Ebook: Ion Traps for Tomorrow's Applications

Ion trapping initiated in Europe more than 50 years ago. Since then, both fundamental research and development of applications have been growing steadily, and a world-wide recognition was given with the Nobel prize in Physics earned by Wolfgang Paul and Hans Dehmelt in 1989 (see Paul W., Electromagnetic traps for charged and neutral particles, in Rev. Mod. Phys., 62 (1990) 531 and Dehmelt H., Experiments with an isolated subatomic particle at rest, in Rev. Mod. Phys., 62 (1990) 525). The last decades have seen a remarkable growth due, mainly, to the improvement of laser-based techniques for spectroscopy, cooling, and manipulation of ions. Nowadays ion trapping plays a crucial role in a wide range of applications, including atomic and plasma physics, chemistry, high-precision measurements, high-energy physics, and most recently the emerging field of quantum technologies, such as quantum information processing, quantum simulations, and quantum metrology. This is, perhaps, the research direction that in the last years experienced the most dramatic developments and exciting achievements, recognized by the Nobel prize in Physics to David Wineland (Wineland D. J., Nobel Lecture: Superposition, entanglement, and raising Schroedinger's cat, in Rev. Mod. Phys., 85 (2013) 1103), jointly awarded with Serge Haroche in 2012.

Trapping of charged particles requires a portfolio of theoretical and experimental competences, from the more fundamental physical issues to the technological details of the interactions between an ion and the electromagnetic radiation. Early-stage researchers typically have different backgrounds and receive various training and education. Nevertheless, they face quite similar theoretical questions and experimental challenges, which they often tackle with complementary approaches. The fundamental common tool has fostered the emergence of a larger community, who has realized that only a joint effort across the topical boundaries could further boost the field.

In 2013, for the first time in its history, the International School of Physics “Enrico Fermi” hosted a course completely devoted to ion trapping and designed to bring together and address the needs of this heterogenous population. One of the aims of the course was to exploit diversity and stimulate cross fertilization, by offering lectures and seminars on cutting-edge physics in all those fields where trapped ions play a prominent role, with some more emphasis on ion spectroscopy and manipulation. The lectures and reports contained in this volume partly review the wide range of subjects discussed along the course and provide, at the same time, an overview of the topical domain.

The book is opened with the lecture by Dietrich Leibfried and by David Lucas, which introduces the basic concepts and lays the foundations of ion trapping and laser manipulation of trapped particles. This contribution is meant to provide graduate students with the essential experimental toolbox and theoretical framework to perform spectroscopy with trapped ions. Building on this introduction, Shuichi Hasegawa's lecture reviews more specialized work on the creation and use of ion ensembles composed of various isotopes for physics and chemistry applications.

Clusters and crystals of ions in Paul traps are the subject of the lecture by Michael Drewsen, who provides an overview on their properties and applications. His lecture is followed by the theory lecture of Shmuel Fishman and coworkers, who show how a specific structural transition in ion crystals, the linear-to-zigzag transition, can be used as a testbed of fundamental models in statistical mechanics. The contributed paper by Tobias Burgermeister and Tanja Mehlstaubler then describes experiments which analyse the formation of structural defects of ion chains in Paul traps after performing parameter quenches across mechanical instabilities. Ion trapping and crystallization in multipole traps are reviewed in the lecture of Martina Knoop and collaborators, setting the focus on novel ion crystal structures and metrological applications. Ion clocks and frequency standards are the topics of Helen Margolis's lecture, which is accompanied by the contribution of Joseph Thom et al., developing a specific laser system for coherent manipulation of ions in microfabricated traps.

Quantum information processing and simulations with trapped ions were discussed in detail in a series of lectures which build on Leibfried and Lucas' contribution. This book contains several contributions on quantum technological applications, which were never previously reviewed in the school. Spectacular and most recent progress in the realization of quantum simulators with ion crystals is reviewed in Christopher Monroe's lecture. Jurgen Eschner's lecture gives a detailed account of the basic concepts and the remarkable advances in the control of single-ion/single-photon interactions, setting the basis for the realization of a quantum network whose nodes are trapped ions. A related progress report by a major Australian laboratory is presented in Ben Norton et al.'s contribution. Irene Marzoli's lecture focuses on the first proposed protocols for performing quantum computation with trapped electrons. The following report by Andreas Lemmer and collaborators discusses the performances of trapped-ion geometric phase gates for trapped ions in the presence of noise, whereas Humairah Bassa et al. show how to apply unsharp measurements to monitor the dynamics of single quantum systems.

Stefan Willitsch's lecture, and the participant contributions from Jyothi Saraladevi et al. and Henry Lopez et al. are placed at the end of this book, but at the forefront of this interdisciplinary research, and review the interaction of atoms and ions at the frontier between physics and chemistry. These investigations allow to gain insight at the very heart of chemical reactions, working at low temperatures and with an unprecedented control onto the experimental parameters.

