Two-dimensional quantum walk under artificial magnetic field

TL;DR

This paper explores how artificial magnetic fields influence the spreading and entanglement in two-dimensional quantum walks, revealing localization, diffusive behavior, and entanglement dynamics depending on flux ratios.

Contribution

It introduces the Peierls substitution into 2D quantum walks to study effects of artificial gauge fields on spreading and entanglement, highlighting new dynamical regimes.

Findings

Faster spreading for small steps at certain flux ratios

Localization around the origin for specific flux ratios

Diffusive spreading for irrational flux ratios

Abstract

We introduce the Peierls substitution to a two-dimensional discrete-time quantum walk on a square lattice to examine the spreading dynamics and the coin-position entanglement in the presence of an artificial gauge field. We use the ratio of the magnetic flux through the unit cell to the flux quantum as a control parameter. For a given flux ratio, we obtain faster spreading for a small number of steps and the walker tends to be highly localized around the origin. Moreover, the spreading of the walk can be suppressed and decreased within a limited time interval for specific rational values of flux ratio. When the flux ratio is an irrational number, even for a large number of steps, the spreading exhibit diffusive behavior rather than the well-known ballistic one as in the classical random walk and there is a significant probability of finding the walker at the origin. We also analyze the coin-position entanglement and show that the asymptotic behavior vanishes when the flux ratio is different from zero and the coin-position entanglement become nearly maximal in a periodic manner in a long time range.