the consequences of leaving the scope of the approximations originally made, such as the Lamb–Dicke approximation. We explain the consequential deviations from the idealized QW for different experimental realizations and an increasing number of steps by taking into account higher-order terms of the quantum evolution. It turns out that these already become significant after a few steps, which is confirmed by experimental results and is currently limiting the scalability of this approach. Finally, we propose a new scheme using short laser pulses, derived from a protocol from the field of quantum computation. We show that this scheme is not subject to the above-mentioned restrictions and analytically and numerically evaluate its limitations, based on a realistic implementation with our specific setup. Implementing the protocol with state-of-the-art techniques should allow for substantially increasing the number of steps to 100 and beyond and should be extendable to higher-dimensional QWs.

Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems.

We recently reported on a proof-of-principle experiment demonstrating optical trapping of an ion in a single-beam dipole trap superimposed by a static electric potential [ Ch. Schneider, M. Enderlein, T. Huber and T. Schaetz Nat. Photon. 4 772 (2010)]. Here, we discuss, first, the experimental procedures focusing on the influence and consequences of the static electric potential. This potential can easily prevent successful optical trapping, if its configuration is not chosen carefully. Afterward, we analyze the dipole trap experiments with different analytic models, in which different approximations are applied. According to these models the experimental results agree with recoil heating as the relevant heating effect. In addition, a Monte Carlo simulation has been developed to refine the analysis. It reveals a large impact of the static electric potential on the dipole trap experiments in general. While it supports the results of the analytic models for the parameters used in the experiments, the analytic models are no longer valid for significantly different parameters. Finally, we propose technical improvements for future realizations of experiments with optically trapped ions.

Quantum simulations with trapped ions are an emerging field with great potential for future applications. However, up to now, experiments are restricted to less than ten ions arranged in a linear chain. In this thesis two approaches for scaling quantum simulations with trapped ions are presented and experimentally investigated: One approach aims at radio-frequency (RF) surface electrode traps with optimized electrode shapes providing a two-dimensional micro-trap array. A different approach is based on optical trapping of ions and the first demonstration of an optical confinement of a single ion is presented. First, the approach based on RF surface electrode traps is treated. A theoretical derivation of the toolbox available for quantum simulations is presented and extended to be applicable to more-dimensional arrays of ions. The results are discussed in the context of geometric phase gates and proof-of-principle experiments on the simulation of the quantum Ising Hamiltonian. As a first step towards a two-dimensional array of ions, a basic setup is presented and its operability is demonstrated with a linear surface electrode trap. The trapping results are discussed with regard to future surface electrode traps potentially allowing for two-dimensional arrays of ions. Finally, an outlook on a surface electrode trap with three trapping zones arranged in a triangle is given. This trap has been developed in a collaboration of Roman Schmied (MPQ, University of Basel), the group of Dietrich Leibfried (National Institute of Standards and Technology), Sandia National Laboratories, and us. It is currently fabricated at Sandia National Laboratories and will replace the linear trap in our setup. Second, optically trapped ions are addressed as an alternative approach. Our experiment demonstrates optical trapping of an ion in a single-beam dipole trap superimposed by a static electric potential. The experimental procedures and peculiarities are described in detail. In particular, the static electric potential is of importance, because it can easily prevent successful optical trapping, if its configuration is not chosen carefully. Afterwards, the dipole trap experiments are analysed with different analytic models. According to these models the experimental results agree with recoil heating as the relevant heating effect. To confirm our conclusions, a Monte Carlo simulation has been developed. It reveals a large impact of the static electric potential on the dipole trap experiments in general. While it supports the results of the analytic models for the parameters used in the experiments, the analytic models are no longer valid for significantly different parameters. Finally, technical improvements for future realizations of experiments with optically trapped ions are proposed and possible applications of optical ion traps in quantum simulations and ultracold collisions are presented.

### 2011

Erstmals ließ sich ein Quanten-Spin-System mit atomarer Auflösung in einem System ultrakalter Atome simulieren.

Caution: Pedestrians might cross themselves! Quantum walks, the quantum extension of classical random walks, had already been realized for different quantum particles. Now two walkers realized as photons were observed to pass through the same optical path-network (see picture). For the first time, the two indistinguishable walkers were shown to interfere with each other.

### 2010

Isolating ions and atoms from the environment is essential in experiments on a quantum level. For decades, this has been achieved by trapping ions with radiofrequency fields and neutral particles with optical fields. Here we demonstrate the trapping of an ion by interaction with light. The lifetime in the optical trap is several milliseconds, allowing hundreds of oscillations in the optical potential, and could be enhanced by established methods. These results could form the starting point for combining the advantages of optical trapping and ions. Extending the approach to optical lattices could support developments in experimental quantum simulations. As well as simulating complex spin systems with trapped ions, a new class of quantum simulations could be enabled that combines atoms and ions in a common lattice (Cirac, J.I., personal communication; Zoller, P., personal communication). Furthermore, ions could be embedded into quantum degenerate gases, thereby avoiding the inevitable excess kinetic energy of ions in radiofrequency traps, which currently limits cold-chemistry experiments.

### 2009

We implement the proof of principle for the quantum walk of one ion in a linear ion trap. With a single-step fidelity exceeding 0.99, we perform three steps of an asymmetric walk on the line. We clearly reveal the differences to its classical counterpart if we allow the walker or ion to take all classical paths simultaneously. Quantum interferences enforce asymmetric, nonclassical distributions in the highly entangled degrees of freedom (of coin and position states). We theoretically study and experimentally observe the limitation in the number of steps of our approach that is imposed by motional squeezing. We propose an altered protocol based on methods of impulsive steps to overcome these restrictions, allowing to scale the quantum walk to many, in principal to several hundreds of steps.