Parrondo's paradox for discrete-time quantum walks in momentum space

TL;DR

This paper explores how sequences of quantum walks in momentum space can exhibit Parrondo's paradox, where combined walks have a positive outcome despite individual walks being negative, with practical implications for Bose-Einstein condensate experiments.

Contribution

It demonstrates the feasibility of observing Parrondo's paradox in momentum-space quantum walks with realistic experimental conditions.

Findings

Parrondo's paradox can be observed in quantum walks in momentum space.

Experimental issues like phase fluctuations and finite momentum width are manageable.

The paradox persists for hundreds of steps under realistic experimental conditions.

Abstract

We investigate the possibility of implementing a sequence of quantum walks whose probability distributions give an overall positive winning probability, while it is negative for the single walks (Parrondo's paradox). In particular, we have in mind an experimental realisation with a Bose-Einstein condensate in which the walker's space is momentum space. Experimental problems in the precise implementation of the coin operations for our discrete-time quantum walks are analysed in detail. We study time-dependent phase fluctuations of the coins as well as perturbations arising from the finite momentum width of the condensate. We confirm the visibility of Parrondo's paradox for experimentally available time scales of up to a few hundred steps of the walk.