Quantum Walk in Position Space with Single Optically Trapped Atoms

Abstract

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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