Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Oxford University Press eBooks

Atoms in a box

S. Haroche, J. M. Raimond

Published Aug 10, 2006• 0 citations
Publisher

Abstract

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.

DOI
10.1093/acprof:oso/9780198509141.003.0008

Related papers

Trapped ions

Jonas Larson, Th. K. Mavrogordatos

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.

Institute of Physics eBooks•Sep 1, 2024•0 citations

A tutorial review: Cold trapped ions as quantum information processors

Marek Šašura, Vladimír Bužek

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.

•Jan 1, 2002•1 citation

Chapter Ion Trap: A Versatile Tool for the Atomic Clocks of the Future!

Raymond E. March, John F.J Todd

Since the birth of ion trapping techniques in the 1960s, physics and chemistry applications have evolved fruitfully in concert, leading to the award of one-quarter of the 1989 Nobel Prize in Physics to each of W. Paul [1] and H.G. Dehmelt [2]. Although radiofrequency ion traps were used largely for high resolution atomic spectroscopy, spin exchange experiences, and lifetimes of atomic levels [3,4], the so-called ‘QUISTOR’[5] (QUadrupole Ion STORe) opened a new vista in mass spectrometry not only for component analysis but also for studies of chemical reaction paths also. Atomic excitations that are employed in lasers and the subsequent manipulation of such atomic lasers have stimulated the realization of the huge possibilities presented by ion trapping. Laser cooling, which has permitted the attainment of extreme accuracy in atomic spectroscopy measurements, has provided the means for precise internal and external ion energy manipulation thus opening the way to novel and powerful applications, such as quantum information and atomic clocks in the optical domain [6]. In general, lasers afford quite extraordinary means for both the formation of monatomic and polyatomic ions in specic excitation states and for probing such species in excited states. Recent progress in the development of a wide range of lasers, including the advent of laser diodes, offers myriad opportunities for new kinds of investigations. Another important research direction was opened by the liberties taken with the hyperboloidal geometry of the quadrupole ion trap. Enhanced understanding of the connement properties of quadrupole ion traps allowed the exploitation of new geometries that were easier to construct, such as cylindrical ion traps that permitted ready access for experimentation, exploited new characteristics such an non-linear modes of excitation, and introduced a stretched geometry that led to improvement in mass resolution. Recently, miniaturization of cages [7] or traps on micro-chips [8] have been exploited in atomic quantum physics as well as in chemistry analysis.* It is worthy to note that the extent of progress made in each of these domains was realized due to the curiosity of researchers and their desire to learn from the results of the experiments carried out. The purpose of this chapter is to expound upon the specic topic of atomic clocks utilizing ion traps and the new challenges engaged presently for the measurement of time with extremely high precision. Today, ion atomic clocks are designed for various systems (that is, the ion-trap-oscillator ensemble) that could offer new opportunities for the design of new ion trapping applications.

CRC Press eBooks•Apr 19, 2016•0 citations

Quantum optics experiments in a microstructured ion trap

Ulrich Poschinger

This dissertation describes a prototype experiment aiming at the realization of scalable quantum information. The essential feature is the usage of a novel microstructured ion trap derived from the Paul trap. It allows for storing and manipulating a large number of ions, as compared to conventional linear Paul traps. This thesis describes how the way is paved towards the realization of quantum information experiments in this ion trap. An analysis of the electrostatic properties of the ion trap is presented, which is laying the foundation for understanding the limits of confinement stability and effects beyond standard Paul trap behavior. The focus of this work lies on the realization and characterization of single and dual qubit operations, which are achieved by means of (semiclassical) atom-light interaction. In our experiment, the qubit is implemented in the Zeeman sublevels of the ion’s ground state, i.e. in the spin of the bright electron of a 40Ca+ ion. The main body of this thesis then describes the realization of the necessary steps of preparation, manipulation and readout of this qubit. The preparation includes optical pumping and cooling close to the motional quantum ground state by means of sideband cooling. Several possible techniques for these steps are tested and analyzed. Coherent manipulations are carried out by means of stimulated Raman transitions. Here, a strong emphasis is put on the characterization of the various decoherence mechanisms, which are dominated by the motional excitation of the ion due to thermalization of the ion with the trap electrodes, and by imperfections in the ion-laser interactions. As by-product of the latter investigation, a new measurement scheme for the experimental determination of atomic dipole matrix elements is presented.

•Jan 1, 2010•4 citations

Quantum information science: experimental implementation with trapped ions

Thomas Monz, Philipp Schindler, Daniel Nigg +1 more

Abstract This chapter discusses ion-trap-based quantum computation. Itexplains why ion traps constitute the most advanced quantum information processors to date.

•Jun 12, 2014•0 citations

Trapped atoms and ions

Jonathan A. Jones, Dieter Jaksch

As discussed in Part I of this book, a qubit can in principle be encoded using two energy levels in an atom or ion. These levels are frequently referred to as | g ⧽ and | e ⧽, suggesting the ground state and some excited state, but the actual choice of levels is made so as to optimize the behavior of the system, and it is common to use two hyperfine sublevels of the ground state. As usual, we will simply call the levels |0⧽ and |1⧽. A quantum computer must, of course, have more than one qubit, and this is achieved by using more than one atom or ion, with one qubit encoded on each physical object. In order to make this approach practical, however, it is essential to trap the atoms or ions so that they can be held in a well-controlled environment where they can easily be manipulated. This can be achieved using electric and magnetic fields. The use of trapped ions was one of the first proposals for building quantum computers, and is still one of the best developed. Proposals involving trapped atoms are slightly more recent, and have both substantial advantages and disadvantages in comparison with trapped ions. These differences can ultimately be traced back to the fact that ions interact strongly with their environment and have long-range interactions with one another, while atoms interact more weakly and over shorter ranges. Comparing and contrasting the two approaches provides a useful general introduction to the problems underlying many other proposals. Ion traps It is relatively easy to trap an ion as it will interact strongly with an electric field through the Coulomb interaction.

