Robustness of Aharonov-Bohm cages in quantum walks

TL;DR

This paper investigates the stability of Aharonov-Bohm cages in quantum walks under various perturbations, revealing how different types of disorder and interactions affect their robustness and the resulting quantum dynamics.

Contribution

It provides a comprehensive analysis of how static and dynamic disorders, measurements, and interactions influence the existence and stability of AB cages in quantum walks.

Findings

Quenched disorder causes exponential wavefunction decay similar to Anderson localization.

Dynamical disorder and measurements turn quantum walks into diffusive classical walks.

Interactions can break cages but also restore ballistic motion in bound states.

Abstract

It was recently shown that Aharonov-Bohm (AB) cages exist for quantum walks (QW) on certain tilings -- such as the diamond chain or the dice (or $\mathcal{T}_3$) lattice -- for a proper choice of coins. In this article, we probe the robustness of these AB cages to various perturbations. When the cages are destroyed, we analyze the leakage mechanism and characterize the resulting dynamics. Quenched disorder typically breaks the cages and leads to an exponential decay of the wavefunction similar to Anderson localization. Dynamical disorder or repeated measurements destroy phase coherence and turn the QW into a classical random walk with diffusive behavior. Combining static and dynamical disorder in a specific way leads to subdiffusion with an anomalous exponent controlled by the quenched disorder distribution. Introducing interaction to a second walker can also break the cages and restore a ballistic motion for a "molecular" bound-state.