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.Comment: 7 pages, 4 figure