Contents -- Preface -- 1. Physics with Trapped Charged Particles -- 1.1 Introduction -- 1.2 History of Ion Traps -- 1.3 Principles of Ion Traps -- 1.3.1. The Penning trap -- 1.3.2. The radiofrequency (RF) Paul trap -- 1.3.3. The linear RF trap -- 1.3.4. Low-energy storage rings -- 1.4 Creation, Cooling and Detection of Ions -- 1.4.1. Creation of ions -- 1.4.2. Cooling of ions -- 1.4.2.1. Buffer-gas cooling -- 1.4.2.2. Resistive cooling -- 1.4.2.3. Laser cooling -- 1.4.2.4. Sympathetic cooling -- 1.4.3. Detection of ions -- 1.5 Applications of Ion Traps -- 1.6 Conclusions and Outlook -- Acknowledgments -- References -- 2. Detection Techniques for Trapped Ions -- 2.1 Electronic Techniques -- 2.1.1. Instruments -- 2.1.1.1. Faraday Cup -- 2.1.1.2. Electron multiplier -- 2.1.1.3. Microchannel plate -- 2.1.2. Techniques -- 2.1.2.1. Ion loss -- 2.1.2.2. Depletion techniques -- 2.1.2.3. Ejection with or without additional perturbation -- 2.1.2.4. Time-of-flight profiles -- 2.1.2.5. Image currents -- 2.2 Fluorescence Techniques -- 2.2.1. Lineshape -- 2.2.2. Single-ion detection -- 2.2.3. Motional frequencies -- 2.2.4. Ions as a spatial probe -- 2.2.5. Temporal Ramsey -- 2.2.6. Quantum logic spectroscopy -- 2.2.7. Imaging techniques -- 2.2.8. Optical setup and instrumentation -- References -- 3. Cooling Techniques for Trapped Ions -- 3.1 Introduction -- 3.2 Non-laser Cooling Techniques -- 3.2.1. Electron cooling -- 3.2.2. Resistive cooling -- 3.2.3. Buffer-gas cooling -- 3.3 Laser Cooling -- 3.3.1. Ion-laser interaction Hamiltonian -- 3.3.2. Lamb-Dicke regime -- 3.3.3. Coupling strength -- 3.3.4. Sideband cooling -- 3.3.4.1. Raman sideband excitation -- 3.3.5. Sideband cooling using RF radiation -- 3.3.5.1. Simultaneous cooling of many vibrational modes -- 3.4 Laser Cooling Using Electromagnetically Induced Transparency -- 3.5 Cavity Cooling.

3.6 Cooling Scheme Combining Laser Light and RF -- References -- 4. Accumulation, Storage and Manipulation of Large Numbers of Positrons in Traps I - The Basics -- 4.1 Overview -- 4.2 Positron Trapping -- 4.3 Positron Cooling -- 4.4 Confinement and Characterization of Positron Plasmas in Penning-Malmberg Traps -- 4.5 Radial Compression Using Rotating Electric Fields - the "Rotating-wall" (RW) Technique -- 4.6 Concluding Remarks -- Acknowledgments -- References -- 5. Accumulation, Storage and Manipulation of Large Numbers of Positrons in Traps II - Selected Topics -- 5.1 Overview -- 5.2 Extraction of Beams with Small Transverse Spatial Extent -- 5.3 Multicell Trap for Storage of Large Numbers of Positrons -- 5.4 Electron-Positron Plasmas -- 5.5 Concluding Remarks -- Acknowledgments -- References -- 6. Waves in Non-neutral Plasma -- 6.1 Diocotron Waves -- 6.1.1. Infinite length description -- 6.1.2. A negative energy mode -- 6.1.3. Finite amplitude shift of diocotron mode -- 6.1.4. Finite length diocotron -- 6.1.5. Magnetron regime -- 6.1.6. Higher-order diocotron modes -- 6.2 Plasma Waves -- 6.2.1. Finite length Trivelpiece-Gould modes -- 6.2.2. Thermally excited TG modes -- 6.2.3. Higher-order Trivelpiece-Gould modes -- 6.2.4. Electron acoustic waves -- 6.3 Cyclotron Waves -- Acknowledgments -- References -- 7. Internal Transport in Non-neutral Plasma -- 7.1 Types of Collisions -- 7.1.2. Long-range E x B drift collisions -- 7.2 Test Particle Transport -- 7.2.1. Classical diffusion -- 7.2.2. Long-range E x B drift diffusion -- 7.2.3. Experimental measurements of test particle transport -- 7.2.4. Test particle transport in 2D systems -- 7.2.4.1. Shear-free case -- 7.2.4.2. Effect of shear on 2D test particle transport -- 7.3 Heat Transport -- 7.3.1. Classical heat transport -- 7.3.2. Long-range E x B drift heat transport.

