A detailed investigation of ion crystals produced by laser and sympathetic cooling in a linear RF trap has been conducted. The laser cooling methods were examined and applied to the trapped ^24Mg^(positive) ions. The crystals produced by the laser cooling were studied, including the dependence on RF voltage, end cap DC voltage, laser power and laser frequency. By manipulating the different RF voltages and endcap DC voltages, the structure phase transition of the ion crystals was observed. In addition, the sympathetic cooling of different ion species with the laser cooled 24Mg^(positive) was carried out. In this process, the mixed Mg^(positive) and He^(positive) crystals were created andidentified, and mixed Mg^(positive) and H2^(positive) crystals were produced. The effect of an unwanted chemical reaction of Mg^(positive) and H2 was observed and minimized. After sympathetic cooling of light ion species, the sympathetic cooling of heavy molecular ions such as fullerene ions was also carried out. The efficiencies and final temperature in both cases are very different. Theoretically to interpret the results, molecular dynamics simulations of the laser cooling and sympathetic cooling were implemented. And the simulations were compared with the experimental results. In the process of carrying out this research, the optics were rebuilt to provide reliable UV sources for the photoionization and laser cooling of Mg ions. The imaging system was reconfigured to take the images of ion crystals. New elements were added tin the ion trap to improve the ability to manipulate ions.

<p>The trapped atomic ion qubits feature desirable properties for use in a quantum computer such as long coherence times, high qubit readout fidelity, and universal logic gates. While these essential properties have been demonstrated, the ability to scale a trapped ion quantum system has not yet been shown. The challenge of scaling the system calls for methods to realize high-fidelity logic gates in scalable trap structures. Surface electrode ion traps, that are microfabricated from a silicon substrate, provide a scalable platform for trapping ion qubits only if high-fidelity operations are achievable in these structures. Here, we present a system for trapping and manipulating ions in a scalable surface trap. Trapping times exceeding 20 minutes without laser cooling, and heating rates as low as 0.8 quanta/ms indicate stable trapping conditions in these microtraps. Coherence times of more than one second verify adequate qubit and control field stability. We demonstrate low-error single-qubit gates performed using stimulated Raman transitions driven by lasers that are tightly focused on the ion qubit. Digital feedback loops are implemented to control the driving field's amplitude and frequency. Gate errors are measured using a randomized benchmarking protocol for single qubit gates, where residual amplitude error in the control beam is compensated using various pulse sequence techniques. Using pulse compensation, we demonstrate single qubit gates with an average error per randomized Clifford group gate of $3.6(3)\times10^{-4}$, which is below the fault-tolerant threshold for some error-correction schemes.</p> / Dissertation

