Quantum random walks in a coherent atomic system via eleetromagnetically induced transparency

We propose a scheme to realize the quantum random walk in a coherent five-level atomic system via electromagnetically induced transparency (EIT). From optical Bloch equations describing the dynamics of the electromagnetic field and atomic population and coherence, we show that two circular-polarized components of a probe field display different dispersion properties and hence acquire different phase-shift modifications when passing through atomic cells. We demonstrate that the quantum coherence and interference owing to the EIT effect result in a low absorption of the probe field and hence provide a possibility of realizing a many-step phase-shift quantum random walk. The scheme may be used to experimentally highlight the characteristics of quantum random walk and lead to a promising application for quantum computation.