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...

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...

We report the experimental estimation of arbitrary qubit states using a succession of N measurements on individual qubits, where the measurement basis is changed during the estimation procedure conditioned on the outcome of previous measurements ͑self-learning estimation͒. Two hyperfine states of a single trapped 171 Yb ϩ ion serve as a qubit. It is demonstrated that the difference in fidelity between this adaptive strategy and passive strategies increases in the presence of decoherence.

A modified 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 + , we have implemented an adaptive algorithm for state estimation involving sequential measurements on arbitrary qubit states.