Entanglement, its generation, manipulation and fundamental understanding is at the very heart of quantum mechanics. The phrase entanglement was coined by Erwin Schrödinger in 1935 for particles that are described by a common wave function where individual particles are not independent of each other but where their quantum properties are inextricably interwoven 1 . Entanglement properties of two and three particles have been studied extensively and are very well understood. Entanglement of four 2 and five 3 particles was demonstrated experimentally. However, both creation and characterization of entanglement become exceedingly difficult for multi-particle systems. Thus the availability of such multiparticle entangled states together with the full information on these states in form of their 1

Teleportation of a quantum state encompasses the complete transfer of information from one particle to another. The complete specification of the quantum state of a system generally requires an infinite amount of information, even for simple two-level systems (qubits). Moreover, the principles of quantum mechanics dictate that any measurement on a system immediately alters its state, while yielding at most one bit of information. The transfer of a state from one system to another (by performing measurements on the first and operations on the second) might therefore appear impossible. However, it has been shown that the entangling properties of quantum mechanics, in combination with classical communication, allow quantum-state teleportation to be performed. Teleportation using pairs of entangled photons has been demonstrated, but such techniques are probabilistic, requiring post-selection of measured photons. Here, we report deterministic quantum-state teleportation between a pair of trapped calcium ions. Following closely the original proposal, we create a highly entangled pair of ions and perform a complete Bell-state measurement involving one ion from this pair and a third source ion. State reconstruction conditioned on this measurement is then performed on the other half of the entangled pair. The measured fidelity is 75%, demonstrating unequivocally the quantum nature of the process.

A crucial building block for quantum information processing with trapped ions is a controlled-NOT quantum gate. In this paper, two different sequences of laser pulses implementing such a gate operation are analyzed using quantum process tomography. Fidelities of up to 92.6(6) % are achieved for single gate operations and up to 83.4(8) % for two concatenated gate operations. By process tomography we assess the performance of the gates for different experimental realizations and demonstrate the advantage of amplitude-shaped laser pulses over simple square pulses. We also investigate whether the performance of concatenated gates can be inferred from the analysis of the single gates.PACS numbers: 03.65. Wj, 03.67.Lx, 32.80.Qk Processing information with well-controlled quantum systems has the fascinating perspective of being much more powerful than classical computers for certain applications. A promising candidate for the experimental realization of quantum computing are strings of ions stored in linear Paul traps [1] as recently demonstrated by various key experiments, including the preparation of multi-particle entangled states [2,3], quantum teleportation [4,5] and quantum error correction [6]. Quantum information processing depends on the ability to implement single qubit rotations and most importantly an entangling two-qubit quantum gate [7,8,9,10]. Proper characterization and understanding of the action of gate operations and their imperfections is of vital importance in order to successfully apply them in complex computations.Generally, the implementations of quantum gates are imperfect due to decoherence and various systematic error sources present in experimental setups. A proper description of such an operation which accounts for the possibly non-unitary evolution of the qubits is provided by quantum process tomography [11,12]. Process tomography has already been applied for characterizing quantum gates in NMR and linear-optics quantum computing [13,14,15]. Here, we show that process tomography is a valuable tool for comparing different ion trap quantum gate implementations and optimizing the experimental parameters. This way, we were able to improve our controlled-NOT (CNOT) gate fidelity from 71 % [7] to almost 93 %. Moreover, the action of two successively applied gate operations is investigated and compared to the predictions from the single gate tomography result.We realize entangling gates between 40 Ca + ions held in a linear trap [16]. Quantum information is stored in superpositions of the |S ≡ S 1/2 (m = −1/2) ground state and the metastable |D ≡ D 5/2 (m = −1/2) state and is manipulated by laser pulses at a wavelength of 729 nm exciting the electric quadrupole transition between those states. A focus size smaller than the inter-ion distance and precise control of the focus position allows us to address single qubits. Detection of the qubit's quantum state is achieved by scattering light on the S 1/2 ↔ P 1/2 dipole transition and detecting the presence or absence of resonance fluorescence of t...

Quantum computers hold the promise to solve certain computational task much more efficiently than classical computers. We review the recent experimental advancements towards a quantum computer with trapped ions. In particular, various implementations of qubits, quantum gates and some key experiments are discussed. Furthermore, we review some implementations of quantum algorithms such as a deterministic teleportation of quantum information and an error correction scheme.

It is common belief among physicists that entangled states of quantum systems loose their coherence rather quickly. The reason is that any interaction with the environment which distinguishes between the entangled sub-systems collapses the quantum state. Here we investigate entangled states of two trapped Ca + ions and observe robust entanglement lasting for more than 20 seconds.

