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Institute of Physics eBooks

Trapped ions

Jonas Larson, Th. K. Mavrogordatos

Published Sep 1, 2024• 0 citations
Publisher

Abstract

Chapter 5 focuses on trapped ions, and covers model Hamiltonians, state preparation and tomography, and quantum information processing. An important closing chapter on further aspects and perspectives relates trapped ion systems to quantum simulators. First, this is discussed in the trivial case of a single Jaynes–Cummings (JC) model, but then turning to genuine many-body spin chains constructed from arrays of JC models.

DOI
10.1088/978-0-7503-6452-2ch5

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Chapter 5 focuses on trapped ions, and covers model Hamiltonians, state preparation and tomography, and quantum information processing. An important closing chapter on further aspects and perspectives relates trapped ion systems to quantum simulators. First, this is discussed in the trivial case of a single Jaynes–Cummings (JC) model, but then turning to genuine many-body spin chains constructed from arrays of JC models.
This chapter describes the essential features of ion traps and the quantum information science that these systems make possible. Section 8.1 analyses the Paul trap design generally used in these experiments and describes how it operates with a single ion or with a set of ions making up a string of qubits. Section 8.2 focuses on the manipulation of the ion's motional states. Section 8.3 includes in the spin-spring model the ionic relaxation due to spontaneous emission, using the quantum jump language introduced in Chapter 4. Section 8.4 focuses on the scheme proposed by Cirac and Zoller that has been implemented in the laboratory on Ca+ ions by the Innsbruck group. The results of a teleportation experiment involving three ions are presented. In an alternative scheme, the Boulder group working on Be+ has realized gates in which the ions are addressed collectively. Section 8.5 shows how this has made it possible to prepare and analyse GHZ states with up to six ions. Section 8.6 concludes by discussing some of the perspectives opened by ion trap physics in quantum information science.
In this chapter, we examine ion-trap-based quantum simulators. This is the same type of hardware that is employed for ion-trap quantum computers, but we do not describe gated quantum computing in this book. Instead, we focus on examining the complex quantum dynamics in systems where individual ions can be trapped and manipulated. These systems are one of the hallmarks of the second quantum revolution, where we can manipulate quantum systems at the single-quantum level. We describe the phonon modes for ions in a trap, Raman transitions, spin-dependent forces that lead to effective spin models, how to prepare spin ground states, and extensions to the Lipkin-Meshkov-Glick and Dicke models.
Abstract We have experimentally observed the dynamics of a single polariton and two polaritons in a two-ion chain. By driving two trapped ions at a motional blue-sideband (BSB) transition, we realize the anti-Jaynes–Cummings–Hubbard (JCH) model. When a single polariton exists in a trapped-ion chain, the polariton hops between the ion sites. On the other hand, when there are single polaritons at each ion site, the hopping of the polaritons is suppressed because of the polariton–polariton interaction induced by the nonlinearity of the anti-Jaynes–Cummings (JC) interaction, thereby realizing the blockade of polariton hopping in the anti-JCH model with trapped ions. Our work is a step towards the development of a trapped-ion based quantum simulator for strongly interacting polaritonic systems.