Publications
Articles, Theses, and Preprints
2024
LiSrAlF6 crystals doped with 229Th are used in a laser-based search for the nuclear isomeric transition. Two spectroscopic features near the nuclear transition energy are observed. The first is a broad excitation feature that produces red-shifted fluorescence that decays with a timescale of a few seconds. The second is a narrow, laser-linewidth-limited spectral feature at 148.38219(4)stat(20)sys nm (2020407.3(5)stat(30)sys GHz) that decays with a lifetime of 568(13)stat(20)sys s. This feature is assigned to the excitation of the 229Th nuclear isomeric state, whose energy is found to be 8.355733(2)stat(10)sys eV in 229Th:LiSrAlF6.
Ultracold atomic gases hold unique promise for space science by capitalizing on quantum advantages and extended freefall, afforded in a microgravity environment, to enable next-generation precision sensors. Atom interferometers are a class of quantum sensors which can use freely falling gases of atoms cooled to sub-photon-recoil temperatures to provide unprecedented sensitivities to accelerations, rotations, and gravitational forces, and are currently being developed for space-based applications in gravitational, earth, and planetary sciences, as well as to search for subtle forces that could signify physics beyond General Relativity and the Standard Model. NASA's Cold Atom Lab (CAL) operates onboard the International Space Station as a multi-user facility for studies of ultracold atoms and to mature quantum technologies, including atom interferometry, in persistent microgravity. In this paper, we report on path-finding experiments utilizing ultracold 87Rb atoms in the CAL atom interferometer, which was enabled by an on-orbit upgrade of the CAL science module: A three-pulse Mach-Zehnder interferometer was studied to understand limitations from the influence of ISS vibrations. Additionally, Ramsey shear-wave interferometry was used to manifest interference patterns in a single run that were observable for over 150 ms free-expansion time. Finally, the CAL atom interferometer was used to remotely measure the photon recoil from the atom interferometer laser as a demonstration of the first quantum sensor using matter-wave interferometry in space.
2023
We present the design, construction, and simulation of a simple, low-cost external cavity diode laser with a measured free-running frequency drift rate of 1.4(1) MHz/h at 852 nm. This performance is achieved in a compact aluminum structure held inside an airtight, temperature-controlled enclosure. The high thermal conductivity of the laser cavity and the stable temperature environment inside the enclosure minimize the time-varying, spatial temperature gradients across the laser cavity. We present thermal finite element method simulations, which quantify the effects of temperature gradients, and suggest that the drift rate is likely limited by the laser-diode and piezo-aging.
The Cold Atom Laboratory (CAL) is a quantum facility for studying ultra-cold gases in the microgravity environment of the International Space Station. It enables research in a temperature regime and force-free environment inaccessible to terrestrial laboratories. In the microgravity environment, observation times over a few seconds and temperatures below 100 pK are achievable, unlocking the potential to observe new quantum phenomena. CAL launched to the International Space Station in May 2018 and has been operating since then as the world's first multi-user facility for studying ultra-cold atoms in space. CAL is the first quantum science facility to produce the fifth state of matter called a Bose-Einstein condensate with rubidium-87 and potassium-41 in Earth orbit. We will give an overview of CAL's operational setup, outline its contributions to date, present planned upgrades for the next few years, and consider design choices for microgravity BEC successor-mission planning.
Existing space-based cold atom experiments have demonstrated the utility of microgravity for improvements in observation times and for minimizing the expansion energy and rate of a freely evolving coherent matter wave. In this paper we explore the potential for space-based experiments to extend the limits of ultracold atoms utilizing not just microgravity, but also other aspects of the space environment such as exceptionally good vacuums and extremely cold temperatures. The tantalizing possibility that such experiments may one day be able to probe physics of quantum objects with masses approaching the Planck mass is discussed.
2022
We briefly describe a `third generation' follow-on to the Cold Atom Lab mission, currently operating aboard the ISS and the Bose-Einstein Condensate and Cold Atom Lab mission, which is expected to launch in 2026. This mission would feature a modular design that would allow critical hardware to be optimized for specific investigations while allowing easy exchange with other hardware to enable a multi-user facility.
