Persistence of topological phases in non-Hermitian quantum walks

Vikash Mittal,Aswathy Raj,Sandeep K Goyal,Sanjib Dey

doi:10.1038/s41598-021-89441-8

Abstract

Discrete-time quantum walks are known to exhibit exotic topological states and phases. Physical realization of quantum walks in a lossy environment may destroy these phases. We investigate the behaviour of topological states in quantum walks in the presence of a lossy environment. The environmental effects in the quantum walk dynamics are addressed using the non-Hermitian Hamiltonian approach. We show that the topological phases of the quantum walks are robust against moderate losses. The topological order in one-dimensional split-step quantum walk persists as long as the Hamiltonian respects exact {{mathcal {P}}}{{mathcal {T}}}-symmetry. Although the topological nature persists in two-dimensional quantum walks as well, the {{mathcal {P}}}{{mathcal {T}}}-symmetry has no role to play there. Furthermore, we observe topological phase transition in two-dimensional quantum walks that is induced by losses in the system.

Highlights

We introduce the topics which are relevant to understand our results
We find a strong correspondence between the spontaneous exact PT -symmetry breaking and the loss of topological order in 1D SSQW, i.e, the system retains its topological order for any value of γ, as long as the system respects the exact PT -symmetry
Due to the absence of PT -symmetry in 2D DTQW, we do not observe such correspondence in these systems

Summary

Introduction

We introduce the topics which are relevant to understand our results. One can extend 1D SSQW to a non-unitary quantum walk by introducing a scaling operator G43, with tunable parameters in the dynamics.

Results

Conclusion