The role of the geometric phases in adiabatic populations tracking for non-hermitian hamiltonians

TL;DR

This paper investigates how geometric phases can resolve inconsistencies in defining populations in non-Hermitian quantum systems, preventing false population inversions and adiabaticity artifacts.

Contribution

It introduces a new approach incorporating geometric phases to accurately define populations in non-Hermitian Hamiltonians, addressing previous inconsistencies.

Findings

Geometric phases prevent false population inversions.

The new definition removes artifacts in adiabatic evolution.

An example demonstrates the effectiveness of the approach.

Abstract

We show that the definition of instantaneous eigenstate populations for a dynamical non-self-adjoint system is not obvious. The naive direct extension of the definition used for the self-adjoint case leads to inconsistencies; the resulting artifacts can induce a false inversion of population or a false adiabaticity. We show that the inconsistency can be avoided by introducing geometric phases in another possible definition of populations. An example is given which demonstrates both the anomalous effects and their removal by our approach.