https://github.com/terrygeng/rate-equation

Rate equation model for simulating the atomic population evolution under external laser fields, implemented in python.
https://github.com/terrygeng/rate-equation

atomic physics python quantum simulation

Last synced: about 2 months ago
JSON representation

Rate equation model for simulating the atomic population evolution under external laser fields, implemented in python.

• Host: GitHub
• URL: https://github.com/terrygeng/rate-equation
• Owner: TerryGeng
• Created: 2023-07-16T20:43:50.000Z (over 1 year ago)
• Default Branch: master
• Last Pushed: 2023-07-18T14:33:43.000Z (over 1 year ago)
• Last Synced: 2024-11-02T00:27:34.286Z (3 months ago)
• Topics: atomic, physics, python, quantum, simulation
• Language: Jupyter Notebook
• Homepage:
• Size: 296 KB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

Awesome Lists containing this project

README

        
# `rate_equation`: Rate equation model implemented in python

![Figure: Ground state population vs. laser detuning, under given magnetic

field](./screenshot.png)

_Figure: Ground state population vs. laser detuning, under given magnetic

field_

This package implements rate equation model in python. Rate equation model is

commonly used to simulate the evolution of atomic populations in different

ground states, under given external radiation (e.g. lasers) and magnetic

fields.

Rate equation model assumes the time atoms spend in excited states is

negligible. That is, once excited, they immediately decay back to ground

states. Therefore, all coherence terms are discarded, leaving a set of

equations describing the population transfer from one ground state to others.

This assumption is equivalent to assuming the timescale of interest is much

larger than the decay rate of studied energy levels, while the laser intensity

is way below saturation intensity.

A very good reference for this approach can be found at:

[F. Atoneche and A. Kastberg, Simplified Approach for Quantitative Calculations

of Optical Pumping, Eur. J. Phys. 38, 045703 (2017)](

https://doi.org/10.1088/1361-6404/aa6e6f).

## Features

This package

- Takes hyperfine structure and transition strength as input, normalizes

  transition strength properly and produces the rate equation matrix $G$.

- Supports configurations that include multiple radiation fields with different

  frequencies and polarizations.

- Provides flexible ways of defining detuning terms (Zeeman shift and Doppler

  shift).

- Each part is [individually tested](./test/) against published results to ensure

  correctness.

## Limitations

- This package is designed to work with hyperfine states $I, J, F, m_F$ as the

  eigenstates of the unperturbed Hamiltonian. However, under strong magnetic

  field, hyperfine states are no longer eigenstates and the system is better

  described by $I, J, m_J, m_I$ (Paschen-Back effect). The only way to

  correctly deal with this is to diagonalize the Hamiltonian under all magnetic

  field configurations and use the acquired eigenstates to perform calculation.

  This package is not well geared to achieve this.

## Usage And Examples

In the [example.ipynb](./example.ipynb) IPython notebook, I reproduced all relevant

figures in [Atoneche (2017)](https://doi.org/10.1088/1361-6404/aa6e6f).