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Journal of Physics B Atomic Molecular and Optical Physics

Spin resonance with trapped ions

Ch. Wunderlich, Ch. Balzer, Th. Hannemann, Florian Mintert, Werner Neuhauser, Davide Rei, P. E. Toschek

Published Feb 24, 2003• 13 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/36/5/325

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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.
Internal states of different ions in an electrodynamic trap are coupled when a static magnetic field is applied -- analogous to spin-spin coupling in molecules used for NMR. This spin-spin interaction can be used, for example, to implement quantum logic operations in ion traps using NMR methods. The collection of trapped ions can be viewed as a NNN-qubit molecule with adjustable coupling constants.
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.
Recently it has been shown that the simulation of one quantum system by means of observing the dynamics of another suitably tailored quantum system can be experimentally far less demanding than universal quantum computation. A system of pair-wise coupled spins described by a Heisenberg model, or a variant thereof, is particularly useful for quantum simulations that in turn are relevant, for instance, for condensed matter physics. We work on the implementation of a pseudo-spin many-body system that will serve as a well controlled prototype system and will allow for the exploration of quantum simulations: in a particular type of ion trap individual atomic ions interact via an adjustable pseudo-spin-spin coupling and, in addition, each spin is individually accessible, thus providing us with an "ion spin molecule". An important milestone towards realizing such ion spin molecules is the individual addressing of a particular spin employing a spatially varying magnetic field. We demonstrate for the first time individual addressing of ions using radio frequency radiation. Yb+ions are confined in a linear Paul trap and laser cooled such that they form a linear Coulomb crystal. Then, an RF-optical double resonance experiment is performed.
A quantum information processor is proposed that combines experimental techniques and technology successfully demonstrated either in nuclear magnetic resonance experiments or with trapped ions. An additional inhomogeneous magnetic field applied to an ion trap (i) shifts individual ionic resonances (qubits), making them distinguishable by frequency, and (ii) mediates the coupling between internal and external degrees of freedom of trapped ions. This scheme permits one to individually address and coherently manipulate ions confined in an electrodynamic trap using radiation in the radiofrequency or microwave regime.
We propose a design for a quantum-information processor where qubits are encoded into hyperfine states of ions held in a linear array of individually tailored linear microtraps and sitting in a spatially varying magnetic field. The magnetic field gradient introduces spatially dependent qubit transition frequencies and a type of spin-spin interaction between qubits. Single- and multiqubit manipulation is achieved via resonant microwave pulses as in liquid-NMR quantum computation while the qubit readout and reset is achieved through trapped-ion fluorescence shelving techniques. By adjusting the microtrap configurations we can tailor, in hardware, the qubit resonance frequencies and coupling strengths. We show that the system possesses a sideband transition structure which does not scale with the size of the processor, allowing scalable frequency discrimination between qubits. By using large magnetic field gradients, one can reset individual qubits in the ion chain via frequency selective optical pulses to implement quantum-error correction, thus avoiding the need for many tightly focused laser beams.
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.