Experiments with individual trapped ions are ideally suited to investigate fundamental issues of quantum mechanics such as the measurement process. At the same time electrodynamically trapped ions have been used with great success to demonstrate quantum logic operations and are a candidate for scalable quantum computing. In this article a brief introduction is given to the basic steps that constitute a quantum measurement; in particular, measurements on single quantum systems are considered. Then experiments with single Yb+ are reviewed demonstrating the quantum Zeno paradox, as well as an experiment where an adaptive algorithm for quantum state estimation of qubits was implemented. In the last section of this article -- devoted to experiments and new ideas related to quantum information processing (QIP) with trapped ions -- the realization of various quantum channels using a hyperfine qubit of Yb+ is briefly discussed. Then a concept for QIP with trapped ions is reviewed where rf or microwave radiation is used instead of laser light for coherent manipulation of a collection of ions. In a suitably modified trap the ions form an artificial ion "molecule" to which the techniques developed in nuclear magnetic resonance and electron spin resonance experiments can be directly applied. Finally, coherent excitation of optical electric quadrupole transitions in Yb+ and Ba+ is reported. In addition, robust Raman cooling of a pair of Ba+ ions is reviewed.
Experiments with individual trapped ions are ideally suited to investigate fundamental issues of quantum mechanics such as the measurement process. At the same time electrodynamically trapped ions have been used with great success to demonstrate quantum logic operations and are a candidate for scalable quantum computing. In this article a brief introduction is given to the basic steps that constitute a quantum measurement; in particular, measurements on single quantum systems are considered. Then experiments with single Yb+ are reviewed demonstrating the quantum Zeno paradox, as well as an experiment where an adaptive algorithm for quantum state estimation of qubits was implemented. In the last section of this article -- devoted to experiments and new ideas related to quantum information processing (QIP) with trapped ions -- the realization of various quantum channels using a hyperfine qubit of Yb+ is briefly discussed. Then a concept for QIP with trapped ions is reviewed where rf or microwave radiation is used instead of laser light for coherent manipulation of a collection of ions. In a suitably modified trap the ions form an artificial ion "molecule" to which the techniques developed in nuclear magnetic resonance and electron spin resonance experiments can be directly applied. Finally, coherent excitation of optical electric quadrupole transitions in Yb+ and Ba+ is reported. In addition, robust Raman cooling of a pair of Ba+ ions is reviewed.
Am odified ion trap is described where experiments (in particular related to quantum information processing) that usually require optical radiation can be carried out using microwave or radio frequency electromagnetic fields. Instead of applying the usual methods for coherent manipulation of trapped ions, a string of ions in such a modified trap can be treated like a molecule in nuclear magnetic resonance experiments taking advantage of spin–spin coupling. The collection of trapped ions can be viewed as an N-qubit molecule with adjustable spin–spin coupling constants. Given N identically prepared quantum mechanical two-level systems (qubits), the optimal strategy to estimate their quantum state requires collective measurements. Using the ground state hyperfine levels of electrodynamically trapped 171 Yb + ,w e hav ei mplemented an adaptive algorithm for state estimation involvin gs equential measurements on arbitrary qubit states.
This chapter reviews the basic experimental techniques which enable quantum information processing (QIP) with trapped ions and, more briefly, with trapped atoms. In particular, it is explained how the fundamental concepts of quantum computing, such as quantum bits (qubits), qubit rotations, and quantum gates, translate into experimental procedures in a quantum optics laboratory. Furthermore, the recent progress of quantum computing with ions and atoms is summarised, and new approaches to meet the future challenges of scaling up QIP and of atom-photon qubit interfacing are discussed. The chapter is intended to provide an intuitive understanding of the subject and enable the non-specialist student to appreciate the paradigmatic role and the potential of trapped single ions and atoms in the field of quantum computation or, more generally, of quantum optical information technology.
Trapped ions are currently one of the most promising architectures for realising the quantum information processor. The long lived internal states are ideal for representing qubit states and, through controlled interactions with electromagnetic radiation, ions can be manipulated to execute coherent logic operations. In this thesis an experiment capable of trapping Yb+ ions, including 171Yb+, is presented. Since ion energy can limit the coherence of qubit manipulations, characterisation of an ion trap heating rate is vital. Using a trapped 174Yb+ ion a heating rate consistent with previous measurements of other ion species in similar ion traps is obtained. This result shows abnormal heating of Yb+ does not occur, further solidifying the suitability of this species for quantum information processing. Efficient creation, and cooling of trapped ions requires exact wavelengths for the ionising, cooling and repump transitions. A simple technique to measure the 1S0 ? 1P1 transition wavelengths, required for isotope selective photoionisation of neutral Yb, is developed. Using the technique new wavelengths, accurate to 60 MHz, are obtained and differ from previously published results by 660 MHz. Through a simple modification the technique can also predict Doppler shifted transition frequencies, which may be required in non-perpendicular atom-laser interactions. Using trapped ions, the 2S1=2 ? 2P1/2 Doppler cooling and 2D3/2 ? 2D[3/2]1/2 repump transitions are also measured to a greater accuracy than previously reported. Many experiments require wavelengths which can only be obtained using complex expensive laser systems. To remedy this a simple cost effective laser is developed to enable laser diodes to be operated at sub zero temperatures, extending the range of obtainable wavelengths. Additional diode modulation capabilities allow for the manipulation of atoms and ions with hyperfine structures. The laser is shown to be suitable for manipulating Yb+ ions by cooling a diode from 372 nm to 369 nm and simultaneously generating 2.1 GHz frequency sidebands. Coherent manipulation such as arbitrary qubit rotations, motional coupling and ground state cooling, are required for trapped ion quantum computing. Two photon stimulated Raman transitions are identified as a suitable technique to implement all of these requirements and an investigation into implementing this technique with 171Yb+ is conducted. The possibility of exciting a Raman transition via either a dipole or quadrupole transitions in 171Yb+ is analysed, with dipole transitions preferred because quadrupole transitions are found to be too demanding experimentally. An inexpensive setup, utilising a dipole transition, is designed and tested. Although currently limited the setup shows potential to be an inexpensive, high fidelity method of exciting a Raman transition.
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.
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.
Trapped atomic ions are among the most advanced platforms for quantum simulation, computation, and metrology, offering long coherence times and precise, individual control over both internal and motional degrees of freedom. In this review, we present a pedagogical introduction to trapped-ion systems, covering the physics of ion trapping, qubit encodings, and laser-ion interactions. We explain how spin-dependent forces generated by light fields enable both analog and digital quantum simulations of spin and spin-boson models, as well as high-fidelity quantum logic gates. We then highlight an emerging frontier in the simulation of chemical dynamics, summarizing recent experiments that demonstrate the capability of trapped ions to simulate vibronic models and excitation-transfer processes. Finally, we outline future directions in quantum simulation and discuss open challenges in scaling up trapped-ion architectures.