# Pairinteraction - A Rydberg Interaction Calculator
[![PyPI Package][pypi-svg]][pypi-link]
[![arXiv:1612.08053][arXiv-svg]][arXiv-link]
[![License: LGPL v3][license-lgpl-svg]][license-lgpl-link]
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[![Python Coverage - pytest][coverage-python-pytest-svg]][coverage-python-pytest-link]
[![Documentation][docs-svg]][docs-link]
[pypi-svg]: https://img.shields.io/pypi/v/pairinteraction.svg?style=flat
[pypi-link]: https://pypi.org/project/pairinteraction/
[arXiv-svg]: https://img.shields.io/badge/arXiv-1612.08053-b31b1b.svg?style=flat
[arXiv-link]: https://arxiv.org/abs/1612.08053
[license-lgpl-svg]: https://img.shields.io/badge/License-LGPL_v3-blue.svg?style=flat
[license-lgpl-link]: https://www.gnu.org/licenses/lgpl-3.0.html
[gh-workflow-svg]: https://github.com/pairinteraction/pairinteraction/actions/workflows/python-wheel.yml/badge.svg
[gh-workflow-link]: https://github.com/pairinteraction/pairinteraction/actions/workflows/python-wheel.yml
[sonarcloud-svg]: https://sonarcloud.io/api/project_badges/measure?project=pairinteraction_pairinteraction&metric=alert_status
[sonarcloud-link]: https://sonarcloud.io/dashboard?id=pairinteraction_pairinteraction
[coverage-cpp-ctest-svg]: https://img.shields.io/badge/C%2B%2B_coverage-ctest-blue.svg?style=flat
[coverage-cpp-ctest-link]: https://www.pairinteraction.org/pairinteraction/coverage/cpp-ctest/html/index.html
[coverage-cpp-pytest-svg]: https://img.shields.io/badge/C%2B%2B_coverage-pytest-blue.svg?style=flat
[coverage-cpp-pytest-link]: https://www.pairinteraction.org/pairinteraction/coverage/cpp-pytest/html/index.html
[coverage-python-pytest-svg]: https://img.shields.io/badge/Python_coverage-pytest-blue.svg?style=flat
[coverage-python-pytest-link]: https://www.pairinteraction.org/pairinteraction/coverage/python-pytest/html/index.html
[docs-svg]: https://img.shields.io/badge/Documentation-pairinteraction.org-blue.svg?style=flat
[docs-link]: https://www.pairinteraction.org/pairinteraction/sphinx/html/
**Note: This is a completely new version of the pairinteraction software that is not backward compatible to versions below v1.0.**
The *pairinteraction* software calculates properties of Rydberg atoms. The software consists of a Python library and a graphical user interface for obtaining single-atom properties and calculating pair potentials, making use of a high-performance C++ backend. For a more detailed description of the software that is written to be accessible also to non-specialists, see the [About page][about-link] of the project. The software can be installed via pip (requires Python >= 3.9, for tips see our [extended installation instructions][installation-link]):
```bash
pip install pairinteraction
```
You can use the pairinteraction software as a Python library, see our [quick start guide to get started in 5 minutes][tutorial-link], or you can launch its graphical user interface from the command line:
```bash
pairinteraction gui
```
[about-link]: https://www.pairinteraction.org/pairinteraction/sphinx/html/about.html
[installation-link]: https://www.pairinteraction.org/pairinteraction/sphinx/html/installation/installation.html
[tutorial-link]: https://www.pairinteraction.org/pairinteraction/sphinx/html/tutorials/examples_python/quick_start.html
## Highlights
* For calculating Rydberg pair potentials, the software uses a similar approach as the [old version of pairinteraction](https://github.com/pairinteraction/pairinteraction/tree/v0.9.10), the [Alkali.ne Rydberg Calculator](https://github.com/nikolasibalic/ARC-Alkali-Rydberg-Calculator), and the [rydcalc library](https://github.com/ThompsonLabPrinceton/rydcalc). We optimized the construction and diagonalization of Hamiltonians, typically achieving a **speedup of 5-20x** compared to other implementations.
![benchmarking results][benchmark-results-link]
*Figure: Benchmarking the construction and diagonalization of a Hamiltonian of a pair of Rb 60S atoms for 100 different internuclear distances on an AMD Ryzen 7 5700G CPU using Windows 11. The Hilbert space comprises pair states that differ at most by 4 in n, l and 25GHz in energy. When supported, symmetries where used to reduce the Hilbert space size. See the [benchmarking tool][benchmark-tool].*
* The software uses single-channel quantum defect theory (SQDT) and also **multi-channel quantum defect theory (MQDT)** for the accurate description of atoms.
