Realization of a quantum walk in momentum space with a Bose-Einstein condensate

Randomness is the essence of many processes in nature and human society. It can provide important insights into phenomena as diverse as disease transmission, financial markets, and signal processing. Quantum randomness is intrinsically different from classical stochasticity since it is affected by interference and entanglement. This entanglement makes quantum walks promising candidates for the implementation of quantum computational algorithms and as a detector of quantum behavior. We present a discrete-time quantum walk that uses the momentum of ultra-cold rubidium atoms as the walk space and two internal atomic states as the degree of freedom. We demonstrate the principle features of a quantum walk, contrasting them to the behavior of a classical walk. By manipulating either the walk or coin operator we show how the walk dynamics can be biased or reversed. Our walk offers distinct advantages arising from the robustness of its dynamics in momentum space, and extendability to higher dimensions and many-body regimes.