Single-point position and transition defects in continuous time quantum walks

TL;DR

This paper analyzes how single-point position and transition defects affect continuous time quantum walks, revealing bound states, interference effects, and tunable spreading for potential quantum control applications.

Contribution

It provides analytical solutions for CTQW with defects, showing how defect parameters influence bound states and wavefunction localization, advancing understanding of quantum walk dynamics.

Findings

Number of bound states depends on defect parameters

Localized probability peaks relate to bound states

Interference observed between bound states in transition defects

Abstract

We present a detailed analysis of continuous time quantum walks (CTQW) with both position and transition defects defined at a single point in the line. Analytical solutions of both traveling waves or bound states are obtained, which provide valuable insight into the dynamics of CTQW. The number of bound states is found to be critically dependent on the defect parameters, and the localized probability peaks can be readily obtained by projecting the CTQW wavefunction on to these bound states. The interference between two bound states are also observed in the case of a transition defect. The spreading of CTQW probability over the line can be finely tuned by varying the position and transition defect parameters, offering the possibility of precision quantum control of the system.