This thesis is a numerical study of fields within ion traps having segmented electrodes1. The focus is on two cylindrical ion trap structures, two Orbit rap structures and one planar structure which mimics the field of the Orbit rap. In all these geometries, the segments which comprise the electrodes are easily Machin able rings and plates. By applying suitable potential to the different segments, the fields within these geometries are made to mimic the fields in the respective ideal structures. This thesis is divided into 6 chapters. Chapter 1 presents introduction and background information relevant to this work. A brief description of the Quadrupole Ion Trap (QIT) and the Orbit rap is given. The role of numerical simulations in the design of an ion trap geometry is briefly outlined. The motivation of this thesis is presented. The chapter ends by describing the scope of the thesis. Chapter 2 presents a general description of computational methods used throughout this work. The Boundary Element Methods (BEM) is first described. Both 2D and 3D BEM are used in this work. The software for 3D BEM is newly developed and hence 3D BEM is described in more detail. A verification of 3D BEM is presented with a few examples. The Runge-Kutta method used to compute the trajectory of ion is presented. A brief overview of the Nelder-Mead method of function minimization is given. The computational techniques specifically used to obtain the results in Chapter 3, 4 and 5 are presented in the respective chapters. Chapter 3 presents segmented electrode geometries of the Cylindrical Ion Trap (CIT). In these geometries, the electrodes of the CIT are split into number of mini-electrodes and different voltages are applied to these segmented electrodes to achieve the desired field. Two geometries of the segmented electrode CIT will be investigated. In the first, we retain the flat end cap electrodes of the CIT but split the ring electrode into five mini-rings. In the second configuration, we split the ring electrode of the CIT into three mini-rings and 1The term ‘segmented electrode’ used in this thesis has the same connotation as the term ‘split-electrode’ used in Sonalikar and Mohanty (2013). also divide the end caps into two mini-discs. By applying different potentials to the mini-rings and mini-discs of these geometries we will show that the field within the trap can be optimized to desired values. Two different types of fields will be targeted. In the first, potentials are adjusted to obtain a linear electric field and, in the second, a controlled higher order even multipole field are obtained by adjusting the potential. It will be shown that the different potentials to the segmented electrodes can be derived from a single RF generator by connecting appropriate capacitor terminations to segmented electrodes. The field within the trap can be modified by changing the value of the external capacitors. Chapter 4 presents segmented electrode geometries which are possible alternatives for the Orbitrap. Two segmented-electrode structures, ORB1 and ORB2, to mimic the electric field of the Orbitrap, will be investigated. In the ORB1, the inner spindle-like electrode and the outer barrel-like electrode of the Orbitrap are replaced by rings and discs of fixed radii, respectively. In this structure two segmented end cap electrodes are added. In this geometry, different potentials are applied to the different electrodes keeping top-bottom symmetry intact. In the second geometry, ORB2, the inner and outer electrodes of the Orbitrap are replaced by an approximate step structure which follows the profile of the Orbitrap electrodes. For the purpose of comparing the performance of ORB1 and ORB2 with that of the Orbitrap, the following studies will be undertaken: (1) variation of electric potential, (2) computation of ion trajectories, (3) measurement of image currents. These studies will be carried out using both 2D and 3D Boundary Element Method (BEM), the 3D BEM is developed specifically for this study. It will be seen in these investigations that ORB1 and ORB2 have performance similar to that of the Orbitrap, with the performance of the ORB1 being seen to be marginally superior to that of the ORB2. It will be shown that with proper optimization, geometries containing far fewer electrodes can be used as mass analysers. A novel technique of optimization of the electric field is proposed with the objective of minimizing the dependence of axial frequency of ion motion on the initial position of an ion. The results on the optimization of 9 and 15 segmented-electrode trap having the same design as ORB1 show that it can provide accurate mass analysis. Chapter 5 presents a segmented electrode planar geometry named as PORB used to mimic the electric field of the Orbit rap. This geometry has two planes, each plane consisting of 30 concentric ring electrodes. Although the geometry of PORB does not have conventional inner and outer electrodes of the Orbit rap, it will be shown that by selecting appropriate geometry parameters and suitable potentials for the ring electrodes, this geometry can trap the ions into an orbital motion similar to that in the Orbit rap. The performance of the planar geometry is studied by comparing the variation of potential, ion trajectories and image current in this geometry with that in the Orbit rap. The optimization of applied potentials is performed to correct the errors in the electric field so that the variation of axial frequency of ions with their initial position is minimized. Chapter 6 presents the summary and a few concluding remarks

<p>Advances in mass spectrometry (MS) instrumentation and techniques have provided approaches for complementing current biochemical research. Native mass spectrometry, which aims to analyze intact biomolecules and biomolecular complexes, has become a powerful tool for identifying and measuring different units of complex structures as well as probing interactions among the different units. Ion traps generally are important in native MS workflows because of their ability to accumulate ions and perform multi-stage analyses including fragmentation, photoreactions, and gas-phase reactions with reagent molecules or ions. Native MS, however, has shortcomings primarily due to the preferred ionization technique, electrospray ionization (ESI). ESI tends to distribute signal from a single analyte among a range of charge states. Additionally, the ions generated from droplets tend to carry adducted molecules and ions proportional to the size of the analyte. For analysis of high mass and heterogeneous biomolecular complexes, these shortcomings lead to wide overlapping charge states for different components that might be difficult to interpret correctly. Charge reduction via gas-phase ion/ion reactions facilitates interpretation of native mass spectra by generating product ions that are well separated in <i>m/z</i>. Current sine wave technology limits the upper <i>m/z</i> range of ion traps required for stabilizing and measuring high mass ion/ion reaction products. Digital ion trapping (DIT) technology circumvents the voltage limitations of sine wave technology by varying frequency to achieve high <i>m/z</i>. The combination of ion/ion reactions and DIT operation facilitates further unique probing reactions such as fragmentation reactions of charge reduced biomolecular complexes via neutral collisions and photoreactions. DIT operation also provides a straightforward approach for isolation of high <i>m/z</i> ions using duty cycle modulation to further facilitate analysis of heterogeneous mixtures. This work highlights developments of a home-built 3D ion trap mass spectrometer as a viable native MS platform.</p>