We also mention the lecturers, who gave exciting courses but whose contributions are not contained in this book: Rainer Blatt delivered a series of lectures on quantum computation with trapped ions, starting from the basic building blocks till the most recent experimental realizations of quantum algorithms and error correction. Alex Retzker reviewed recent experimental observations and characterizations of kinks and solitons in ion crystals. Klaus Blaum reviewed the applications of ion trapping to nuclear physics and, in particular, to precision mass measurements of short-lived radioactive nuclides. Gerald Gabrielse presented and discussed the basic concepts, the latest advancements, and the challenges in trapping and manipulating single particles and antiparticles for high-precision measurements, determination of fundamental constants and tests of QED. Stefan Schlemmer reviewed experimental investigations of ion-molecule reactions which are of relevance for astrophysical studies. We finally mention Wolfgang Schleich, who gave a passionate and enlightening talk on Herbert Walther's seminal contribution to the development of the field of trapped ions.

Course 189 took place in 2013 from July 22nd to July 30th in the beautiful surroundings of Villa Monastero in Varenna on lake Como, and was inaugurated in presence of Luisa Cifarelli, president of the Italian Physical Society (SIF), on the special occasion of the 60th anniversary of the school. The spectacular location and the perfect organisation by the highly professional SIF staff, led by Barbara Alzani, have made Course 189 an extremely enjoyable, fruitful and successful event, fostering the interaction and stimulating the discussion between all participants. We are glad to acknowledge support by SIF and its Italian partners (Camera di Commercio di Lecco, Istituto Nazionale di Fisica Nucleare), as well as CNRS, Aix-Marseille Universite and TOPTICA Photonics AG. This School was organized in the frame of a wide collaboration network of ion trappers, financially supported by the COST framework. COST Action MP1001 “Ion Traps for Tomorrow's Applications” provided the largest part of funding, in particular for the young researchers.

We hope that the present volume, with its collection of selected topics and highlights, may serve as a useful reference and guidance to all the participants and as a source of inspiration for the next generation of scientists in ion trapping.

M. Knoop, I. Marzoli, G. Morigi

Trapped atomic ions can represent elementary quantum systems that are well isolated from the environment. They can be brought nearly to rest by laser cooling and both their internal electronic states and external motion can be coupled to and manipulated by light fields. This makes them ideally suited for studies in quantum optics, quantum dynamics and quantum information processing. This lecture covers the physics of confinement in ion traps, the coupling of ions to laser fields, laser cooling of single ions and ion crystals, sympathetic cooling between different ion species and near ground-state transport, separation and recombination of ions.

This lecture reviews the isotope-selective manipulation of ions by trapping electric fields and lasers. Loading methods into a trap are also surveyed. The topics discussed here are loading ions into a trap (electron impact, laser ablation, photoionization, mass-selected injection), mass selection by quadrupole electric fields (mass filter, nonlinear resonance, parametric resonance), laser cooling and heating. These techniques have been used for many years and the ion trap continues to find new applications.

The following text will give a brief introduction to the physics of the spatially ordered structures, so-called Coulomb crystals, that appear when confined ions are cooled to sufficiently low temperatures. It will as well briefly comment on the very diverse scientific applications of such crystals, which have emerged in the past two decades. While this document lacks figures, it includes a substantial number of references in which more detailed information can be found. It is our hope that the text will stimulate the readers to dig deeper into one or more of the discussed subjects, and inspire them to think about new potential applications.

A chain of singly charged particles confined by a harmonic potential exhibits a structural transition to a zigzag configuration when the radial potential frequency is at a critical value, which depends on the particle number. This structural change is a phase transition of second order, whose order parameter is the ions' transverse displacement from the chain axis. The transition is driven by transverse, short-wavelength vibrational modes. At ultra-low temperatures the linear-zigzag instability is a quantum phase transition of the same universality class of Ising models.

We discuss our recent studies of topological defects (kinks) in ion Coulomb crystals. Experimentally two different types of kinks are created by non-adiabatically driving the second-order phase transition from a linear to a zigzag phase. The kink creation rates are investigated in relation to the inhomogeneous Kibble-Zurek mechanism. Stability and dynamic properties of both types of kinks are explained by the Peierls-Nabarro potentials. In addition, we report on the influence of mass defects on kinks. We show how the application of electric fields can change the influence of mass defects in a controlled way and present a first evidence for a deterministic creation and manipulation of kinks.

Rings of ions trapped in radiofrequency (rf) multipole traps are extremely interesting candidates for a number of applications concerning high-resolution spectroscopy, in particular due to their (symmetry) properties. This lecture reviews the characteristics of these structures, the required experimental conditions, and proposes applications for these novel ensembles. It will be shown, that rings of ten or twenty ions can reach very similar high-resolution performances as single-ion systems, with a dedicated example in frequency metrology. Numerical simulations of ion dynamics and the experimental realisation of a multipole system give insight into opportunities and limits of rings of trapped ions.

