Laser-cooled, trapped ions are a highly controlled experimental system that allows one to engineer novel quantum states of both fundamental and practical interest.For a string of ions in a linear radio frequency (RF) Paul trap, the linear-zigzag structural phase transition is an intriguing system to investigate quantum dynamics near the critical point of a prototype second-order phase transition, including the preparation of superposition states of different structural configurations.This thesis focuses on two technological improvements required for studying the linear-zigzag structural phase transition in the quantum regime.The first is the development of a compact and cost-effective RF synthesizer setup to provide multiple modulation sources for the laser manipulation of ion strings.The functionality and limitations of a prototype design, based on Direct Digital Synthesizer (DDS) development boards with a microcontroller interface, are evaluated and future improvements are identified.The second part of this thesis focuses on the stabilization of the secular trap frequencies in a linear Paul trap, which is necessary to obtain a stable critical point for the studies of the linear-zigzag transition.To this end, this thesis presents the implementation of a Ramsey spectroscopic technique to measure the secular frequencies and presents the preliminary results from the stability tests.
Laser-cooled, trapped ions are a highly controlled experimental system that allows one to engineer novel quantum states of both fundamental and practical interest.For a string of ions in a linear radio frequency (RF) Paul trap, the linear-zigzag structural phase transition is an intriguing system to investigate quantum dynamics near the critical point of a prototype second-order phase transition, including the preparation of superposition states of different structural configurations.This thesis focuses on two technological improvements required for studying the linear-zigzag structural phase transition in the quantum regime.The first is the development of a compact and cost-effective RF synthesizer setup to provide multiple modulation sources for the laser manipulation of ion strings.The functionality and limitations of a prototype design, based on Direct Digital Synthesizer (DDS) development boards with a microcontroller interface, are evaluated and future improvements are identified.The second part of this thesis focuses on the stabilization of the secular trap frequencies in a linear Paul trap, which is necessary to obtain a stable critical point for the studies of the linear-zigzag transition.To this end, this thesis presents the implementation of a Ramsey spectroscopic technique to measure the secular frequencies and presents the preliminary results from the stability tests.
An array of ions in a linear radio-frequency (RF) Paul trap is a good candidate for investigating structural phase transitions, such as the linear-to-zigzag (LZ) transition, due to the convenient control provided by modification of the trap confinement strength. In such studies, the trap secular frequencies are a key factor that limits the stability of the critical point (CP). In this paper, we implement secular-frequency stabilization, including active feedback stabilization of the RF voltage near the trap electrodes, and achieve a stability of better than 5~ppm over 200~s for both transverse and axial potentials. To evaluate the combined long-term stability of the trap potential in both directions, we measure the zigzag (ZZ) mode frequency near the CP, where the effect of instability in both trap directions is substantially amplified. The short-term noise within a limited spectral window is also suppressed by this scheme, as inferred from decoherence rates of the ZZ mode measured at different frequencies with Ramsey fringes. We also identify that the limitation of the secular frequency stability is mainly from the imperfect temperature insensitivity of voltage dividers and RF detectors, and as a result improvement of lab temperature stability is of great help for stabilizing the trap frequency.
Laser-cooled ions held in a linear Paul trap with strong transverse confinement organize into a one-dimensional (1-D) linear crystal. If the transverse confinement is relaxed, the linear ion crystal undergoes a continuous, structural phase transition to a 2-D zigzag configuration. We study the dynamics near the critical point of the linear-zigzag transition. In the first part of this thesis, we study the spontaneous nucleation and dynamics of topological kink defects, formed as a result of a rapid quench across the linear-zigzag transition. The experimental results are compared to the Kibble-Zurek mechanism, which provides an intuitive model of defect formation and predicts a power-law scaling for the number of defectsformed as a function of transition quench rate. The second part of this thesis is focused on one of the key requirements for investigations of the near-transition dynamics in the quantum regime. To achieve an efficient ground state cooling of the zigzag vibrational mode, we demonstrate 3-D polarization-gradient cooling of strings of 1-4 trapped ions as an intermediate step between Doppler and sideband cooling, and study the polarization-gradient cooling rate and cooling limit as a function of the cooling beam intensity in and near the Lamb-Dicke regime. The results of this thesis pave the way towards our future experiments aimed at assessing the coherence time of a zigzag superposition state through measurements of tunneling oscillations.
