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Physica Scripta

Quantum optics of a single trapped ion

Bernd Appasamy, Jürgen Eschner, Yves Stalgies, Ingo Siemers, P. E. Toschek

Published Jan 1, 1995• 5 citations
Publisher

Abstract

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.

DOI
10.1088/0031-8949/1995/t59/038

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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.
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.
When a single trapped ion is laser excited to a metastable state, its ``quantum jump'' inhibits the laser-excited light scattering on a resonance line. This event, and its inverse, modifies the distribution over the oscillator levels (n)(n)(n) of the ion's vibration in the trap. In particular, unsuccessful attempts to deexcite on vibrational sidebands decrease 〈n〉〈n〉〈n〉 to sub-Doppler values and may leave the ion in a ``trapped'' Fock state decoupled from the light.
Ion traps and cw dye lasers allow one to prepare small clouds of ions, or single ions. They can be detected even by absorptive techniques, such that the information is contained in one field mode only, the mode of the irradiating light. The noise can approach the limit. For excitation on weak and narrow lines, random breaks of the scattering on a competing resonance line can reveal the quantized signal absorption. These interruptions are the signature of quantum jumps which characterize the internal dynamics of a single atomic particle under quasi-continuous observation.
In this article I review some results obtained during my PhD work in the group of Professor Messina, at the University of Palermo. I discuss some proposals aimed at exploring fundamental issues of quantum theory, e.g. entanglement and quantum superpositions, in the context of single trapped ions. This physical context turns out to be extremely well suited both for studying fundamental features of quantum mechanics, such as the quantum–classical border, and for technological applications such as quantum logic gates and quantum registers. I focus on some procedures for engineering nonclassical states of the vibrational motion of the centre of mass of the ion. I consider both the case in which the ion interacts with classical laser beams and the case of interaction with a quantized mode of light. In particular, I discuss the generation of Schrodinger cat-like states, Bell states and Greenberger–Horn–Zeilinger states. The schemes for generating nonclassical states stem from two different quantum processes: the parity effect and the quantum state manipulation via quantum non-demolition measurement. Finally, I consider a microscopic theory of the interaction of a quantum harmonic oscillator (the centre of mass of the ion in the trapped ion context) with a bosonic thermal environment. Using an exact approach to the dynamics, I discuss a quantum theory of heating of trapped ions able to describe both the short time non-Markovian regime and the thermalization process. I conclude showing briefly how the trapped ion systems can be used as simulators of key models of open quantum systems such as the Caldeira–Leggett model.
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.