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.
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.
Trapped ions, trapped atoms, and NMR spin systems are all fine ways of building small “toy” quantum computers, each with its own advantages and disadvantages. There are also many other techniques which have been suggested, although these three so far remain in the lead for general-purpose quantum computing. However, the most powerful general-purpose quantum computers constructed to date have only about a dozen qubits, and this is not nearly large enough to make quantum computers useful rather than merely interesting. (Larger systems have been used to demonstrate particular quantum information processing techniques, but these cannot as yet be used to implement arbitrary quantum algorithms.) Although it is not completely clear how complex a general-purpose quantum computer needs to be, it is clear that such a device will involve thousands or even millions of qubits, rather than the dozens involved today. It is, therefore, important to consider whether there is any hope of scaling up these technologies to useful sizes, and we will consider each of the three approaches in turn, before turning briefly to alternative technologies which have not been discussed so far. Trapped ions Trapped ions initially look very promising as a candidate for scaling up, as it is possible to trap thousands of ions while keeping a reasonable distance between them. Early experiments relied on particular tricks which only work with systems of two ions, but this is not true of more recent work, and there is no reason in principle why these large strings of ions could not be controlled.
Many approaches have been proposed towards the realization of practical quantum information processing. They include laser manipulation of the energy states in atomic or ion traps, nuclear magnetic resonance in molecules, quantum computation in optical lattices, and in Bose-Einstein condensates. For any of these system to be viable quantum computation, it should have stable and long-lived internal states. In addition it should be possible to quantum- mechanically entangle two or more qubits and the entangled states should be capable of non-local realism phenomena. The ground state and metastable states of low Z atoms especially the single and two-electron atoms and their ions are the most commonly used qubits for quantum information processing systems. Efforts to exhibit these phenomena in high Z elements has been much more challenging. In part because of the high energy needed to ionize the high Z elements into effective one- or two-electron system suitable for quantum information processing. Furthermore the energy difference between two stable states of the High Z elements that are possible qubits states turn to be very high. Preferably the energy difference of two qubits levels should be in the meV to a few tens of electron volts for practical realization of a quantum computing system. In general any two stable terms of an atomic or molecular system with low to moderate energy separation, that do not violate term rules for selection and symmetry, may be viable qubits states.
To begin with, we need a quantum register made of many qubits to store information. Recall that a classical computer also requires memory to store information. The simplest way to realize a qubit physically is to use a two-level quantum system. For example, an electron, a spin 1/2 nucleus or two mutually orthogonal polarization states (horizontal and vertical, for example) of a single photon can be a qubit. We may also employ a two-dimensional subspace, such as the ground state and the first excited state, of a multi-dimensional Hilbert space, such as atomic energy levels. In the latter case, special care must be taken to avoid leakage of the state to the other part of the Hilbert space. In any case, the two states are identified as the basis vectors, |0〉 and |1〉, of the Hilbert space so that a general single qubit state takes the form |ψ〉 = α|0〉 + β|1〉, where |α|2 + |β|2 = 1. A multiqubit state is expanded in terms of the tensor products of these basis vectors. Each qubit must be separately addressable. Moreover it should be scalable up to a large number of qubits. The two-dimensional vector space of a qubit may be extended to be three-dimensional (qutrit) or, more generally, d-dimensional (qudit). A system may be made of several different kinds of qubits. Qubits in an ion trap quantum computer, for instance, may be defined as: (1) hyperfine/Zeeman sublevels in the electronic ground state of ions (2) a ground state and an excited state of a weakly allowed optical transition and (3) normal mode of ion oscillation. A similar scenario is also proposed for Josephson junction qubits, in which two flux qubits are coupled through a quantized LC circuit. Simultaneous usage of several types of qubits may be the most promising way to achieve a viable quantum computer.
Trapped ions offer a controlled and versatile platform for the simulation of spin and spin-boson quantum systems. The Coulomb interaction between ions trapped in a harmonic potential can be used to mediate interactions between effective spins in the ion chain. Generally, coherent operations on ions are performed on ground-state qubits encoded in magnetically insensitive hyperfine sublevels. In this thesis, we extend this toolbox with the aim of simultaneously manipulating both ground-state and optical qubits, with the latter encoded in metastable optically excited states. The optical qubit provides another set of coherent and dissipative operations that can be performed on the ions, opening new avenues for quantum computing and simulation. In our experiment, we use 171Yb+ and 172Yb+ ions to encode ground-state and optical qubits. We discuss the laser setup needed to address the narrow quadrupole transition from 2S1/2 →2 D3/2 of 3.02 Hz linewidth, and we describe spectroscopy techniques to study this transition in both the isotopes. We describe how the low linewidth allows resolved sideband cooling on the shared motional modes in an ion chain, enabling sympathetic cooling with one ion, 172Yb+ , while simultaneously performing coherent operations on the 171Yb+ ion. Finally, we discuss the prospects of using this tool for light-shift entangling gates, showing the flexibility of this trapped-ion system for simulating coherent as well as dissipative quantum systems.
The current proposals for the realization of quantum computer such as NMR, quantum dots and trapped ions are based on the using of an atom or an ion as one qubit. In these proposals a quantum computer consists from several atoms and the coupling between them provides the coupling between qubits necessary for a quantum gate. We discuss whether a {\it single} atom can be used as a quantum computer. Internal states of the atom serve to hold the quantum information and the spin-orbit and spin-spin interaction provides the coupling between qubits in the atomic quantum computer. In particular one can use the electron spin resonance (ESR) to process the information encoded in the hyperfine splitting of atomic energy levels. By using quantum state engineering one can manipulate the internal states of the natural or artificial (quantum dot) atom to make quantum computations.
Ion traps are fantastic tools to explore the world of electrons, atomic and molecular ions, or charged clusters, in the classical as well as in the quantum regime. Extremely long storage times allow probing even of single particles with very high precision. The mass selectivity of the trapping devices is exploited in many experiments, in particular for mass metrology. An overwhelming part of the experiments and ideas rely on the very high level of parameter control which is offered by the ion trap. Manipulation of individual ions and engineering of well defined quantum states are the fundamental techniques to take the experiments beyond existing frontiers and to unprecedented precision. This special issue presents state-of-the-art theory and experiments in a variety of tutorials, reviews and research papers. More than half of these contributions form a follow-up to the first workshop on Modern Applications of Trapped Ions held in Les Houches, France, in May 2008. A great number of topics is covered in atomic and molecular physics, with ion traps as a common tool. The variety of approaches is meant to make this digest a helpful resource to the whole ion trapping community. Among the contributions, four major – while still overlapping – domains can be identified. Novel ion trap design is the motor of future developments and applications. Spectacular progress has been made in the domain of quantum information processing, such as the realization of planar traps, which opens the way to large-scale quantum computation. In this issue, this enthralling subject is introduced by a tutorial and two review articles, completed by contributions on different experimental realizations. Precision measurements belong to a more traditional domain which nevertheless evolves at the forefront of research: metrology of frequencies and fundamental constants, measurements of g-factors or high-precision mass measurements are the foundations of atomic and molecular physics. The creation and investigation of cold molecular ions and clusters are among the fastest growing topics, leading to ultracold chemistry at the single-particle scale. The next edition of this meeting series will take the name of European Conference on Trapped Ions (ECTI) and will be held in the UK in 2010. We are looking forward to this event, which will offer the possibility to continue the fruitful interaction between research groups that employ ion traps in widely different contexts, and to take the next snapshot of this dynamic research area.