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Each step in a quantum random walk is typically understood to have two basiccomponents; a `coin-toss' which produces a random superposition of two states,and a displacement which moves each component of the superposition by differentamounts. Here we suggest the realization of a walk in momentum space with aspinor Bose-Einstein condensate subject to a quantum ratchet realized with apulsed, off-resonant optical lattice. By an appropriate choice of the latticedetuning, we show how the atomic momentum can be entangled with the internalspin states of the atoms. For the coin-toss, we propose to use a microwavepulse to mix these internal states. We present experimental results showing anoptimized quantum ratchet, and through a series of simulations, demonstrate howour proposal gives extraordinary control of the quantum walk. This should allowfor the investigation of possible biases, and classical-to-quantum dynamics inthe presence of natural and engineered noise.

A quantum random walk of a Bose-Einstein condensate in momentum space