The Bloch Equation Generator -- SimuF\'isica

TL;DR

The Bloch Equation Generator is a free, browser-based tool that automates the creation and solution of Bloch equations for multilevel quantum systems, facilitating research in atomic optics.

Contribution

It introduces a user-friendly software that generates and solves Bloch equations for systems with up to 30 levels, streamlining complex quantum dynamics analysis.

Findings

Successfully models two-level, $\Lambda$-type, and 12-level systems.

Demonstrates phenomena like CPT, EIT, and Autler-Townes effect.

Provides C code for numerical solutions in time and frequency domains.

Abstract

The interaction between multilevel quantum systems and coherent radiation underlies several phenomena in modern atomic optics. The formulation and solution of the Bloch equations, which describe the dynamics of such systems, become complex as the number of levels increases. In this work, we present the Bloch Equation Generator, a free, browser-based computational tool developed to automate the generation and numerical solution of Bloch equations for systems with up to 30 levels. Users can configure the level diagram, select allowed transitions, define decay rates, and choose whether or not to apply the rotating wave approximation. The software automatically generates the complete set of equations and provides C source code for numerical solutions in both the time and frequency domains. To illustrate its applicability, we present three examples: (i) a two-level system, (ii) a $\Lambda$-type system with analysis of CPT, EIT, and the Autler-Townes effect, and (iii) a realistic 12-level system based on the Zeeman-resolved $5S_{1/2} \to 5P_{3/2}$ transition of rubidium-87.