after annealing to 20 K, lnR-T ' ' was found. These films did not exhibit superconductivity as measured resistively down to the lowest temperatures attainable (T-1.5 K). The above-described behavior suggests that the Hg-Xe system exhibits a metal-nonmetal transition which occurs with a dependence on concentration and with a critical concentration close to that of continuous percolation in 3D. Beyond the percolation threshold, the systems acquire a negative TCR but are still superconductors. With further increase in Xe concentration, a regime in which the conductivity is dominated by hopping is entered. The approach to an insulating configuration beyond the percolation threshold is probably the Mott-Anderson transition of Refs. 2-4 and is accompanied by the eventual disappearance of superconductivity as determined resistively. The authors would like to thank R. Mikkelson for many helpful discussions. This work was supported by the U. S. Department of Energy under Contract No. EY-V6-S-02-1569-A002.

The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to extensive applications in quantum information science. In our experiment, we implemented a quantum walk on the line with single neutral atoms by deterministically delocalizing them over the sites of a one-dimensional spin-dependent optical lattice. With the use of site-resolved fluorescence imaging, the final wave function is characterized by local quantum state tomography, and its spatial coherence is demonstrated. Our system allows the observation of the quantum-to-classical transition and paves the way for applications, such as quantum cellular automata.Interference phenomena with microscopic particles are a direct consequence of their quantum-mechanical wave nature [1,2,3,4,5]. The prospect to fully control quantum properties of atomic systems has stimulated ideas to engineer quantum states that would be useful for applications in quantum information processing, for example, and also would elucidate fundamental questions, such as the quantum-to-classical-transition [6]. A prominent example of state engineering by controlled multipath interference is the quantum walk of a particle [7]. Its classical counterpart, the random walk, is relevant in many aspects of our life providing insight into diverse fields: It forms the basis for algorithms [8], describes diffusion processes in physics or biology [8,9], such as Brownian motion, or has been used as a model for stock market prices [10]. Similarly, the quantum walk is expected to have implications for various fields, for instance, as a primitive for universal quantum computing [11], systematic quantum algorithm engineering [12] or for deepening our understanding of the efficient energy transfer in biomolecules for photosynthesis [13].Quantum walks have been proposed to be observable in several physical systems [12,14,15]. Special realizations have been reported in either the populations of nuclear magnetic resonance samples [16,17]; or in optical systems, in either frequency space of a linear optical resonator [18], with beam splitters [19], or in the continuous tunneling of light fields through waveguide lattices [20]. Recently, a three-step quantum walk in the phase space of trapped ions has been observed [21]. However, the coherent walk of an individual quantum particle with controllable internal states as originally proposed by Feynman [22] has so far not been observed. We present the experimental realization of such a single quantum particle walking in a one-dimensional (1D) lattice in position space. This basic example of a walk provides all of the relevant features necessary to understand the fundamental properties and differences of the quantum and classical regimes. For example, the atomic wave func- * Electronic address: karski@uni-bonn.de † Electronic address: widera@uni-bonn.de tion resulting from a quantum walk exhibit...

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We study in detail the mechanisms causing dephasing of hyperfine coherences of cesium atoms confined by a far off-resonant standing wave optical dipole trap [S. Kuhr et al., Phys. Rev. Lett. 91, 213002 (2003)]. Using Ramsey spectroscopy and spin echo techniques, we measure the reversible and irreversible dephasing times of the ground state coherences. We present an analytical model to interpret the experimental data and identify the homogeneous and inhomogeneous dephasing mechanisms. Our scheme to prepare and detect the atomic hyperfine state is applied at the level of a single atom as well as for ensembles of up to 50 atoms.

