Steering random walks with kicked ultracold atoms

TL;DR

This paper demonstrates how to control the momentum distribution of ultracold atoms in a kicked rotor setup by applying a probabilistic sequence of kicks, enabling the realization of Levy walks and power-law distributions.

Contribution

It introduces a method to steer quantum random walks in momentum space using randomized kicking sequences based on probability distributions, including power-law distributions.

Findings

Power-law kicking strengths induce Levy walks in momentum space.

The resulting momentum distribution follows a power-law with the same exponent.

Predictions remain stable under realistic experimental conditions with Bose-Einstein condensates.

Abstract

A kicking sequence of the atom optics kicked rotor at quantum resonance can be interpreted as a quantum random walk in momentum space. We show how to steer such a random walk by applying a random sequence of intensities and phases of the kicking lattice chosen according to a probability distribution. This distribution converts on average into the final momentum distribution of the kicked atoms. In particular, it is shown that a power-law distribution for the kicking strengths results in a L\'evy walk in momentum space and in a power-law with the same exponent in the averaged momentum distribution. Furthermore, we investigate the stability of our predictions in the context of a realistic experiment with Bose-Einstein condensates.