Quantum Computing 

The basic building block of a quantum computer is a qubit: a quantum mechanical system that can exist in two distinct states, 0 and 1, similar to the “bit,” which is the fundamental switching unit of a classical computer. The key difference is that a qubit can exist in both states 0 and 1 simultaneously. Such quantum mechanical superposition states are highly unstable and quickly cease to exist as soon as the qubit comes into contact with the rest of the world (which is why we cannot observe them in our macroscopic environment). The basis for the practical implementation of quantum computers is the targeted manipulation of these sensitive quantum superposition states. Experimental approaches that have been successfully used to control qubits and even to demonstrate complete quantum algorithms include nuclear magnetic resonance (NMR) using molecules in a liquid state, as well as electrodynamically trapped ions manipulated by laser light.

Quantum Simulation

One way to overcome the difficulties associated with universal quantum computing is to use one quantum system to simulate the dynamics of another quantum system. This general idea was originally developed by R. Feynman. Recently, concrete proposals have been put forward for quantum simulations using a chain of pairwise-coupled spins described by a Heisenberg model or a variant thereof. Such models serve as a starting point for numerous theoretical studies in various fields of physics, particularly in solid-state physics, where collective effects such as (anti-)ferromagnetism and superconductivity are investigated. To date, experimental quantum simulations are still in their infancy and have so far been realized with only a few qubits.

We are developing a spin chain consisting of individual electrodynamically trapped ions, which makes it possible to coherently manipulate and read out individual elements of this many-particle system. Furthermore, the strength of the spin-spin coupling and the range of the interaction can be controlled by the experimenter.

Quantum Control 

To physically implement universal quantum computations and apply them to interesting problems, quantum logic gates must be executed with extremely high precision and applied to a large number of qubits. One way to meet the enormous demands of universal quantum computing is to develop practical concepts for better control of the quantum evolution of individual components of quantum information processing, i.e., error correction, characterization and subsequent control of decoherence, as well as robust and optimized quantum gates.

RF radiation for the coherent manipulation of trapped ions 

The potential of trapped ions as a physical system for quantum information processing (QIP) was first recognized in [PRL 74 (1995)], and since then, many important experimental steps have been taken toward realizing a basic quantum computer using this system. At the same time, advanced experiments with trapped ions highlight the difficulties that still need to be overcome.

In addition to the ability to perform arbitrary single-qubit operations, a second fundamental type of operation is required for QIP: conditional quantum dynamics involving at least two qubits. Any quantum algorithm can then be synthesized using these elementary building blocks [PRA 51 (1995), PRA 52 (1995) ]. While two internal states of each trapped ion serve as qubits, the communication between these qubits required for conditional dynamics occurs via the vibrational motion of the ion chain in a linear trap (the “bus qubit”) [PRL 74 (1995)]. Therefore, it is necessary to couple external (motion) and internal degrees of freedom. Most experiments conducted to date—whether in the context of QIP or other fields of research—that require coupling between the internal and external degrees of freedom of atoms have in common the use of optical radiation for this purpose. The recoil energy E_r=(ħk)²/2m, which an atom absorbs upon the absorption or emission of a photon, can alter the atomic state of motion (k = 2πλ, where λ is the wavelength of the incident electromagnetic radiation and m is the mass of the ion). For this to occur with a significant probability in the case of a harmonically trapped atom, the ratio between E_r and the quantized kinetic energy of the trapped atom, ħν, must not be too small (ν is the angular frequency of the vibrational mode to be excited). Therefore, in typical cases, excitation radiation in the optical range is required to couple the internal and external dynamics of the trapped atoms.

The distance δz between neighboring ions in a linear electrodynamic ion trap is determined by the mutual Coulomb repulsion of the ions and the time-averaged force exerted on the ions by the electrodynamic trapping field. The manipulation of individual ions is usually achieved by focusing electromagnetic radiation onto a spot size that is much smaller than δz. Here, too, only optical radiation is suitable.

In the references [QIS3, QIS8, QIS13, QIS14], a concept for ion traps is presented that enables experiments requiring individual addressing of ions and conditional dynamics involving multiple ions, even when using radiation in the radio frequency (RF) range (i.e., with frequencies ranging from kHz to GHz). It is shown how an additional magnetic field gradient applied to an electrodynamic trap individually shifts the resonances of the ion qubits, thereby making them distinguishable in frequency space. This enables individual addressing for the purpose of single-qubit operations using long-wavelength radiation [QIS22, QIS33]. At the same time, a magnetic gradient-induced coupling (MAGIC) arises between internal and motion states [QIS3, QIS22]. Consequently, specific quantum dynamics can be realized in this modified electrodynamic trap, and in such a novel trap, all schemes originally developed for optical QIP in ion traps can also be applied in the RF range.

Trapped ions as a tailor-made spin molecule 

Many phenomena that have only recently been studied in the optical realm form the basis for techniques that are part of the standard repertoire of coherent manipulation of nuclear and electron magnetic moments associated with their spins. Nuclear magnetic resonance (NMR) experiments have been extremely successful in the field of quantum information physics (QIP) through the use of highly sophisticated experimental techniques. However, NMR experiments typically involve macroscopic spin ensembles, and considerable effort is required to prepare pseudopure spin states with an initial thermal occupation distribution. This preparation leads to exponentially increasing costs (with the number N of qubits), whether in terms of signal strength or the number of experiments required [arXiv:quant-ph/0012108 (2000)], since the proportion of spins in the ground state is proportional to N/2^N.

Trapped ions, on the other hand, provide individual qubits—for example, hyperfine states, as described in this paper—that are well isolated from their environment and exhibit a readout efficiency close to one. It would be desirable to combine the advantages of trapped ions and NMR techniques in future experiments, either using “conventional” ion trap methods, but now with RF radiation as described above [QIS3], or by treating the ion chain as an N-qubit molecule with adjustable spin-spin coupling constants [QIS8, QIS14, QIS33]: In a correspondingly modified ion trap, ionic qubit states are coupled in pairs via MAGIC. This spin-spin coupling can be formally described in the same way as the J-coupling in molecules used for NMR, even though the physical origin of the interaction is entirely different. Thus, proven techniques and technologies developed in spin-resonance experiments such as NMR or ESR can be directly applied to trapped ions. One advantage of an artificial “molecule” in a trap is that the coupling constants J_ij between qubits i and j can be chosen by the experimenter by adjusting the magnetic field gradient, the secular trap frequency, and the type of ions used. In addition, individual spins can be detected in a state-selective manner with an efficiency of nearly 100% by collecting scattered resonance fluorescence, whereby the state remains essentially unchanged.