The construction of Hamiltonians is accelerated by using pre-calculated matrix elements, which are stored in database tables. These tables are automatically downloaded from GitHub \[[1],[2]\] and cached locally when needed.
[1]: https://github.com/pairinteraction/database-sqdt/releases
[2]: https://github.com/pairinteraction/database-mqdt/releases
[benchmark-tool]: https://github.com/pairinteraction/pairinteraction/tree/master/tools/benchmarking
* **Electric and magnetic fields in arbitrary directions** can be included in the calculations. Diamagnetism is supported.
[benchmark-results-link]: https://github.com/pairinteraction/pairinteraction/raw/master/data/benchmarking_results/0845d67063_1.4.2-cp313-win_amd-ryzen-7-5700g-with-radeon-graphics_reps4.png
## How to Cite
If you use pairinteraction in your research, please cite our tutorial paper:
> Sebastian Weber, Christoph Tresp, Henri Menke, Alban Urvoy, Ofer Firstenberg, Hans Peter Büchler, Sebastian Hofferberth, *Tutorial: Calculation of Rydberg interaction potentials*, [J. Phys. B: At. Mol. Opt. Phys. 50, 133001 (2017)][journal-link], [arXiv:1612.08053][arXiv-link]
**Quantum Defects**
<a id="quantum-defects"></a>
Pairinteraction relies on quantum defects provided by the community. Consider citing relevant publications for your atomic species alongside pairinteraction.
<p><details>
<summary><b>Click to expand for quantum defect references</b></summary>
| Element | Model | Identifier | References |
|---------|-----------------------|----------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------|
| H | SQDT | `H` | Schrödinger equation for hydrogen |
| Li | SQDT | `Li` | [10.1017/CBO9780511524530] (1994)<br>[10.1103/PhysRevA.34.2889] (1986) |
| Na | SQDT | `Na` | [10.1088/0953-4075/30/10/009] (1997)<br>[10.1070/QE1995v025n09ABEH000501] (1995)<br>[10.1103/PhysRevA.45.4720] (1992) |
| K | SQDT | `K` | [10.1088/0031-8949/27/4/012] (1983)<br>[10.1016/0030-4018(81)90225-X] (1981) |
| Rb | SQDT | `Rb` | [10.1103/PhysRevA.83.052515] (2011)<br>[10.1103/PhysRevA.74.054502] (2006)<br>[10.1103/PhysRevA.74.062712] (2006)<br>[10.1103/PhysRevA.67.052502] (2003) |
| Cs | SQDT | `Cs` | [10.1103/PhysRevA.93.013424] (2016)<br>[10.1103/PhysRevA.35.4650] (1987)<br>[10.1103/PhysRevA.26.2733] (1982) |
| Sr88 | SQDT, singlet sector | `Sr88_singlet` | [10.1103/PhysRevA.108.022815] (2023)<br>[10.17169/refubium-34581] (2022) |
| Sr88 | SQDT, triplet sector | `Sr88_triplet` | [10.1016/j.cpc.2020.107814] (2021) |
| Sr87 | MQDT | `Sr87_mqdt` | [10.1088/1361-6455/ab4c22] (2019) |
| Sr88 | MQDT | `Sr88_mqdt` | [10.1088/1361-6455/ab4c22] (2019) |
| Yb171 | MQDT | `Yb171_mqdt` | [10.48550/arXiv.2406.01482] (2024) |
| Yb173 | MQDT | `Yb173_mqdt` | MQDT model formulated by us |
| Yb174 | MQDT | `Yb174_mqdt` | [10.48550/arXiv.2406.01482] (2024) |
The identifier can be used to specify an atomic species in the pairinteraction software.