We report on a stringent test of the non-classicality of the motion of a massive quantum particle, which propagates on a discrete lattice. Measuring temporal correlations of the position of single atoms performing a quantum walk, we observe a 6 σ violation of the Leggett-Garg inequality. Our results rigorously excludes (i.e. falsifies) any explanation of quantum transport based on classical, well-defined trajectories. We use so-called ideal negative measurements an essential requisite for any genuine Leggett-Garg test to acquire information about the atom's position, yet avoiding any direct interaction with it. The interaction-free measurement is based on a novel atom transport system, which allows us to directly probe the absence rather than the presence of atoms at a chosen lattice site. Beyond the fundamental aspect of this test, we demonstrate the application of the Leggett-Garg correlation function as a witness of quantum superposition. We here employ the witness to discriminate different types of walks spanning from merely classical to wholly quantum dynamics. Subject Areas: Quantum Physics, Atomic and Molecular Physics Keywords: Leggett-Garg inequality, ideal negative measurements, quantum walks, quantum witnesses arXiv:1404.3912v2 [quant-ph] 10 Feb 2015 ≈ 0.2 %. Hence, we quantify the relative frequency of non-ideal negative measurements with ζ = 1 %. Along the lines of Ref. 26, the correlation function K measured in our experiment can be decomposed as K = 1 + (1 − ζ)K ideal 23 + ζK corrupt 23 − K 13 , where K ideal 23 and K corrupt 23denote the correlation function Q(t 3 )Q(t 2 ) which has been measured with an ideal negative measurement Q(t 2 ) and with a corrupted one, respectively.

We report on the experimental realization of electric quantum walks, which mimic the effect of an electric field on a charged particle in a lattice. Starting from a textbook implementation of discrete-time quantum walks, we introduce an extra operation in each step to implement the effect of the field. The recorded dynamics of such a quantum particle exhibits features closely related to Bloch oscillations and interband tunneling. In particular, we explore the regime of strong fields, demonstrating contrasting quantum behaviors: quantum resonances versus dynamical localization depending on whether the accumulated Bloch phase is a rational or irrational fraction of 2π.

We demonstrate the realization of a quantum register using a string of single neutral atoms which are trapped in an optical dipole trap. The atoms are selectively and coherently manipulated in a magnetic field gradient using microwave radiation. Our addressing scheme operates with a high spatial resolution and qubit rotations on individual atoms are performed with 99 % contrast. In a final read-out operation we analyze each individual atomic state. Finally, we have measured the coherence time and identified the predominant dephasing mechanism for our register.PACS numbers: 32.80.Pj, 39.25.+k, 42.50.Vk Information coded into the quantum states of physical systems (qubits) can be processed according to the laws of quantum mechanics. It has been shown that the quantum concepts of state superposition and entanglement can lead to a dramatic speed up in solving certain classes of computational problems [1,2]. Over the past decade various quantum computing schemes have been proposed. In a sequential network of quantum logic gates quantum information is processed using discrete one-and two-qubit operations [3]. Another approach is the oneway quantum computer which processes information by performing one-qubit rotations and measurements on an entangled cluster state [4]. All of these schemes rely on the availability of a quantum register, i. e. a well known number of qubits that can be individually addressed and coherently manipulated. There are several physical systems, such as trapped ions [5,6,7], nuclear spins in molecules [8], or magnetic flux qubits [9] that can serve as quantum registers.Neutral atoms exhibit favourable properties for storing and processing quantum information. Their hyperfine ground states are readily prepared in pure quantum states including state superpositions and can be well isolated from their environment. In addition, using laser cooling techniques, countable numbers of neutral atoms can be cooled, captured and transported [10,11]. The coherence properties of laser trapped atoms have been found to be adequate for storing quantum information [12,13]. Moreover, controlled cold collisions [14] or the exchange of microwave [15] or optical [16,17] photons in a resonator offer interesting schemes for mediating coherent atom-atom interaction, essential for the realization of quantum logic operations.In our experiment we use a string of an exactly known number of neutral caesium atoms. The atoms are trapped in the potential wells of a spatially modulated, light induced potential created by a far detuned standing wave dipole trap [10,18]. They can be optically resolved with an imaging system using an intensified CCD camera (ICCD) [19,20]. Our experimental setup is schematically depicted in Fig. 1. Two focussed counter-propagating Nd:YAG laser beams at a wavelength of λ = 1064 nm FIG. 1: Scheme of the experimental setup. Two focussed counter-propagating Nd:YAG laser beams form the dipole trap. We illuminate the trapped atoms by an optical molasses and split the fluorescence light with a beamsplit...

We report on controlled doping of an ultracold Rb gas with single neutral Cs impurity atoms. Elastic two-body collisions lead to a rapid thermalization of the impurity inside the Rb gas, representing the first realization of an ultracold gas doped with a precisely known number of impurity atoms interacting via s-wave collisions. Inelastic interactions are restricted to a single three-body recombination channel in a highly controlled and pure setting, which allows us to determine the Rb-Rb-Cs three-body loss rate with unprecedented precision. Our results pave the way for a coherently interacting hybrid system of individually controllable impurities in a quantum many-body system.