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AIP conference proceedings

Quantum optics with trapped ions

Richard Claude Thompson

Published Jan 1, 1999• 3 citations
Publisher

Abstract

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.

DOI
10.1063/1.58228

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•Jan 1, 2002•1 citation
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.
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.
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.
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 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.
New developments in spectroscopy and quantum optics with stored ions are summarized and discussed. Currently used ion trap devices are briefly described, and newly proposed cooling techniques are indicated. Recent results in precision spectroscopy are reviewed with particular emphasis on time and frequency standards. New applications of stored ions in the field of quantum optics are proposed such as the preparation of nonclassical states of motion in an ion trap. These can be detected by observation of the quantum collapse and revival phenomenon.
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.