Position-defect-induced reflection, trapping, transmission, and resonance in quantum walks

Z. J. Li*, J. A. Izaac, J. B. Wang

*Corresponding author for this work

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

We investigate the scattering properties of quantum walks by considering single and double position defects on a one-dimensional line. This corresponds to introducing, at designated positions, delta potential defects for continuous-time quantum walks and phase-defect Hadamard coins for discrete time quantum walks. The delta potential defects can be readily considered as potential barriers in discrete position space, which affect the time evolution of the system in a similar way as the quantum wave-packet dynamics in a continuous position space governed by Schrödinger's equation. Although there is no direct analogy of potential barriers in the theoretical formulation of discrete time quantum walks, in this paper we show that the phase defects in the coin space can be utilized to provide similar scattering effects. This study provides means of controlling the scattering properties of quantum walks by introducing designated position-dependent defects.

Original languageEnglish
Article number012314
Pages (from-to)1-9
Number of pages9
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume87
Issue number1
DOIs
Publication statusPublished - 17 Jan 2013
Externally publishedYes

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