2021
We describe a project that brings together researchers from atomic physics, nuclear physics and sub-atomic particle physics, to develop a high-precision laboratory-scale experiment able to search for very weakly coupled sterile neutrinos in the mass range extending from 5-10 keV/c2 to several hundred keV/c2 . Observed neutrino flavor eigenstates are known to be quantum mixtures of at least three sub-eV/c2 mass eigenstates. There is a strong theoretical belief that there may exist further neutrino mass eigenstates at higher mass levels, and which, if in the keV/c2 mass range, might form all or part of the Galactic dark matter. This has led to many searches for anomalous events in both astrophysical and particle physics experiments, and searches for distortions in beta decay spectra. The present experiment utilizes K-capture events in a population of 131-Cs atoms suspended in vacuum by a magneto-optical trap. Using AMO and nuclear physics techniques, individual events are fully reconstructed kinematically. Normally each event would be consistent with an emitted neutrino mass close to zero, but the existence of a sterile neutrino of keV/c2 mass that mixes with the electron type neutrino produced in the decay would result in a separated population of events with non-zero reconstructed missing mass (up to the Q = 350 keV available energy of the reaction). Detailed calculations and simulations of all significant background processes have been made, in particular for scattering in the source itself, radiative K-capture, local radioactivity, cosmic ray muons, and spallation of electrons by X-rays. A Phase 1 of the experiment is under construction with funding from the W. M. Keck Foundation, and having the potential ability to reach sterile neutrino mixing angles down to sin2 theta ~ 10e-4 . With further upgrades this technique could be progressively improved to eventually reach much lower coupling levels ~ 1e-10 , in particular reaching the level needed to be consistent with Galactic dark matter below the astrophysical x-ray limits.
2020
Dipole--phonon quantum logic (DPQL) leverages the interaction between polar molecular ions and the motional modes of a trapped-ion Coulomb crystal to provide a potentially scalable route to quantum information science. Here, we study a class of candidate molecular ions for DPQL, the cationic alkaline-earth monoxides and monosulfides, which possess suitable structure for DPQL and can be produced in existing atomic ion experiments with little additional complexity. We present calculations of DPQL operations for one of these molecules, CaO$^+$, and discuss progress towards experimental realization. We also further develop the theory of DPQL to include state preparation and measurement and entanglement of multiple molecular ions.
2019
Recent advances have enabled studies of atom--ion chemistry at unprecedentedly low temperatures, allowing precision observation of chemical reactions and novel chemical dynamics. So far, these studies have primarily involved reactions between atoms and atomic ions or non-polar molecular ions, often in their electronic ground state. Here, we extend this work by studying an excited atom--polar-molecular-ion chemical reaction ($\text{Ca}^{*} + \text{Ba}\text{Cl}^{+}$) at low temperature in a hybrid atom--ion trapping system. The reaction rate and product branching fractions are measured and compared to model calculations as a function of both atomic quantum state and collision energy. At the lowest collision energy we find that the chemical dynamics differ dramatically from capture theory predictions and are primarily dictated by the radiative lifetime of the atomic quantum state instead of the underlying excited-state interaction potential. This reaction blockading effect, which greatly suppresses the reactivity of short-lived excited states, provides a means for directly probing the reaction range and also naturally suppresses unwanted chemical reactions in hybrid trapping experiments.
Using a recently developed method for precisely controlling collision energy, we observe a dramatic suppression of inelastic collisions between an atom and ion ($\text{Ca}+{\text{Yb}}^{+}$) at low collision energy. This suppression, which is expected to be a universal phenomenon, arises when the spontaneous emission lifetime of the excited state is comparable to or shorter than the collision complex lifetime. We develop a technique to remove this suppression and engineer excited-state interactions. By dressing the system with a strong catalyst laser, a significant fraction of the collision complexes can be excited at a specified atom-ion separation. This technique allows excited-state collisions to be studied, even at ultracold temperature, and provides a general method for engineering ultracold excited-state interactions.
