We implement the proof of principle for the quantum walk of one ion in a linear ion trap. With a single-step fidelity exceeding 0.99, we perform three steps of an asymmetric walk on the line. We clearly reveal the differences to its classical counterpart if we allow the walker/ion to take all classical paths simultaneously. Quantum interferences enforce asymmetric, non-classical distributions in the highly entangled degrees of freedom (of coin and position states). We theoretically study and experimentally observe the limitation in the number of steps of our approach, that is imposed by motional squeezing. We propose an altered protocol based on methods of impulsive steps to overcome these restrictions, in principal allowing to scale the quantum walk to several hundreds of steps.PACS numbers: 03.67. Ac, 05.40Fb, 0504Jc A quantum walk[1] is the deterministic quantum mechanical extension of a classical random walk. A simple classical version requires two basic operations: Tossing the coin (coin-operation), allowing for two possible and random outcomes. Dependent on this outcome, the walker performs a step to the right or left (stepoperation). In the quantum mechanical extension the operations allow for coherent superpositions of entangled coin and position states. After several iterations the probability to be in a certain position is determined by quantum mechanical interference of the walker state that leads to fundamentally different characteristics of the walk [2].The motivation for studying quantum walks is twofold. On the one hand, many classical algorithms include random walks. Examples can be found in biology, psychology, economics and physics, for example Einstein's simple model for Brownian motion [3]. The extension of the walk to quantum mechanics might allow for substantial speedup of related quantum versions [2], as in prominent algorithms suggested by Shor[4] and Grover [5] due to other quantum-subroutines. On the other hand, the quantum walk could lead to new insights into entanglement and decoherence in mesoscopic systems [6]. These topics might be explored by increasing the amount of walkers -even before any algorithm might benefit from the quantum random walk.Quantum walks have been thoroughly investigated theoretically and first attempts at implementation have been performed with a very limited amount of steps due to a lack of operation fidelity or fundamental restrictions within the protocol. Some aspects have been realized on the longitudinal modes of a linear optical resonator [7] and in a nuclear magnetic resonance experiment [8]. An implementation based on neutral atoms in a spin-dependent optical lattice[9, 10, 11] has resulted in an experiment recently. Other proposals considered an array of microtraps illuminated by a set of microlenses [12] and Bose-Einstein condensates [13]. Travaglione and Milburn[14] proposed a scheme for trapped ions to transfer the high operational fidelities [6] obtained in quantum information processing (QIP) into To implement the deterministic "tossing of t...

Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems.

The authors report on AlAs∕GaAs micropillar cavities with unprecedented quality factors based on high reflectivity distributed Bragg reflectors (DBRs). Due to an increased number of mirror pairs in the DBRs and an optimized etching process record quality (Q) factors up to 165.000 are observed for micropillars with diameters of 4μm. Optical studies reveal a very small ellipticity of 5×10−4 of the pillar cross section. Because of the high Q factors, strong coupling with a vacuum Rabi splitting of 23μeV is observed for micropillars with a diameter of 3μm.

For several decades, ions have been trapped by radio frequency (RF) and neutral particles by optical fields. We implement the experimental proof-of-principle for trapping an ion in an optical dipole trap. While loading, initialization and final detection are performed in a RF trap, in between, this RF trap is completely disabled and substituted by the optical trap. The measured lifetime of milliseconds allows for hundreds of oscillations within the optical potential. It is mainly limited by heating due to photon scattering. In future experiments the lifetime may be increased by further detuning the laser and cooling the ion. We demonstrate the prerequisite to merge both trapping techniques in hybrid setups to the point of trapping ions and atoms in the same optical potential.