We report adiabatic passage experiments with a single trapped 40 Ca + ion. By applying a frequency chirped laser pulse with a Gaussian amplitude envelope we reach a transfer efficiency of 0.990(10) on an optical transition from the electronic ground state S 1/2 to the metastable state D 5/2 . This transfer method is shown to be insensitive to the accurate setting of laser parameters, and therefore is suitable as a robust tool for ion based quantum computing.PACS numbers: 03.67. Lx,32.80.Qk It is the interplay between different technologies that is stimulating novel developments aiming at the ambitious goal of a future large-scale quantum computer [1]. As recent research has shown, considerable promise lies in the application of nuclear magnetic resonance (NMR) technology to ion-trap based quantum computing [2,3]. While ion based quantum computing has strong assets concerning the preparation of multi-particle entangled states [4,5] and the highly efficient readout of qubit states using projective measurements [6,7,8], liquid state NMR quantum computing relies on well developed radio frequency (rf) techniques which have enabled the most complex [9, 10, 11] sequences of quantum logic gate operations to date with about 10 2 to 10 3 rf-pulses [12].The basic construction principle of an elementary quantum computer with trapped ions relies on linear cold ion crystals serving as quantum register. Two of each of the ions' electronic states serve to store elementary bits of quantum information (qubits) which are coherently manipulated by the application of laser [13] or microwave pulses [14] with well defined timing, frequency and phase. With a number of operations applied, on single ions individually or on groups of ions a quantum algorithm may be implemented.Composite gate operations [2], initially developed in the context of NMR experiments, have already enabled complex tasks in ion traps like the demonstration of quantum teleportation [6,7], which comprises about 30 laser pulses of different frequency, phase and amplitude. In order to further increase the complexity of algorithms and to improve the robustness of single and multiqubit quantum logic gates, all parameters characterizing the * Present address: University of Siegen, Fachbereich Physik, 57068-Siegen, Germany electromagnetic field driving qubit transitions have to be freely adjustable, thus allowing for the implementation of pulses with arbitrary amplitude and phase envelope. For this purpose, a suitable waveform having these characteristics is digitally generated in the rf-domain and then mapped phase-coherently onto a fixed frequency laser or microwave field for qubit manipulation. Here, as a first application we demonstrate robust adiabatic passage (RAP) in a single trapped ion qubit system.In this publication first we briefly review some elements of the theory of rapid adiabatic passage (RAP), then give a short description of the experimental setup which allows the generation of complex laser pulses. Subsequently, experimental data demonstarting RAP a...

Relaxation spectra of molecular glass formers devoid of secondary relaxation maxima, as measured by dielectric spectroscopy (DS), nuclear magnetic resonance (NMR) relaxometry, photon correlation spectroscopy (PCS), and Fabry–Perot interferometry, are quantitatively compared in terms of the Kohlrausch stretching parameter βK. For a reliable estimate of βK, the excess wing contribution has to be included in the spectral analysis. The relaxation stretching probed by PCS and NMR varies only weakly among the liquids (βK = 0.58 ± 0.06). It is similar to that found in DS, provided that the liquid is sufficiently nonpolar (relaxation strength Δε≲6). For larger strengths, larger βKDS (narrowed relaxation spectra) are found when compared to those reported from NMR and PCS. Frequency–temperature superposition (FTS) holds for PCS and NMR. This is demonstrated by data scaling and, for the few glass formers for which results are available, by the equivalence of the susceptibilities χPCS″ωτ∝χNMR″τ∝χNMR″ω, i.e., measuring at a constant frequency is equivalent to measuring at a constant temperature or constant correlation time. In this context, a plot of the spin–lattice relaxation rate R1(T) as a function of the spin–spin relaxation rate R2(T) is suggested to reveal the stretching parameter without the need to perform frequency-dependent investigations. Dielectrically, we identify a trend of increasing deviations from FTS with increasing Δε. Depending on the technique and glass former, the relative relaxation strength of the excess wing varies, whereas its exponent appears to be method independent for a given substance. For polar liquids, we discuss possible reasons for the discrepancy between the results from PCS and NMR as compared to those from DS.

Various (2)H and (31)P nuclear magnetic resonance (NMR) spectroscopy techniques are applied to probe the component dynamics of the binary glass former tripropyl phosphate (TPP)/polystyrene-d3 (PS) over the full concentration range. The results are quantitatively compared to those of a dielectric spectroscopy (DS) study on the same system previously published [R. Kahlau, D. Bock, B. Schmidtke, and E. A. Rössler, J. Chem. Phys. 140, 044509 (2014)]. While the PS dynamics does not significantly change in the mixtures compared to that of neat PS, two fractions of TPP molecules are identified, one joining the glass transition of PS in the mixture (α1-process), the second reorienting isotropically (α2-process) even in the rigid matrix of PS, although at low concentration resembling a secondary process regarding its manifestation in the DS spectra. Pronounced dynamical heterogeneities are found for the TPP α2-process, showing up in extremely stretched, quasi-logarithmic stimulated echo decays. While the time window of NMR is insufficient for recording the full correlation functions, DS results, covering a larger dynamical range, provide a satisfactory interpolation of the NMR data. Two-dimensional (31)P NMR spectra prove exchange within the broadly distributed α2-process. As demonstrated by (2)H NMR, the PS matrix reflects the faster α2-process of TPP by performing a spatially highly hindered motion on the same timescale.