Quantum Walk in Position Space with Single Optically Trapped Atoms

Abstract

Strolling Out on a Quantum Walk In a random walk, a walker moves one step to the left or one step to the right depending on the outcome of a coin toss. The distribution between possible locations is well known and forms the basis for algorithms in information processing, describing diffusion processes in physics or biology, and has even been used as a model for stock market prices. Karski et al. (p. 174 ) use a single caesium atom trapped in a one-dimensional optical lattice to implement the quantum counterpart—a quantum walk. The coherence of a quantum system results in a departure from the classical picture, producing a distribution that is quite different that depends on the internal state of the atom. The results may have implications for search algorithms and quantum information processing protocols.