Local boson-nonlocal boson coupling in a four-level system: Adiabatic, non-adiabatic, and non-Hermitian effects

TL;DR

This paper explores the dynamics of a four-level open quantum system with boson coupling, comparing Lindblad and non-Hermitian models to understand their differences in describing decay and non-Hermitian effects.

Contribution

It derives the full Liouvillian for both Lindblad and non-Hermitian formalisms, highlighting their fundamental differences in modeling dissipative quantum dynamics.

Findings

Lindblad formalism includes decay and repopulation effects.

Non-Hermitian approach captures decay but not repopulation.

Significant distinction in probability conservation between models.

Abstract

We investigates the dynamics of an open quantum system comprising a two-level electronic system coupled to local boson mode and a bosonic bath. The system is described by four distinct states, including the ground and excited electronic states, each with its corresponding zero- and one-boson vibrational levels. The dissipative dynamics arising from interactions with an external environment are modeled using two distinct theoretical frameworks: the standard Lindblad master equation and a non-Hermitian effective Hamiltonian approach. We derive the full Liouvillian superoperator for both formalisms, revealing a crucial distinction: while the Lindblad equation accounts for both state decay and repopulation via quantum jumps, the non-Hermitian formalism only captures the decay, leading to non-conservation of the total system probability.