Non-Hermitian wave packet approximation of Bloch optical equations

TL;DR

This paper presents a non-Hermitian wave packet approach to approximate Bloch optical equations, enabling faster simulations of quantum systems' dynamics with maintained accuracy, including effects like relaxation and dephasing.

Contribution

The authors introduce a novel non-Hermitian wave packet method that simplifies the simulation of quantum optical systems, reducing computational cost while accurately capturing key dynamics.

Findings

The wave packet scheme is significantly faster than full density matrix propagation.

It accurately reproduces transmission, reflection, and absorption spectra.

The method's limits and error scaling are characterized.

Abstract

We introduce a non-Hermitian approximation of Bloch optical equations. This approximation provides a complete description of the excitation, relaxation and decoherence dynamics of ensembles of coupled quantum systems in weak laser fields, taking into account collective effects and dephasing. In the proposed method one propagates the wave function of the system instead of a complete density matrix. Relaxation and dephasing are taken into account via automatically-adjusted time-dependent gain and decay rates. As an application, we compute the numerical wave packet solution of a time-dependent non-Hermitian Schrodinger equation describing the interaction of electromagnetic radiation with a quantum nano-structure and compare the calculated transmission, reflection, and absorption spectra with those obtained from the numerical solution of the Liouville- von-Neumann equation. It is shown that the proposed wave packet scheme is significantly faster than the propagation of the full density matrix while maintaining small error. We provide the key ingredients for easy-to-use implementation of the proposed scheme and identify the limits and error scaling of this approximation.