Tunable Aharonov-Bohm-like cages for quantum walks

TL;DR

This paper demonstrates tunable Aharonov-Bohm-like cages in quantum walks on specific lattices, showing how interference effects can be controlled to confine particles and engineer cage properties.

Contribution

It introduces a method to realize and tune Aharonov-Bohm-like cages in discrete-time quantum walks using specific coin operators and lattice structures.

Findings

Cages occur for quantum walks on diamond and $ ext{T}_3$ lattices with specific coins.

The Floquet-Hofstadter butterfly exhibits pinching near a tunable critical flux.

Spatial extension of cages can be engineered.

Abstract

Aharonov-Bohm cages correspond to an extreme confinement for two-dimensional tight-binding electrons in a transverse magnetic field. When the dimensionless magnetic flux per plaquette $f$ equals a critical value $f_c=1/2$, a destructive interference forbids the particle to diffuse away from a small cluster. The corresponding energy levels pinch into a set of highly degenerate discrete levels as $f\to f_c$. We show here that cages also occur for discrete-time quantum walks on either the diamond chain or the $\mathcal{T}_3$ tiling but require specific coin operators. The corresponding quasi-energies versus $f$ result in a Floquet-Hofstadter butterfly displaying pinching near a critical flux $f_c$ and that may be tuned away from 1/2. The spatial extension of the associated cages can also be engineered.