This thesis investigates ion-molecule reaction studies with the use of an apparatus with a cryogenic 22-pole RF ion trap. In the introduction, we explain the suitability of an ion trap technique for measurements with conditions replicating interstellar medium. We created a technical draft by which we propose an upgrade of ion optics in a region between a mass analyser and a detector. The draft consists of a set of electrostatic electrodes. The proper effect on the ion optics was theoretically tested by multiple simulations in a programmed model of the detection system. We installed the set of electrodes into the apparatus. The new configuration was optimized by using an algorithm for finding extremes of a function. Finally, we tested the upgraded apparatus on a study of an ion- molecule reaction. The new configuration shows stability and greater control over the trajectory of an ion beam. The study's results are being prepared for publication in an impacted journal. 1

The cylindrical ion trap (CIT) is made up of two planar endcap electrodes and a cylindrical ring electrode. The investigation of simpler geometries like CIT has been started off in recent years with a view towards miniaturization. As a step towards this, numerical studies on CITs were carried out in our laboratory. Here in this study, our motive is to characterize a CIT through experiments. We have designed a mass spectrometer where a CIT is used as the mass analyzer. The trap performance was observed by varying six parameters associated with our experiment. The parameters are (1) the ionization voltage, (2) the ramp time, (3) the ionization time, (4) the cooling time, (5) the dead time and (6) the bias voltage applied across the filaments. All the experiments have been performed in the mass selective boundary ejection mode.

The objective of this research is to design, fabricate, and demonstrate a microfabricated monolithic ion trap for applications in quantum computation and quantum simulation. Most current microfabricated ion trap designs are based on planar-segmented surface electrodes. Although promising scalability to trap arrays containing ten to one hundred ions, these planar designs suffer from the challenges of shallow trap depths, radial asymmetry of the confining potential, and electrode charging resulting from laser interactions with dielectric surfaces. In this research, the design, fabrication, and testing of a monolithic and symmetric two-level ion trap is presented. This ion trap overcomes the challenges of surface-electrode ion traps. Numerical electrostatic simulations show that this symmetric trap produces a deep (1 eV for 171Yb+ ion), radially symmetric RF confinement potential. The trap has an angled through-chip slot that allows back-side ion loading and generous through laser access, while avoiding surface-light scattering and dielectric charging that can corrupt the design control electrode compensating potentials. The geometry of the trap and its dimensions are optimized for trapping long and linear ion chains with equal spacing for use with quantum simulation problems and quantum computation architectures.

This thesis investigates the loss of high mass ions due to the initial thermal energy in ion trap mass analyzers. It provides an analytical expression for estimating the percentage loss of ions of a given mass at a particular temperature, in a trap operating with a set of conditions. The investigations have been carried out on quadrupole and cylindrical ion trap geometries. The three-dimensional Maxwellian velocity distribution function has been assumed to derive an expression for the percentage of ions lost. Adopting an approximation based on the observed escape velocity profiles of ions, an expression for the percentage loss of ions of a given mass has been derived as a function of the temperature for an ensemble of ions, its mass and its escape velocity. An analytical expression for the escape velocity has also been developed. It is seen that the escape velocity is a function of the trapping field, drive frequency and ion mass. Because the trapping field is determined by trap design parameters and operating conditions, it has been possible to study the influence of these parameters on ion loss. The parameters investigated include ion temperature, magnitude of the initial potential applied to the ring electrode (which determines the low mass cut-off), trap size, dimensions of apertures in the endcap electrodes and RF drive frequency. The studies demonstrate that ion loss due to initial thermal energy increases with increase in mass and that ion escape occurs in the radial direction. Reduction in the loss of high mass ions is favoured by lower ion temperatures, increasing low mass cut-off, increasing trap size, and higher RF drive frequencies. The dimensions of the apertures in the endcap electrodes do not influence ion loss in the range of aperture sizes considered.