Forbidden optical transitions in single laser-cooled trapped ions make excellent references for accurate optical frequency standards, because the ion trap provides an environment in which external perturbations can be well controlled and characterised. This review provides an introduction to trapped-ion optical frequency standards, covering their principles of operation, the current state-of-the-art for the different standards being studied worldwide, and the various contributions to their systematic uncertainty budgets. Finally, future prospects for redefining the SI second in terms of an optical frequency standard are discussed.

We demonstrate a system for fast and agile digital control of laser phase, amplitude and frequency for coherently manipulating trapped ions. The full versatility of a direct digital synthesis radiofrequency source is faithfully transferred to laser radiation via acousto-optic modulation. Optical beatnotes are used to measure phase steps up to 2π, which are accurately implemented with a resolution of ≤10 mrad. By linearizing the optical modulation process, amplitude-shaped pulses of durations ranging from 500 ns to 500 ms, in excellent agreement with the programmed functional form, are demonstrated. Pulse durations are limited only by the 30 ns rise time of the modulation process. The laser will be used for the coherent control of ions in the NPL microfabricated trap. We also demonstrate the deterministic transport of ions between the trap segments; this combined with the described trap characteristics offers a promising route to scalability.

Laser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting quantum spin models. Effective spins are represented by appropriate internal energy levels within each ion, and the spins can be measured with near-perfect efficiency using state-dependent fluorescence techniques. By applying optical fields that exert optical dipole forces on the ions, their Coulomb interaction can be modulated to give rise to long-range and tunable spin-spin interactions that can be reconfigured by shaping the spectrum and pattern of the laser fields. Here we review the theory behind this system, recent experimental data on the adiabatic prepration of complex ground states and dynamical studies with small collections of ions, and speculate on the near future when the system becomes so complex that its behavior cannot be modeled with conventional computers.

This lecture addresses the application of trapped single ions in the context of quantum networks. It intends to provide an introduction into the basic physical principles, the experimental challenges, and the state of the art.

A microfabricated phase Fresnel lens was used to obtain high-resolution fluorescence and absorption images of ¹⁷⁴Yb⁺ ions trapped in a radiofrequency Paul trap. Fluorescence imaging was used to perform spatial thermometry of a single ion reaching ±5 mK accuracy and ±1 mK precision. By using absorption imaging we measured a phase shift of 1.3 radians imparted on an illumination beam by a single atom.

In this lecture we review quantum information processing with single trapped electrons in a Penning trap: from the theoretical proposals to the first experimental attempts to trap and detect a single particle. We discuss the potential advantages as well as the open challenges of this alternative approach to quantum computation.

We present a study of the performance of the trapped-ion driven geometric phase gates (New J. Phys., 15 (2013) 083001) when realized using a stimulated Raman transition. We show that the gate can achieve errors below the fault-tolerance threshold in the presence of laser intensity fluctuations. We also find that, in order to reduce the errors due to photon scattering below the fault-tolerance threshold, very intense laser beams are required to allow for large detunings in the Raman configuration without compromising the gate speed.

The purpose of this paper is to provide a concise review of the theory of unsharp measurements and its utility for high-fidelity state monitoring of a dynamic quantum system. Unsharp measurements are a special set of generalised measurements that have a weaker influence on the state of a system than projective measurements. We review a method for the estimation and control of a dynamic two-level system via unsharp measurements and show that finite estimation fidelity is obtained even in the presence of external noise.

The study of interactions between simultaneously trapped cold ions and atoms has emerged as a new research direction in recent years. The development of ion-atom hybrid experiments has paved the way for investigating elastic, inelastic and reactive collisions between these species at very low temperatures, for exploring new cooling mechanisms of ions by atoms and for implementing new hybrid quantum systems. The present lecture reviews experimental methods, recent results and upcoming developments in this emerging field.

We present a unique experimental arrangement which permits the simultaneous trapping and cooling of ions and neutral atoms, within a Fabry-Perot (FP) cavity. The versatility of this hybrid trap experiment enables a variety of studies with trapped mixtures. The motivations behind the production of such a hybrid trap system are explained, followed by details of how the experiment is put together. Several experiments that have been performed with this system are presented and some opportunities with this system are discussed.

We are developing a new hybrid atom-ion trap to study the interaction of ultracold rubidium atoms with mass-selected OH⁻ molecules. The ions are trapped inside an octupole rf-trap made of thin wires instead of the commonly used rods. This ensures good optical access to the center of the trap where the ions can be overlapped with laser-cooled rubidium atoms stored in a dark spontaneous force optical trap (dark SPOT). This setup provides high collision rates since the density in a dark SPOT is about one order of magnitude higher than in a standard magneto-optical trap. Further, inelastic collisions with excited atoms are suppressed since almost all atoms are in the ground state. Numerical simulations of our setup using SIMION predict that cooling of the ions is feasible.