A comparative study on different non-Hermitian approaches for modeling open quantum systems

TL;DR

This paper compares two non-Hermitian methods for modeling open quantum systems, finding that the corrected NHEH approach outperforms NHQM in accurately describing system dynamics.

Contribution

It provides a comprehensive comparison of NHQM and corrected NHEH methods using the Jaynes-Cummings model, highlighting the superior accuracy of the corrected NHEH approach.

Findings

Corrected NHEH aligns well with Lindblad master equation results.

NHQM fails to accurately describe the system's time evolution.

Corrected NHEH shows excellent agreement with simulations.

Abstract

In this paper, we test and compare the performance of two different theoretical methods that use anti-Hermitian terms for modeling open quantum systems. It is, the non-Hermitian quantum mechanics method (NHQM) and the recent methodology known as corrected non-Hermitian effective Hamiltonian (corrected NHEH) approach. In particular, we provide a comprehensive analysis of the performance of these two theoretical approaches by describing the dynamics of the pumped-dissipative Jaynes--Cummings model. Our results demonstrate that whereas the NHQM method fails for describing correctly the time evolution of the density matrix elements as well as the quantum fidelity measure. The corrected NHEH approach shows an excellent agreement with simulations based on the Lindblad master equation formalism.