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...

Laser cooling and trapping techniques allow us to control and manipulate neutral atoms. Here we rearrange, with submicrometre precision, the positions and ordering of laser-trapped atoms within strings by manipulating individual atoms with optical tweezers. Strings of equidistant atoms created in this way could serve as a scalable memory for quantum information.

We overcome the diffraction limit in fluorescence imaging of neutral atoms in a sparsely filled one-dimensional optical lattice. At a periodicity of 433 nm, we reliably infer the separation of two atoms down to nearest neighbors. We observe light induced losses of atoms occupying the same lattice site, while for atoms in adjacent lattice sites, no losses due to light induced interactions occur. Our method points towards characterization of correlated quantum states in optical lattice systems with filling factors of up to one atom per lattice site.PACS numbers: 07.05. Pj, 34.50.Rk, 37.10.Jk, 42.30.Va Neutral atoms in optical lattices have been shown to be an ideal system for engineering novel types of strongly correlated quantum states. Quantum correlations between different lattice sites could be induced with BoseEinstein condensates by precisely adjusting the relevant energy scales through controlling the lattice potential [1,2]. Detection of these novel states was initially only indirect by observing the collapse and revival of the global matter wave interference pattern in time of flight measurements. In contrast, quantum state tomography, as well as many theoretical proposals to employ these correlations for quantum information processing, require single site detection [3], a technically challenging goal for site separations in the optical wavelength domain. In a different regime, where potential wells are separated by several micrometers, single atoms could be resolved [4,5]. However, in this regime the relevant energy scales are not well amenable to control via the external potential, therefore the "standard route" for the preparation of correlated quantum states sketched above seems to favor site separations in the optical wavelength regime. Recently, single site detection has been reported in such a system using focused electron beams from an ultra-high vacuum compatible electron gun [6]. This technique is not easily integrated with many current quantum gas experiments, in which, in contrast, optical imaging by fluorescence light is widely established. The latter has seen great success in other fields, e.g., imaging of single molecules [7]. Comparable success with neutral atoms in optical lattices, however, could not be achieved to date.In this work, we demonstrate the detection of atom pair separations down to nearest neighbors in a onedimensional (1D) lattice with optical wavelength periodicity. We overcome the previous restrictions imposed by the diffraction limit [8] with a markedly improved data quality and reduced noise, together with advanced numerical processing of fluorescence images. Such a new degree of precision in detection allows us to directly observe light induced atom losses and to distinguish between onsite and nearest-neighbor contributions. In contrast, detecting such loss processes have so far relied on ensemble averages in optical lattice systems [9], while interacting atoms in a type of atom blockade effect have been investigated in systems where only a single running wave optic...

We control the quantum mechanical motion of neutral atoms in an optical lattice by driving microwave transitions between spin states whose trapping potentials are spatially offset. Control of this offset with nanometer precision allows for adjustment of the coupling strength between different motional states, analogous to an adjustable effective Lamb-Dicke factor. This is used both for efficient one-dimensional sideband cooling of individual atoms to a vibrational ground state population of 97% and to drive coherent Rabi oscillation between arbitrary pairs of vibrational states. We further show that microwaves can drive well resolved transitions between motional states in maximally offset, shallow lattices, and thus in principle allow for coherent control of long-range quantum transport.

We prepare arbitrary patterns of neutral atoms in a one-dimensional (1D) optical lattice with single-site precision using microwave radiation in a magnetic field gradient. We give a detailed account of the current limitations and propose methods to overcome them. Our results have direct relevance for addressing of planes, strings or single atoms in higher dimensional optical lattices for quantum information processing or quantum simulations with standard methods in current experiments. Furthermore, our findings pave the way for arbitrary single qubit control with single site resolution.

Spin-dependent optical potentials allow us to use microwave radiation to manipulate the motional state of trapped neutral atoms Phys. Rev. Lett. 103, 233001). Here, we discuss this method in greater detail, comparing it to the widely-employed Raman sideband coupling method. We provide a simplified model for sideband cooling in a spin-dependent potential, and we discuss it in terms of the generalized Lamb-Dicke parameter. Using a master equation formalism, we present a quantitative analysis of the cooling performance for our experiment, which can be generalized to other experimental settings. We additionally use microwave sideband transitions to engineer motional Fock states and coherent states, and we devise a technique for measuring the population distribution of the prepared states.

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We recently demonstrated that strings of trapped atoms inside a standing wave optical dipole trap can be rearranged using optical tweezers [Y. Miroshnychenko, Nature 442, 151 (2006)]. This technique allows us to actively set the interatomic separations on the scale of the individual trapping potential wells. Here, we use such a distance-control operation to insert two atoms into the same potential well. The detected success rate of this manipulation is 16(-3)(+4)%, in agreement with the predictions of a theoretical model based on our experimental parameters.