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Individual electrodynamically trapped and laser cooled ions are addressed in frequency space using radio-frequency radiation in the presence of a static magnetic field gradient. In addition, an interaction between motional and spin states induced by an rf field is demonstrated employing rfoptical double resonance spectroscopy. These are two essential experimental steps towards realizing a novel concept for implementing quantum simulations and quantum computing with trapped ions.PACS numbers: 37.10. Vz, 37.10.Ty, 32.60.+i Quantum simulations addressing a specific scientific problem and universal quantum computation are expected to yield new insight into as of yet unsolved physical problems that withstand efficient treatment on a classical computer (e.g., [1]). Already a small number of qubits (i.e., a few tens) used for quantum simulations could solve problems even beyond the realm of quantum information science. Creating and investigating entanglement in large physical systems is a related important experimental challenge with implications for our understanding of the transition between the elusive quantum regime and the classical world [2].Laser cooled atomic ions confined in an electrodynamic cage have successfully been used for quantum information processing (QIP) [3] and advantages and difficulties associated with this system have been and still are subject to detailed investigations. The electromagnetic radiation used to coherently drive ionic resonances that serve as qubits needs to be stable against variations in frequency, phase, and amplitude over the course of a quantum computation or simulation. Experimentally this is particularly challenging when laser light is used for realizing quantum gates. When employing laser light additional issues need to be dealt with to allow for accurate qubit manipulation such as the intensity profile of the laser beam, its pointing stability, and diffraction effects. Furthermore, the motional state of the ion chain strongly affects the gate fidelity which requires ground state cooling and low heating rates during the gate operation [4]. Also, spontaneous scattering of laser light off excited electronic states may pose a limit for the coherence time of a quantum many-body state. The probability for scattering can be reduced by increasing the detuning from excited states (when two laser light fields are used that drive a Raman transition between hyperfine or Zeeman states) which, however, leads to an increasing demand for laser power [5].For generating Raman laser beams with a desired frequency difference, first a radio-frequency (rf) or microwave signal at this difference frequency has to be generated that is then "imprinted" on the laser light and send to the ions. Using rf or microwave radiation directly for coherent driving of qubit transitions is impeded in usual ion trap schemes, since, (i) individual addressing of qubits by focusing radiation on just one ion is difficult due to the long wavelength of rf radiation, and (ii) the required coupling between qubit stat...

The photon pair correlation in the laser-excited fluorescence of a single trapped and cooled Ba + ion shows antibunching and, in addition, novel nonclassical phenomena absent in the fluorescence of twolevel atoms. They include excessive transient values of the correlation caused by optical pumping, and temporally extended sub-Poissonian photon emission probability which arises from the transient excitation of nonabsorbing Raman coherence. The fluorescence also displays sub-Poissonian photon statistics. PACS numbers: 42.50.Dv, 32.50.+d Although light is known to carry information on its source encoded in the correlation functions of all orders, it is the second-order or intensity correlation which provides the main information on intensity fluctuations [1]. Its detection requires two measurements of the light flux. On the microscopic level, the intensity correlation is represented by the correlation of photoelectrons recorded in two events of detection [2], from which the characteristics of photon statistics have been inferred [31. Atomic resonance fluorescence is a case in point: Measurements of its intensity correlation by comparing the timeseparated photon counting signals in one or two channels of detection have revealed nonclassical properties of the light for which the atomic interaction with the excitation light and the vacuum field is responsible. In particular, sub-Poissonian photon statistics [4] have been observed [5,6], and also the rise of the correlation of the two detected photons upon the increase of their time separation T close to zero ("antibunching" [6,7]). So far, the observations have included dilute atomic beams [5,7] or a single ion in a rf trap [6]. The involved atomic particles could be well approximated as two-level systems with the monochromatic laser light cyclically exciting the resonance line.We have, for the first time, recorded the intensity correlation of the resonance fluorescence of a single ion which cannot be modeled as a two-level system. The observed intensity correlation reveals novel features that are not seen in the resonance fluorescence of two-level atoms. These features include a maximum photon correlation which is much larger than what is possible with two-level atoms, and also photon antibunching with much larger time constants of the initial photon anticorrelation.A single Ba + ion, stored in a 1-mm rf trap of 25-MHz drive frequency [8], was laser cooled [9] to less than 3 mK, and its laser-excited resonance fluorescence was recorded by two photon counting channels placed in opposite directions. The relevant levels of Ba + and the wavelengths of the two dye-laser-generated light fields are shown in Fig. 1. The 6 2 / > j/2 resonant level decays with 8-ns lifetime to the ground state 6 2 S\/2 and also to the metastable level 5 2 Z>3/2, with branching ratio 2.85 in favor of the ground state. Since the metastable level lives for 17 s [10], the two light fields are required for the elimination of optical pumping and the generation of a continuous flux of fluorescence. A ...