7.3.3. Experimental measurements of cross-magnetic field heat transport -- 7.4 Transport of Angular Momentum -- 7.4.1. Classical viscosity -- 7.4.2. Long-range viscosity -- 7.4.3. Viscosity in 2D system -- 7.5 Table of Transport Coefficients -- Acknowledgments -- References -- 8. Antihydrogen Formation and Trapping -- 8.1 Introduction -- 8.2 Introduction to Antihydrogen Formation and Trapping -- 8.3 Antiproton Catching and Pre-cooling -- 8.4 Trapped Particles and Magnetic Multipoles -- 8.5 The Rotating-wall Technique -- 8.6 Antiproton Preparation -- 8.7 Positron Preparation -- 8.8 Evaporative Cooling of Charged Particles -- 8.9 Merging Antiprotons and Positrons -- 8.10 Trapped Antihydrogen and its Detection -- 8.11 Conclusions and Outlook -- References -- 9. Quantum Information Processing with Trapped Ions -- 9.1 Introduction -- 9.2 Storing Quantum Information in Trapped Ions -- 9.3 Preparation, Manipulation and Detection of an Optical Qubit -- 9.4 Entangling Quantum Gates -- 9.4.1. Cirac-Zoller-type gate interactions -- 9.4.2. Quantum gates based on bichromatic light fields -- 9.4.3. Conditional phase gates -- 9.4.4. Molmer-Sorensen gates -- 9.5 Quantum State Tomography -- 9.6 Elementary Quantum Protocols and Quantum Simulation -- References -- 10. Optical Atomic Clocks in Ion Traps -- 10.1 Introduction -- 10.2 Principles of Operation -- 10.2.1. Trapping, cooling and probing a single ion -- 10.2.2. Clock laser stabilization -- 10.2.3. Femtosecond optical frequency combs -- 10.3 Systems Studied and State-of-the-art Performance -- 10.4 Systematic Frequency Shifts -- 10.5 Conclusions and Perspectives -- Acknowledgments -- References -- 11. Novel Penning Traps -- 11.1 Introduction -- 11.2 Penning Traps -- 11.2.1. The cylindrical trap -- 11.3 The CPW Penning Trap -- 11.3.1. The ideal CPW-trap -- 11.3.1.1. Expressions of the frequencies.

11.3.1.2. The invariance theorem -- 11.4 The Real CPW Penning Trap -- 11.5 Compensation of Electric Anharmonicities -- 11.5.1. The useful trapping interval -- 11.6 Conclusions -- Acknowledgments -- References -- 12. Trapped Electrons as Electrical (Quantum) Circuits -- 12.1 Introduction -- 12.2 The Induced Charge Density -- 12.3 Detection of the Electron's Motion -- 12.4 Equivalent Electrical Circuit of the Trapped Particle -- 12.4.1. Resistive cooling time constant -- 12.5 Coupling the Cyclotron Motion to a Superconducting Cavity -- 12.6 Conclusions -- Acknowledgments -- References -- 13. Basics of Charged Particle Beam Dynamics and Application to Electrostatic Storage Rings -- 13.1 Introduction -- 13.2 Relativistic Energy and Momentum -- 13.3 Basic Features of Magnetic and Electrostatic Bends -- 13.3.1. Magnetic rigidity -- 13.3.2. Electric rigidity -- 13.4 Betatron Oscillations -- 13.4.1. Radial motion -- 13.4.2. Vertical motion -- 13.4.3. Solution of the equation of motion -- 13.5 Quadrupole Magnets -- 13.6 Strong Focusing -- 13.7 Summary -- Acknowledgments -- References -- 14. Electrostatic Storage Rings - An Ideal Tool for Experiments at Ultralow Energies -- 14.1 Introduction -- 14.2 Common Features of Electrostatic Storage Rings -- 14.3 Electrostatic Deflectors of Different Shapes -- 14.4 Electric Field Distribution in Electrostatic Deflectors -- 14.4.1. Electric field in the vicinity of the equilibrium orbit -- 14.5 Equations of Motion in an Electrostatic Deflector -- 14.6 Nonlinear Effects in ESRs -- 14.7 Ion Kinetics and Long-term Beam Dynamics in Electrostatic Storage Rings -- 14.7.1. Kinetic equations -- 14.7.2. Multiple scattering of ions -- 14.7.2.1. Rate of RMS emittance growth -- 14.7.2.2. Mean square scattering angle -- 14.7.2.3. Ionization energy losses -- 14.7.2.4. Multiple scattering on residual gas.

14.7.3. Particle loss probability -- 14.7.4. Intra-beam scattering -- 14.8 Benchmarking of Experiments -- 14.9 Conclusions and Outlook -- Acknowledgments -- References -- Index.