$^{229}$Th is the only nucleus currently under investigation for the development of a nuclear optical clock (NOC) of ultra-high accuracy. The insufficient knowledge of the first nuclear excitation energy of $^{229}$Th has so far hindered direct nuclear laser spectroscopy of thorium ions and thus the development of a NOC. Here, a nuclear laser excitation scheme is detailed, which makes use of thorium atoms instead of ions. This concept, besides potentially leading to the first nuclear laser spectroscopy, would determine the isomeric energy to $40 \mu \text{eV}$ resolution, corresponding to $10 \text{GHz}$, which is a $10^4$ times improvement compared to the current best energy constraint. This would determine the nuclear isomeric energy to a sufficient accuracy to allow for nuclear laser spectroscopy of individual thorium ions in a Paul trap and thus the development of a single-ion nuclear optical clock.
2018
We demonstrate an ion shuttling technique for high-resolution control of atom-ion collision energy by translating an ion held within a radio-frequency trap through a magneto-optical atom trap. The technique is demonstrated both experimentally and through numerical simulations, with the experimental results indicating control of ion kinetic energies from 0.05 to 1 K with a fractional resolution of $\sim10$ and the simulations demonstrating that kinetic energy control up to 120 K with a maximum predicted resolution of $\sim100$ is possible, offering order-of-magnitude improvements over most alternative techniques. Finally, we perform a proof-of-principle chemistry experiment using this technique and outline how the method may be refined in the future and applied to the study of molecular ion chemistry.
2017
Hypermetallic alkaline earth ($\text{M}$) oxides of formula $\text{M}\text{O}\text{M}$ have been studied under plasma conditions that preclude insight into their formation mechanism. We present here the application of emerging techniques in ultracold physics to the synthesis of a mixed hypermetallic oxide, $\text{Ba}\text{O}\text{Ca}^{+}$. These methods, augmented by high-level electronic structure calculations, permit detailed investigation of the bonding and structure, as well as the mechanism of its formation via the barrierless reaction of $\text{Ca}$ ($^{3}\text{P}_\text{J}$) with $\text{Ba}\text{O}\text{C}\text{H}_3^{+}$. Further investigations of the reaction kinetics as a function of collision energy over the range 0.005 K to 30 K and of individual $\text{Ca}$ fine-structure levels compare favorably with calculations based on long-range capture theory.
We investigate the limiting factors in the standard implementation of the Ca magneto-optical trap. We find that intercombination transitions from the $4s5p\;^{1}{P}_{1}$ state used to repump the electronic population from the $3d4s\;^{1}{D}_{2}$ state severely reduce the trap lifetime. We explore seven alternative repumping schemes theoretically and investigate five of them experimentally. We find that all five of these schemes yield a significant increase in the trap lifetime and consequently improve the number of atoms and peak atom density by as much as $\sim20$ times and $\sim6$ times, respectively. One of these transitions, at 453 nm, is shown to approach the fundamental limit for a Ca magneto-optical trap with repumping only from the dark $3d4s\;^{1}{D}_{2}$ state, yielding a trap lifetime of $\sim5$ s.
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 $275\text{mm}$ long TOF drift tube. The mass resolution exceeds $m/\Delta m = 500$, 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.
Towards Scaling Experimental Quantum Simulations with Ions
Dissertation, Albert-Ludwigs-Universität Freiburg (2012)
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.
We cannot translate quantum behavior arising with superposition states or entanglement efficiently into the classical language of conventional computers (Feynman et al. in Int. J. Theor. Phys. 21:467, 1982). A universal quantum computer could describe and help to understand complex quantum systems. But it is envisioned to become functional only within the next decade(s). A shortcut was proposed via simulating the quantum behavior of interest in another quantum system, where all relevant parameters and interactions can be controlled and observables of interest detected sufficiently well. For example simulating quantum spin systems within an architecture of trapped ions (Porras and Cirac in Phys. Rev. Lett. 92:207901, 2004). Here we specify how we simulate the spin and all necessary interactions and how we calibrate their amplitudes. For example via a two-ion phase-gate operation on two axial motional modes simultaneously at a fidelity exceeding 95%. We explain the complete mode of operation of a quantum simulator on the basis of our simple model case---the proof of principle experiment of simulating the transition of a quantum magnet from paramagnetic into entangled ferromagnetic order (Friedenauer et al. in Nat. Phys. 4:757, 2008) and emphasize some of the similarities and differences with a quantum computer.
