Quantum Walks on a Random Environment

TL;DR

This paper investigates how disorder in a one-dimensional quantum environment affects quantum walks, revealing phenomena like Anderson localization and a quantum-to-classical transition influenced by static or dynamic disorder.

Contribution

It provides a detailed analysis of localization and decoherence effects in quantum walks within disordered media, including a specific study of a dimer lattice model.

Findings

Static disorder causes Anderson localization, hindering quantum walk propagation.

Dynamic disorder induces decoherence, leading to a quantum to classical crossover.

The crossover time scales inversely with the square of disorder strength.

Abstract

Quantum walks are considered in a one-dimensional random medium characterized by static or dynamic disorder. Quantum interference for static disorder can lead to Anderson localization which completely hinders the quantum walk and it is contrasted with the decoherence effect of dynamic disorder having strength W, where a quantum to classical crossover at time $t_{c}\propto W^{-2}$ transforms the quantum walk into an ordinary random walk with diffusive spreading. We demonstrate these localization and decoherence phenomena in quantum carpets of the observed time evolution and examine in detail a dimer lattice which corresponds to a single qubit subject to randomness.