Axially symmetric rf ion traps consists of a mass analyser having three electrodes, one of which is a central ring electrode and the other two are endcap electrodes. In the ideal Paul trap mass spectrometer, the electrodes have hyperboloidal shape (March and Hughes, 1989) and in mass analyser with simplified geometry, such as the cylindrical ion trap (Wu et al.,2005) the central electrode is a cylinder and the two endcap electrode and flat plates. rf-only or rf/dc potential is applied across the ring electrode and the grounded endcap electrodes for conducting the basic experiments of the mass spectrometer. In recent times, the miniaturisation of ion trap is one of the research interests in the field of mass spectrometry. The miniaturisation has the advantages of compactness, low power consumption and portability. However, this is achieved at the cost of the overall performance of the mass spectrometer with its deleterious effect on resolution. Research groups study the field distribution in the trap for better understanding of ion dynamics in the direction of achieving improved performance with the miniaturised traps. One aspect which has not received any attention in research associated with quadrupole ion traps is the possible role of the magnetic field in improving performance of these traps. Since in the quadrupole ion trap mass analyser ion is confined by an oscillating (rf) field, magnetic fields have been considered superfluous. The motivation of the thesis is to understand the dynamics of ions in axially symmetric rf ion traps, in the presence of the magnetic field. The axially symmetric rf ion trap geometries considered in this thesis are the Paul trap and the cylindrical ion trap (CIT). The changes incurred to the ion motion and Mathieu stability diagram in the presence of magnetic field is observed in this work. Also, the relation between the magnetic field and the Mathieu parameter is shown. The thesis contains 4 chapters: Chapter 1 provides the basic back ground of mass spectrometry and the operating principles. The equations of ion motion in the Paul trap is derived and also the solution to Mathieu equation is provided. The solution to the Mathieu equation are the Mathieu parameters and , when plotted with on the x-axis and on the y-axis, results in the Mathieu stability plot, the explanation of which is also given in the chapter. A brief description of the secular frequency associated with the ion dynamics is given in this chapter. The popular experiments conducted (i.e. the mass selective boundary ejection and resonance ejection) with a mass spectrometer is described here. Finally at the end of the chapter is the scope of the thesis. Chapter 2 facilitates with the preliminary study required fort he accomplishment of the task. The Paul trap and the CIT are the rf ion traps considered in this work. The geometries of these two traps are described in this chapter. The computational methods used for the analysis of various aspects of mass spectrometer is introduced. The computational methods used involve the methods used for calculating the charge distribution on the electrodes, potentials, multipole co-efficients and trajectory calculations. The boundary element method(BEM), calculation for Potentials and the Runge-Kutta method used for the trajectory calculations are introduced in this chapter. The expressions for calculating the multipole co-efficients are also specified. Chapter 3 presents the results obtained. The equations of ion motion in a quadrupole ion trap in the presence of magnetic field is derived here. Verification of numerical results with and without the magnetic field are presented at the end of this chapter. The chapter also presents various graphs showing the impact of magnetic field on the ion dynamics in the Paul trap and the CIT. The impact of the presence of magnetic field on the micro motion in -, -and -directions of the rf ion traps are shown in this chapter. Also the figures showing the variation in the Mathieu stability plots, with varying magnetic field intensity are presented in the chapter. At the end of this chapter the relation between the magnetic field and the Mathieu parameter is derived and plotted. Chapter 4 explains the various observations made from the results obtained. This chapter also highlights the future scope of the work for making this a more applicable one. References in the text have been given by quoting the author’s name and year of publication. Full references have been provide, in an alphabetic order, at the end of the thesis.