2007
Entwicklung eines Objektivs hoher numerischer Apertur zum Nachweis der Resonanzfluoreszenz einzelner gespeicherter Ionen
Master's Thesis, Universität Siegen (2007)
Bei Experimenten mit Ionenkristallen in Paulfallen wird eine Optik benötigt, die eine getrennte Auflösung der einzelnen Ionen über den Nachweis von Fluoreszenzphotonen ermöglicht. Dabei ist zu berücksichtigen, dass einerseits die Ausbeute an Fluoreszenzphotonen sehr gering sein kann und andererseits der Abstand der Ionen bei wenigen Mikrometern liegt. Dies macht eine Optik erforderlich, die eine große numerische Apertur aufweist und gleichzeitig praktisch beugungsbegrenzt abbildet. Während die Paulfalle mit den gefangenen Ionen zwangsläufig in einem Ultrahochvakuum platziert ist, befindet sich die Nachweisoptik typischerweise außerhalb des Vakuumrezipienten. Die Optik muss somit zusätzlich einen großen Arbeitsabstand aufweisen und für den Blick durch das Fenster des Vakuumrezipienten optimiert sein. Kondensoren aus zwei bis drei Linsen, die von einigen Herstellern bezogen werden können, würden die Anforderungen an die numerische Apertur durchaus erfüllen, doch ist ihre Abbildungsqualität für eine getrennte Auflösung der Ionen nicht ausreichend. Kommerziell erhältliche, herkömmliche Mikroskopobjektive haben zwar eine sehr große numerische Apertur, aber einen Arbeitsabstand von bestenfalls wenigen Millimetern, und sie sind nicht für den Blick durch das Fenster des Vakuumrezipienten ausgelegt. Eine Platzierung der Optik im Vakuum ist in den geplanten Experimenten unerwünscht. Als Alternative bieten sich "`Long Distance Microscopes"' an, die einen Arbeitsabstand von einigen Zentimetern haben können, wobei dies auf Kosten der numerischen Apertur erreicht wird. Auch diese Objektive sind nicht für das Fenster des Vakuumrezipienten ausgelegt. In Siegen sind Experimente an Kristallen aus Yb+-Ionen geplant, die bei einer Wellenlänge von 369 nm zur Fluoreszenz angeregt werden. Damit befinden wir uns im nahen ultravioletten Bereich, wo günstige Glassorten wie BK7 bereits eine nennenswerte Absorption aufweisen. Damit wird die Optik auf ein Spiegelobjektiv oder ein Objektiv aus Quarzglaslinsen weiter eingeschränkt. In der vorliegenden Arbeit wird gezeigt, wie ein Objektiv aus fünf sphärischen Quarzglaslinsen für eine Wellenlänge von 369 nm mit einer numerischen Apertur von 0,4 entwickelt wurde. Dabei wurde ein 8mm dickes Fenster des Vakuumrezipienten berücksichtigt und ein Abstand von Fenster zu Ionenkette von 25 mm ermöglicht. Das Objektiv ist für die Abbildung einer Ionenkette mit bis zu 500 μm Länge ausgelegt, was bei einem geplanten Ionenabstand von 5 μm etwa 100 Ionen ausmachen würde. Die Abbildung ist für einen großen Teil des Sichtfeldes praktisch beugungsbegrenzt. Die Entwicklung des Objektivs erfolgte mittels einer selbst entwickelten Raytracing-Software. Mit der Anfertigung von drei Exemplaren des Objektivs wurde die Firma Sill Optics in Wendelstein beauftragt. Eine Anfertigung nur der Linsen, wobei die mechanischen Komponenten und das Fassen der Linsen selbst durchgeführt würde, fiel nach Abschätzung der Toleranzen heraus, da im Eigenbau ihre Einhaltung nicht garantiert werden konnte.