Coherent operations constitutive for the implementation of single and multi-qubit quantum gates with trapped ions are demonstrated that are robust against variations in experimental parameters and intrinsically indeterministic system parameters. In particular, pulses developed using optimal control theory are demonstrated for the first time with trapped ions. Their performance as a function of error parameters is systematically investigated and compared to composite pulses.In order to experimentally implement a device capable of performing fault-tolerant universal quantum computation (QC), quantum gate operations involving one or multiple qubits have to be carried out with demandingly high accuracy (see, for instance, [1,2]). According to recent theoretical investigations, the experimentally required accuracy of quantum gates for fault-tolerant universal quantum computation no longer seems daunting or even prohibitive [2]. But still, the desired error probability per gate (EPG) should be as small as possible in order to keep the experimental overhead necessary for quantum computation within a feasible limit. Thus a low error probability is prerequisite for scalable fault-tolerant QC.Any quantum algorithm can be decomposed into a sequence of unitary operations applied to individual qubits (single-qubit gate) and conditional quantum dynamics with at least two qubits [3]. Multi-qubit gates (involving two or more qubits) are synthesized by applying a sequence of elementary unitary operations on a collection of qubits. Each of these elementary operations is often similar, or identical, to what is needed for singlequbit gates, and therefore each operation has to be implemented with an error probability well below the tolerable EPG characterizing the full gate operation.If electrodynamically trapped ions are used as qubits, then a unitary operation amounts to letting ions interact with electromagnetic radiation with prescribed frequency, phase, amplitude, and duration of interaction in order to implement quantum gates. Recently, impressive experimental progress was demonstrated in entangling up to eight ions, and performing 2-qubit quantum gates [4,5,6]. Architectures allowing for scalable QC with trapped ions have been proposed (e.g., [7]), and building blocks necessary for achieving this ambitious goal are currently being investigated using various types of ions.The error budget, for instance, of the geometrical phase gate demonstrated in [6] is dominated by the frequency and amplitude uncertainty of the laser light field. These errors are also responsible for a part of the EPG of the controlled-NOT gate reported in [5]. If an "ion spin molecule", that is, trapped ions coupled via a long range spin-spin interaction, is to be used for quantum information processing, then the exact transition frequency of a particular ionic qubit depends on the internal state of other ions [8]. Therefore, here too, it is important to have quantum gates at hand that are insensitive to the detuning of the radiation driving the qubit tran...

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Highly efficient, nearly deterministic, and isotope selective generation of Yb + ions by 1-and 2-color photoionization is demonstrated. State preparation and state selective detection of hyperfine states in 171 Yb + is investigated in order to optimize the purity of the prepared state and to timeoptimize the detection process. Linear laser cooled Yb + ion crystals ions confined in a Paul trap are demonstrated. Advantageous features of different previous ion trap experiments are combined while at the same time the number of possible error sources is reduced by using a comparatively simple experimental apparatus. This opens a new path towards quantum state manipulation of individual trapped ions, and in particular, to scalable quantum computing.When investigating fundamental questions related to quantum mechanics experiments are called for where individual quantum systems can be accessed and deterministically manipulated. The interaction of trapped atomic ions among themselves and with their environment can be controlled to a high degree of accuracy, and thus allows for the preparation of well defined quantum states of the ions' internal and motional degrees of freedom. Trapped ions have proven to be well suited for a multitude of investigations, for instance, into entanglement, decoherence, and quantum information processing, and for applications such as atomic frequency standards. Quantum information processing, in particular, requires accurate and precise control of internal and often also of motional quantum dynamics of a collection of trapped ions. In order to eliminate sources of possible errors, and thus prepare the ground to attain the ambitious goal of using trapped ions for large scale quantum computing or quantum simulations, it is desirable to simplify the apparatus used for such experiments as far as possible.An unprecedented degree of control of quantum systems has been reached in recent experiments with trapped ions, for instance, with BeMainly the type of ion used in such experiments determines the experimental infrastructure needed for controlled manipulation of these ions. The available ionic transitions, for instance, determine the radiation sources to be used: In Ca + an optical electric quadrupole transition has been used as a qubit leading to a coherence time limited ultimately by spontaneous radiative decay. More importantly, phase fluctuations of the laser light driving the qubit transition limit the available coherence time, even when using a highly sophisticated light source [4]. Phase fluctuations of the radiation driving the qubit transition do not present a major obstacle, if a hyperfine transition is used as a qubit (as, for instance, in Be + or Cd + ), since such a transition is usually excited by a stimulated two-photon Raman process where only relative fluctuations between the two driving fields limit the available coherence time. Choosing magnetic field insensitive states as a qubit, as was demonstrated recently with Be + , may further contribute to achieving the desired long coh...