In dieser Arbeit werden hochgeladene, mit einer Electron Beam Ion Trap produzierte Ionen für die Erforschung des Elektroneneinfangs von Oberflächen und Gasen eingesetzt. Die Untersuchungen mit Gastargets konzentrieren sich auf die Energieabhängigkeit der Verteilung der K-Schalen-Röntgenstrahlen, die nach Elektroneneinfang in Rydberg-Zustände von Ar-17+ und Ar-18+ Ionen am Ende einer Kaskade von Elektronenübergängen entstehen. Die Ionen werden von der Ionenquelle mit einer Energie von 2 keV/u extrahiert, ladungsselektiert und anschließend bis auf 5 eV/u abgebremst, um dann mit einem Argon Gastarget zu interagieren. Für abnehmende Stoßenergien wird eine Verschiebung des Elektroneneinfangs in Zustände mit niedrigen Drehumpulsquantenzahlen beobachtet. Zum Vergleich wird auch die K-Schalen-Röntgenstrahlung auf Grund des Elektroneneinfangs bei Ar-17+ und Ar-18+ von dem Restgas in der Falle gemessen. Dabei wird eine Diskrepanz zu den Resultaten der Extraktionsversuche festgestellt. Mögliche Erklärungen werden diskutiert. In den Untersuchungen zum Elektroneneinfang von Oberflächen werden hochgeladene Ionen von der Ionenquelle mit Energien von 2 bis 3 keV/u extrahiert, ladungsselektiert und auf Targets gelenkt. Diese bestehen aus Siliziumnitridmembranen mit einer Vielzahl nanometergroßer Löcher, welche mittels eines fokussierten Ionenstrahls in Kombination mit ionenstrahlinduzierter Abscheidung dünner Filme erstellt werden. Es werden hierbei Lochdurchmesser von 50 bis 300 nm mit Formfaktoren von 1:5 bis 3:2 erreicht. Bei den hochgeladenen Ionen handelt es sich um Ar-16+ und Xe-44+. Nach dem Transport durch die Kapillare passieren die Ionen einen elektrostatischen Ladungstrenner und werden detektiert. Der Anteil des Elektroneneinfangs von den Wänden der Löcher ist weitaus geringer als Modellberechnungen vorhersagen. Die Resultate werden an Hand eines Kapillareffekts zur Ionenleitung diskutiert. / In this study highly charged ions produced in Electron Beam Ion Traps are used to investigate electron capture from surfaces and gases. The experiments with gas targets focus on spectroscopic measurements of the K-shell x-rays emitted at the end of radiative cascades following electron capture into Rydberg states of Ar-17+ and Ar-18+ ions as a function of collision energy. The ions are extracted from an Electron Beam Ion Trap at an energy of 2 keV/u, charge-selected and then decelerated down to 5 eV/u for interaction with an argon gas target. For decreasing collision energies a shift to electron capture into low orbital angular momentum capture states is observed. Comparative measurements of the K-shell x-ray emission following electron capture by Ar-17+ and Ar-18+ ions from background gas in the trap are made and a discrepancy in the results compared with those from the extraction experiments is found. Possible explanations are discussed. For the investigation of electron capture from surfaces, highly charged ions are extracted from an Electron Beam Ion Trap at energies of 2 to 3 keV/u, charge-selected and directed onto targets comprising arrays of nanoscale apertures in silicon nitride membranes. The highly charged ions implemented are Ar-16+ and Xe-44+ and the aperture targets are formed by focused ion beam drilling in combination with ion beam assisted thin film deposition, achieving hole diameters of 50 to 300 nm and aspect ratios of 1:5 to 3:2. After transport through the nanoscale apertures the ions pass through an electrostatic charge state analyzer and are detected. The percentage of electron capture from the aperture walls is found to be much lower than model predictions and the results are discussed in terms of a capillary guiding mechanism.