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Reviews of Modern Physics

Quantum dynamics of single trapped ions

Dietrich G. Leibfried, R. Blatt, Christopher R. Monroe, David J. Wineland

Published Mar 10, 2003• 2,736 citations
Publisher

Abstract

Single trapped ions 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 quantum-optical and quantum-dynamical studies under well-controlled conditions. Theoretical and experimental work on these topics is reviewed in the paper, with a focus on ions trapped in radio-frequency (Paul) traps.

DOI
10.1103/revmodphys.75.281

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Single trapped ions 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 quantum-optical and quantum-dynamical studies under well-controlled conditions. Theoretical and experimental work on these topics is reviewed in the paper, with a focus on ions trapped in radio-frequency (Paul) traps.
Single trapped ions trapped in Paul traps correspond to ideal candidates for realization of extremely accurate optical atomic clocks and practical studies of the light–atom interactions and nonlinear mechanical dynamics. These systems benefit from both, the superb isolation of the ion from surrounding environment and excellent control of its external and internal\ndegrees of freedom, at the same time, which makes them exquisite platforms for experimental studies and applications of light matter interaction at its most fundamental level. The exceptional degree of control of single or few ion's state enabled in past decade number of major advancements in the applications from the fields of experimental quantum information\nprocessing and frequency metrology, including recent realization of scalable Shor's\nalgorithm, fractional uncertainties of the frequency measurements close to 10-18 level, or simulations of complex quantum many-body effects. These results, together with the rapid advancements in the production of low-noise segmented micro-traps, promise prompt access to long-desired regimes of quantum optomechanics and further development and applications\nof optical atomic clocks.
In these lecture notes, I describe the use of ion traps in experimental investigations of quantum optics. Ion traps are well suited to this type of investigation because of the well-controlled conditions under which ions are held in traps and because they are well isolated from the environment. The notes start with an account of the way that ion traps work, concentrating on the radiofrequency or Paul trap. The techniques of laser cooling in ion traps are then discussed. The rest of the notes deal with various experimental studies undertaken in quantum optics with trapped ions, including observations of quantum jumps: the quantum Zeno effect; cavity quantum electrodynamics; frequency standards; nonclassical states; and quantum logic gates. These notes do not attempt to give a full account of the theory of these phenomena, but rather to give an idea of the very wide range of investigations that have been undertaken with ion traps and the potential they show for future investigations in quantum optics and other fields.
In an iontrap,laser-cooled ions can be confined in a small space in an ultra-high vacuum so that collisions rarely happen and the ions are well isolated from the environment. Since these conditions enable high-resolution spectroscopy of single ions, laser-cooled ions are suitable for use in developing frequency standards. The ions can be cooled to the motional ground state to give a well-defined initial quantum state for quantum state manipulation and quantum computing. In this review, principles of ion traps and laser cooling, and recent progress in optical frequency standards and quantum computing with trapped ions are described.
Abstract Isolating neutral and charged particles from the environment is essential in precision experiments. For decades, this has been achieved by trapping ions with radio-frequency (RF) fields and neutral particles with optical fields. Recently, the trapping of ions by interaction with light has been demonstrated. This might permit the advantages of optical trapping and ions to be combined. For example, we would benefit from superimposing optical traps to investigate ensembles of ions and atoms in the absence of any RF fields and from the versatile and scalable trapping geometries featured by optical lattices. In particular, ions provide individual addressability, and electronic and motional degrees of freedom that can be coherently controlled and detected via high-fidelity, state-dependent operations. Their long-range Coulomb interaction is significantly larger compared to those of neutral atoms and molecules. This enables ultra-cold interaction and the chemistry of trapped ions and atoms to be studied, as well as providing a novel platform for higher-dimensional experimental quantum simulations. The aim of this topical review is to present the current state of the art and to discuss the current challenges and prospects of the emerging field.
In this tutorial we review the physical implementation of quantum computing using a system of cold trapped ions. We discuss systematically all the aspects for making the implementation possible. Firstly, we go through the loading and confining of atomic ions in the linear Paul trap, then we describe the collective vibrational motion of trapped ions. Further, we discuss interactions of the ions with a laser beam. We treat the interactions in the travelling-wave and standing-wave configuration for dipole and quadrupole transitions. We review different types of laser cooling techniques associated with trapped ions. We address Doppler cooling, sideband cooling in and beyond the Lamb-Dicke limit, sympathetic cooling and laser cooling using electromagnetically induced transparency. After that we discuss the problem of state detection using the electron shelving method. Then quantum gates are described. We introduce single-qubit rotations, two-qubit controlled-NOT and multi-qubit controlled-NOT gates. We also comment on more advanced multi-qubit logic gates. We describe how quantum logic networks may be used for the synthesis of arbitrary pure quantum states. Finally, we discuss the speed of quantum gates and we also give some numerical estimations for them. A discussion of dynamics on off-resonant transitions associated with a qualitative estimation of the weak coupling regime and of the Lamb-Dicke regime is included in the Appendix.
The outstanding degree of control over trapped ions in Paul traps gives rise to the development of novel quantum manipulation techniques. Optical transitions can be used for precise manipulation of internal and external states. This way, non-classical states can be created which are a key component of quantum algorithms based on quantum logic operations. This powerful optical toolbox enabled the trapped ion system to assume leadership in the field of quantum computation. This thesis addresses two major challenges in the field of micro ion trap quantum optics. The temperature dependence of the heating rate from the ion trap surface is analysed in a novel cryogenic micro ion trap. Furthermore segmented traps allow state manipulations by time dependent electrical potentials, generated by the control voltages. These electrical fields provide a fast and reliable control handle to the ions external degrees of freedom. Quantum computation in Paul trap arrays is based on a combination of ion crystal transport, splitting and merging operations, while laser driven quantum state manipulations are mainly carried out on small ion crystals. Within this thesis a basic building block was realised by performing transport operations with a single ground-state cooled ion. As a highlight of experimental achievements, shuttling in the non-adiabatic regime, on the timescale of the motional period was demonstrated with low residual energy transfer. For his endeavour a specialised low noise arbitrary function generator was designed and manufactured during this thesis. Arbitrary voltage ramps at a sampling rate of up to 2.5 MS/s on up to 12 channels allow the study of a novel excitation method by directly manipulating the ion using electrical forces. Accurate numerical simulations in combination with the fast high resolution voltage supply allow deterministic quantum manipulations via momentum kicks. I report the first experimental demonstration of displaced number states with trapped ions.