Momentum-Space Quantum Walk of Ultra-Cold Atoms

We report on a discrete-time quantum walk that uses the momentum of ultra-cold rubidium-87 atoms as the walk space and two internal atomic states as the coin degree of freedom. Each step of the walk consists of a coin toss (a microwave pulse) followed by a unitary shift operator (a resonant ratchet pulse). We review the signatures of our quantum walk and carry out a comprehensive study on the effects of various parameters, including the strength of the shift operation, coin parameters, noise, and the initialization of the system on the behavior of the walk. The walk dynamics can be well controlled in our experiment with potential applications in atom interferometry and engineering asymmetric walks.