Cambridge University Press eBooks•Jul 19, 2012•0 citations
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 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.
Since the birth of ion trapping techniques in the 1960s, physics and chemistry applications have evolved fruitfully in concert, leading to the award of one-quarter of the 1989 Nobel Prize in Physics to each of W. Paul [1] and H.G. Dehmelt [2]. Although radiofrequency ion traps were used largely for high resolution atomic spectroscopy, spin exchange experiences, and lifetimes of atomic levels [3,4], the so-called ‘QUISTOR’[5] (QUadrupole Ion STORe) opened a new vista in mass spectrometry not only for component analysis but also for studies of chemical reaction paths also. Atomic excitations that are employed in lasers and the subsequent manipulation of such atomic lasers have stimulated the realization of the huge possibilities presented by ion trapping. Laser cooling, which has permitted the attainment of extreme accuracy in atomic spectroscopy measurements, has provided the means for precise internal and external ion energy manipulation thus opening the way to novel and powerful applications, such as quantum information and atomic clocks in the optical domain [6]. In general, lasers afford quite extraordinary means for both the formation of monatomic and polyatomic ions in specic excitation states and for probing such species in excited states. Recent progress in the development of a wide range of lasers, including the advent of laser diodes, offers myriad opportunities for new kinds of investigations. Another important research direction was opened by the liberties taken with the hyperboloidal geometry of the quadrupole ion trap. Enhanced understanding of the connement properties of quadrupole ion traps allowed the exploitation of new geometries that were easier to construct, such as cylindrical ion traps that permitted ready access for experimentation, exploited new characteristics such an non-linear modes of excitation, and introduced a stretched geometry that led to improvement in mass resolution. Recently, miniaturization of cages [7] or traps on micro-chips [8] have been exploited in atomic quantum physics as well as in chemistry analysis.* It is worthy to note that the extent of progress made in each of these domains was realized due to the curiosity of researchers and their desire to learn from the results of the experiments carried out. The purpose of this chapter is to expound upon the specic topic of atomic clocks utilizing ion traps and the new challenges engaged presently for the measurement of time with extremely high precision. Today, ion atomic clocks are designed for various systems (that is, the ion-trap-oscillator ensemble) that could offer new opportunities for the design of new ion trapping applications.
This dissertation describes a prototype experiment aiming at the realization of scalable quantum information. The essential feature is the usage of a novel microstructured ion trap derived from the Paul trap. It allows for storing and manipulating a large number of ions, as compared to conventional linear Paul traps. This thesis describes how the way is paved towards the realization of quantum information experiments in this ion trap. An analysis of the electrostatic properties of the ion trap is presented, which is laying the foundation for understanding the limits of confinement stability and effects beyond standard Paul trap behavior. The focus of this work lies on the realization and characterization of single and dual qubit operations, which are achieved by means of (semiclassical) atom-light interaction. In our experiment, the qubit is implemented in the Zeeman sublevels of the ion’s ground state, i.e. in the spin of the bright electron of a 40Ca+ ion. The main body of this thesis then describes the realization of the necessary steps of preparation, manipulation and readout of this qubit. The preparation includes optical pumping and cooling close to the motional quantum ground state by means of sideband cooling. Several possible techniques for these steps are tested and analyzed. Coherent manipulations are carried out by means of stimulated Raman transitions. Here, a strong emphasis is put on the characterization of the various decoherence mechanisms, which are dominated by the motional excitation of the ion due to thermalization of the ion with the trap electrodes, and by imperfections in the ion-laser interactions. As by-product of the latter investigation, a new measurement scheme for the experimental determination of atomic dipole matrix elements is presented.
As discussed in Part I of this book, a qubit can in principle be encoded using two energy levels in an atom or ion. These levels are frequently referred to as | g ⧽ and | e ⧽, suggesting the ground state and some excited state, but the actual choice of levels is made so as to optimize the behavior of the system, and it is common to use two hyperfine sublevels of the ground state. As usual, we will simply call the levels |0⧽ and |1⧽. A quantum computer must, of course, have more than one qubit, and this is achieved by using more than one atom or ion, with one qubit encoded on each physical object. In order to make this approach practical, however, it is essential to trap the atoms or ions so that they can be held in a well-controlled environment where they can easily be manipulated. This can be achieved using electric and magnetic fields. The use of trapped ions was one of the first proposals for building quantum computers, and is still one of the best developed. Proposals involving trapped atoms are slightly more recent, and have both substantial advantages and disadvantages in comparison with trapped ions. These differences can ultimately be traced back to the fact that ions interact strongly with their environment and have long-range interactions with one another, while atoms interact more weakly and over shorter ranges. Comparing and contrasting the two approaches provides a useful general introduction to the problems underlying many other proposals. Ion traps It is relatively easy to trap an ion as it will interact strongly with an electric field through the Coulomb interaction.