Dirac monopole magnets in non-Hermitian systems

TL;DR

This paper demonstrates how non-Hermitian perturbations transform point-like Dirac monopoles into extended distributions with unique topological charge configurations, confirmed through geometric phase measurements and proposed soliton-based experiments.

Contribution

It introduces a theoretical framework for topological transformations of Dirac monopoles in non-Hermitian systems and proposes experimental schemes for their observation.

Findings

Non-Hermitian perturbations induce extended monopole charge distributions.

A quantitative relation between energy differences and geometric phases is established.

Proposed soliton dynamics scheme enables direct measurement of topological signatures.

Abstract

We theoretically establish that non-Hermitian perturbations induce a topological transformation of point-like Dirac monopoles into extended monopole distributions, characterized by distinct charge configurations emergent from three distinct Berry connection forms. Using piecewise adiabatic evolution, we confirm the validity of these configurations through observations of complex geometric phases. Most critically, we find a quantitative relation $\Delta \phi_d = \Delta \phi_g$, which quantifies how cumulative minute energy differences (\(\Delta \phi_d\)) manifest as geometric phase shifts (\(\Delta \phi_g\)) uniquely in non-Hermitian systems. We further propose a scheme leveraging soliton dynamics in dissipative two-component Bose-Einstein condensates, enabling direct measurement of these topological signatures. These results establish a milestone for understanding Dirac monopole charge distributions and measuring complex geometric phases in non-Hermitian systems, with far-reaching implications for topological quantum computing and non-Hermitian photonics.