Trapped ions in linear Paul traps are largely isolated from interaction with the environment. This property of trapped ions make them a primary choice for quantum technology. \nOver the last decade, trapped atomic ions in linear radio frequency Paul traps have shown to be an important tool to implement quantum algorithms. The scalability of linear ion \ntraps is required to handle large numbers of qubits, in order to implement useful quantum computation. Advance micro-fabrication technology allows the realisation of scalable ion traps. Further developments of micro-trap designs, for the purpose of scalable quantum technology, requires inter-disciplinary investigations of ion traps. Micro-scale ion trap designs typically require a versatile experimental setup. The first part of this thesis describes such an experimental setup including a chip bracket that can host macroscopic ion traps as well as advanced symmetric and asymmetric ion trap chips with up to 90 control electrodes. The system provides versatile optical access for both type of traps and the vacuum chamber is designed in a way so the ion traps can be replaced within a short amount of time. To test the working of the setup, a macroscopic ion trap with an ion-electrode distance of 310±10 μm is used to trap ytterbium ions (Yb+). The trap is characterised by measuring the heating rate, (n•), and spectral noise density SE(ω). A \nphotoionisation technique is used to ionise the different isotopes of Yb in our trap. Isotope selective photoionisation requires exact measurements of 1So↔1P1 transition for the different Yb isotopes. A technique to measure these resonant frequencies is described. \nThis technique works by observing and aligning fluorescence spots and by using this technique, the 1So↔1P1 transition frequencies for stable isotopes of Yb were measured with an accuracy of 60 MHz. These new measured transition frequencies for stable Yb isotopes differ from previously published work by 660 MHz. Furthermore, this technique can also be used to obtain the transition frequencies at different laser-atomic beam angles, typical for non-perpendicular laser-atomic beam angles. The second part of this thesis discusses the optimisation of surface trap geometries as they are being used to implement scalable ion trap designs which consist of a large number of trapping zones. The trap depth in surface traps is low compared to symmetric traps of similar dimensions. How to optimise the trap geometry to achieve maximum trap depth for a given ion height above the trap electrodes, is discussed. Fast and adiabatic ion shuttling operations in one dimension as well as ion separation and recombination processes are important for many quantum information implementations. The maximum speed of separation of trapped ions for adiabatic shuttling operations depends on the secular frequencies, the trapped ion experiences in the process. It will be shown how such ion trap structures have to be designed for fast ion separation process and linear shuttling. Numerical results of adiabatic shuttling operations for trapped ions in such trap structures are also presented.
Abstract While engineered quantum systems are a general route to the manipulation of multipartite quantum states, access in a physical system to a continuous quantum phase transition under sufficient control offers the possibility of an intrinsic source of entangled states. To this end we realize the quantum version of the linear-zigzag structural transition for arrays of up to five ground state-cooled ions held in a linear Paul trap and we demonstrate several of the control requirements towards entangled-state interferometry near the critical point. Using in situ spectroscopy we probe the energy level structure and occupation of the soft mode associated with the structural transition, and show a stable critical point and majority ground state occupation crossing the transition. We resolve biases arising from trap electrode asymmetries that change the nature of the transition, show that they can be suppressed by varying the ion number, and demonstrate control of the transition bias using optical dipole forces.
In this thesis, the next generation of the ion trapping setup has been designed, constructed, and successfully implemented for studying quantum information science at the University of Bonn. The new setup is designed to include an optical cavity as the endcap electrodes of a linear radio-frequency ion trap. In view of this, a novel method to drive the linear ion trap is invented to apply two-phase radio-frequency voltage. In addition to this, a new method to directly bias all the electrodes of the ion trap with DC voltages is implemented in order to control the static electric fields along all directions. Using these methods, over 6 ytterbium ions in a linear Coulomb crystal can been trapped, and radial trapping frequencies of over 1.2 MHz have been observed using the aforementioned methods. Low axial-micromotion for over 65 µm along the axis of the ion trap has been observed, although the endcap electrodes are just as close to the trapped ions as the linear electrodes. In view of finding a novel approach for photonic interfacing the Yb ions, the lower-lying energy levels involving inner-shell electron excitations are investigated in this thesis. By considering their properties, the 2D3/2 → 4f13 (2Fo5/2)5d6s(3D) 3[5/2]o3/2 transition is successfully interrogated using direct laser excitation for the first time to the best of my knowledge. The transition frequency is measured to be 603013350 ± 162 MHz for the isotope 174Yb. In addition to the study of quantum information science, the new ion trap -- optical cavity setup is also considered for the experimental investigation of microscopic thermodynamics. In view of this, the Hamiltonian of the complete system is derived and compared with the theoretical models of Hamiltonian engines. Various non-linear terms occurring in the system Hamiltonian are described for studying the concept of ignition in a future single ion engine in our linear ion trap.
Recent advancements allow for sympathetic cooling of highly charged ions (HCI) to mK temperatures in a cryogenic linear Paul trap. This makes high precision spectroscopy of HCI possible, paving the way to the search for new physics and novel optical clocks. For this, a highly stable and well-understood Paul trap is required. In particular, excess micromotion needs to be characterized and reduced, since it can limit the lowest achievable ion temperature and therefore spectroscopic precision. Within this thesis, a new cryogenic supply system was partly assembled, which allows for vibrational decoupling of the trap, increasing storage stability. The first cool down test achieved a temperature of 4:23K in the trap environment, which is sufficiently low for superconductive operation of the intended RF-resonator made from niobium. Additionally, a photon-correlation technique was used on the existing cryogenic linear Paul trap using 9Be+ ions for determination of the trap frequency by measuring the phase shift between the driven ions motion and the driving field. From the trap frequency the magnification of the imaging system is deduced. The same photon-correlation technique is used to measure excess micromotion and to demonstrate its reduction by a factor of 100 compared to a previous measurement by using new electronics.