Non-Hermitian wave-packet dynamics and its realization within a non-Hermitian chiral cavity

TL;DR

This paper develops a semiclassical wave-packet dynamics framework for non-Hermitian topological systems using complex Berry phases, validated through a non-Hermitian Haldane model and proposed optical cavity realization.

Contribution

It introduces a novel semiclassical EOM for non-Hermitian systems based on complex Berry phases and demonstrates its validity with a specific non-Hermitian Haldane model.

Findings

Complex Berry curvature affects wave-packet velocity and force.

Real and imaginary parts of complex chirality influence edge state behavior.

Numerical simulations confirm analytical wave-packet dynamics.

Abstract

Topological wave-packet dynamics provide a powerful framework for studying quantum transport in topological materials. However, extending this approach to non-Hermitian quantum systems presents several important challenges, primarily due to ambiguities in defining the Berry phase and the non-unitary evolution of the wave-packets when $\mathcal{P}\mathcal{T}$ symmetry is broken. In this work, we adopt the complex Berry phase definition using the bi-orthogonal formalism and derive the semiclassical equations of motion (EOM) for a wave-packet in a non-Hermitian topological system. Interestingly, we find that the complex Berry curvature introduces both an anomalous velocity and an anomalous force into the semiclassical EOM. To validate the derived EOM, we design a non-Hermitian Haldane model featuring non-reciprocal next-nearest-neighbor (NNN) hopping, where the imbalance in the NNN hopping amplitudes gives rise to an emergent `complex chirality'. We reveal that the real and imaginary components of the complex chirality dictate the signs of both the real and imaginary parts of the complex Berry curvature, as well as the direction and dissipation rate of the edge states. Our analytical findings are confirmed by direct numerical simulations of the wave-packet dynamics. Finally, we suggest a potential experimental realization of this complex Haldane model using a non-Hermitian optical chiral cavity, providing a promising platform for testing our theoretical predictions.