Self-to-self transitions in open quantum systems: the origin and solutions

TL;DR

This paper investigates self-to-self transitions in open quantum systems, identifying their origin and proposing a transformation method to resolve inconsistencies in pathway analysis, validated through numerical simulations.

Contribution

It introduces a transformation technique to eliminate counter-intuitive self-to-self transitions in open quantum systems within the Hamiltonian-encoding framework.

Findings

The method aligns pathway amplitudes with Dyson expansion.

Numerical simulations confirm the effectiveness of the transformation.

The approach works with or without control fields.

Abstract

The information of quantum pathways can be extracted in the framework of the Hamiltonian-encoding and Observable-decoding method. For closed quantum systems, only off-diagonal elements of the Hamiltonian in the Hilbert space is required to be encoded to obtain the desired transitions. For open quantum systems, environment-related terms will appear in the diagonal elements of the Hamiltonian in the Liouville space. Therefore, diagonal encodings have to be performed to differentiate different pathways, which will lead to self-to-self transitions and inconsistency of pathway amplitudes with Dyson expansion. In this work, a well-designed transformation is proposed to avoid the counter-intuitive transitions and the inconsistency, with or without control fields. A three-level open quantum system is employed for illustration, and numerical simulations show that the method are consistent with Dyson expansion.