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Contemporary Physics

Fundamental physics with trapped ions

G. Horváth, Richard Claude Thompson, P. L. Knight

Published Jan 1, 1997• 46 citations
Publisher

Abstract

Ion traps allow us to study single quantum systems, cooled to the lowest vibrational state of motion within confining electric and magnetic fields. In this article, we describe the working principles of ion traps and the methods used to cool the ions (principally laser cooling). We then discuss how these cold ions, held almost at rest in the trap, can be used to illuminate fundamental issues of quantum mechanics: quantum jumps, the quantum Zeno effect and the quantum statistics of photons scattered by the ions. Finally, we describe how several ions loaded in a trap are cooled into ordered quasi crystals.

DOI
10.1080/001075197182540

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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.

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arXiv:quant-ph/0305129•May 22, 2003•52 citations
Ion traps allow us to study single quantum systems, cooled to the lowest vibrational state of motion within confining electric and magnetic fields. In this article, we describe the working principles of ion traps and the methods used to cool the ions (principally laser cooling). We then discuss how these cold ions, held almost at rest in the trap, can be used to illuminate fundamental issues of quantum mechanics: quantum jumps, the quantum Zeno effect and the quantum statistics of photons scattered by the ions. Finally, we describe how several ions loaded in a trap are cooled into ordered quasi crystals.
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.
A single trapped and cooled ion interacting with light is the realization of a fundamental system of quantum optics. Relevant viewpoints include the light scattering and its relation to the preparation of the ion, the dynamics of the ion's internal motion, and the dynamics of its vibrational motion. As cases in point, recent results are reviewed that illustrate those viewpoints: (i) The preparation of the ion, by spontaneous emission, in a superposition of energy eigenstates of quasi-permanent lifetime. (ii) The dispersive effect of quantum jumps of the ion, to and from a metastable state, that gives rise to internally self-locking the ion in either the light-scattering bright or the non-scattering dark state. (iii) The stochastic cooling of the ion by repeated null detection of its resonance scattering. These counter-intuitive phenomena characterize a physical system, where quantum mechanics models ensembles of observations.
Quantum mechanical effects which are manifested in measurements on trapped atomic ions are reviewed. Observation of these effects is facilitated by the long storage times of a fixed number of laser-cooled ions and by high detection sensitivities, primarily through the observation of scattered laser light. We discuss the observation of quantum jumps and the application of quantum jumps to measurement of atomic ion lifetimes and spectra, detection of antibunching of light, the quantum Zeno effect and quantum projection noise. Experiments which detect nonclassical features of fluorescent light from single or a few trapped ions are briefly reviewed. Finally, we discuss experiments which reveal quantum effects in the motion of trapped ions. We briefly describe possible future extensions for each of these topics.
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.
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 multiple-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-resonance transitions associated with a qualitative estimation of the weak-coupling regime is included in Appendix A and of the Lamb-Dicke regime in Appendix B.
Experiments with individual trapped ions are ideally suited to investigate fundamental issues of quantum mechanics such as the measurement process. At the same time electrodynamically trapped ions have been used with great success to demonstrate quantum logic operations and are a candidate for scalable quantum computing. In this article a brief introduction is given to the basic steps that constitute a quantum measurement; in particular, measurements on single quantum systems are considered. Then experiments with single Yb+ are reviewed demonstrating the quantum Zeno paradox, as well as an experiment where an adaptive algorithm for quantum state estimation of qubits was implemented. In the last section of this article -- devoted to experiments and new ideas related to quantum information processing (QIP) with trapped ions -- the realization of various quantum channels using a hyperfine qubit of Yb+ is briefly discussed. Then a concept for QIP with trapped ions is reviewed where rf or microwave radiation is used instead of laser light for coherent manipulation of a collection of ions. In a suitably modified trap the ions form an artificial ion "molecule" to which the techniques developed in nuclear magnetic resonance and electron spin resonance experiments can be directly applied. Finally, coherent excitation of optical electric quadrupole transitions in Yb+ and Ba+ is reported. In addition, robust Raman cooling of a pair of Ba+ ions is reviewed.