Fragile aspects of topological transition in lossy and parity-time symmetric quantum walks

TL;DR

This paper explores the fragility of topological transitions in PT-symmetric and lossy quantum walks, revealing their dependence on initial states and nonlinear effects, with implications for experimental observation.

Contribution

It uncovers how initial states and nonlinearities influence topological transitions in PT-symmetric and lossy quantum walks, providing analytical and simulation validation.

Findings

Transition sensitivity to initial state on the Bloch sphere

Presence of a robust topological component in mean displacement

Transition smearing due to nonlinear effects in PT symmetry broken region

Abstract

Quantum walks often provide telling insights about the structure of the system on which they are performed. In PT-symmetric and lossy dimer lattices, the topological properties of the band structure manifest themselves in the quantization of the mean displacement of such a walker. We investigate the fragile aspects of a topological transition in these two dimer models. We find that the transition is sensitive to the initial state of the walker on the Bloch sphere, and the resultant mean displacement has a robust topological component and a quasiclassical component. In PT symmetric dimer lattices, we also show that the transition is smeared by nonlinear effects that become important in the PT-symmetry broken region. By carrying out consistency checks via analytical calculations, tight-binding results, and beam-propagation-method simulations, we show that our predictions are easily testable in today's experimental systems.