Quantum Walk in Momentum Space with a Bose-Einstein Condensate

TL;DR

This paper demonstrates a flexible discrete-time quantum walk using ultracold rubidium atoms' momentum and internal states, enabling exploration of quantum algorithms, topological phases, and walk dynamics control.

Contribution

It introduces a novel momentum-space quantum walk platform with tunable parameters, allowing for advanced studies of quantum phenomena and control mechanisms.

Findings

Distinct quantum walk features contrasted with classical walks

Walk dynamics can be steered or reversed through operator manipulation

The scheme supports applications in quantum search and topological phase observation

Abstract

We present a discrete-time, one-dimensional quantum walk based on the entanglement between the momentum of ultracold rubidium atoms (the walk space) and two internal atomic states (the "coin" degree of freedom). Our scheme is highly flexible and can provide a platform for a wide range of applications such as quantum search algorithms, the observation of topological phases, and the realization of walks with higher dimensionality. Along with the investigation of the quantum-to-classical transition, we demonstrate the distinctive features of a quantum walk and contrast them to those of its classical counterpart. Also, by manipulating either the walk or coin operator, we show how the walk dynamics can be steered or even reversed.