</details></p>
[journal-link]: https://doi.org/10.1088/1361-6455/aa743a
[10.1103/PhysRevA.34.2889]: https://doi.org/10.1103/PhysRevA.34.2889
[10.1017/CBO9780511524530]: https://doi.org/10.1017/CBO9780511524530
[10.1103/PhysRevA.45.4720]: https://doi.org/10.1103/PhysRevA.45.4720
[10.1070/QE1995v025n09ABEH000501]: https://doi.org/10.1070/QE1995v025n09ABEH000501
[10.1088/0953-4075/30/10/009]: https://doi.org/10.1088/0953-4075/30/10/009
[10.1088/0031-8949/27/4/012]: https://doi.org/10.1088/0031-8949/27/4/012
[10.1016/0030-4018(81)90225-X]: https://doi.org/10.1016/0030-4018(81)90225-X
[10.1103/PhysRevA.83.052515]: https://doi.org/10.1103/PhysRevA.83.052515
[10.1103/PhysRevA.67.052502]: https://doi.org/10.1103/PhysRevA.67.052502
[10.1103/PhysRevA.74.054502]: https://doi.org/10.1103/PhysRevA.74.054502
[10.1103/PhysRevA.74.062712]: https://doi.org/10.1103/PhysRevA.74.062712
[10.1103/PhysRevA.93.013424]: https://doi.org/10.1103/PhysRevA.93.013424
[10.1103/PhysRevA.26.2733]: https://doi.org/10.1103/PhysRevA.26.2733
[10.1103/PhysRevA.35.4650]: https://doi.org/10.1103/PhysRevA.35.4650
[10.1103/PhysRevA.108.022815]: https://doi.org/10.1103/PhysRevA.108.022815
[10.17169/refubium-34581]: https://doi.org/10.17169/refubium-34581
[10.1016/j.cpc.2020.107814]: https://doi.org/10.1016/j.cpc.2020.107814
[10.1088/1361-6455/ab4c22]: https://doi.org/10.1088/1361-6455/ab4c22
[10.48550/arXiv.2406.01482]: https://doi.org/10.48550/arXiv.2406.01482
## Documentation
**User Guide**
- [Installation] - Whether you prefer an installation via pip or compiling from source, we've got all the information you need.
- [Tutorials] - Covering both the graphical user interface and the Python library,
these tutorials enable you to leverage pairinteraction for your projects.
- [API Reference] - Documentation of classes and functions of pairinteraction's Python library.
- [Publications] - Find out more about the theory behind pairinteraction and how to cite it and the quantum defects you use.
**Contributor Guide**
- [Getting Started as a Contributor] - Discover the many ways you can help improve pairinteraction, from contributing to the repository to providing quantum defects.
- [Overview About pairinteraction's Architecture] - Find out how pairinteraction is structured.
- [Style Guide] - Learn about the coding style used in pairinteraction.
- [Database Format] - Explore the database for storing atomic states and matrix elements.
**Utility Tools [External Links]**
- [MQDT.jl] - Learn how to calculate states and matrix elements using multi-channel quantum defect theory with our tool written in Julia.
- [ryd-numerov] - Learn how to calculate states and matrix elements using single quantum defect theory with our tool written in Python.
[Installation]: https://www.pairinteraction.org/pairinteraction/sphinx/html/installation/installation.html
[Tutorials]: https://www.pairinteraction.org/pairinteraction/sphinx/html/tutorials/tutorials.html
[API Reference]: https://www.pairinteraction.org/pairinteraction/sphinx/html/api_reference.html
[Publications]: https://www.pairinteraction.org/pairinteraction/sphinx/html/publications/publications.html
[Getting Started as a Contributor]: https://www.pairinteraction.org/pairinteraction/sphinx/html/contribute/getting_started.html
[Overview About pairinteraction's Architecture]: https://www.pairinteraction.org/pairinteraction/sphinx/html/contribute/architecture.html
[Style Guide]: https://www.pairinteraction.org/pairinteraction/sphinx/html/contribute/style_guide.html
[Database Format]: https://www.pairinteraction.org/pairinteraction/sphinx/html/contribute/database.html
[MQDT.jl]: https://github.com/pairinteraction/MQDT.jl
[ryd-numerov]: https://github.com/pairinteraction/ryd-numerov/
## Contributors
The software is maintained by:
* [Sebastian Weber]
* [Johannes Mögerle]
In addition, the following people contributed significantly to the current and/or previous versions of the software:
* [Henri Menke]
* [Frederic Hummel] - Julia package for multi-channel quantum defect theory, matrix elements
* [Eduard J. Braun] - Perturbative calculations, installation instructions for Windows
* [Johannes Block] - Calculation of Rydberg pair potentials near surfaces *(not yet in new version)*
* [Nicolas Zuber] - Tutorial on Rydberg-ion interaction
* [Simon Hollerith] - Documentation of the graphical user interface *(not yet in new version)*
We warmly welcome new contributions! Please see our [contributor guide][contributor-link] for more information!
The development of the pairinteraction software has been supported by the [Institute for Theoretical Physics III] of the University of Stuttgart, the Federal Ministry of Education and Research under the Grants [QRydDemo] and [MUNIQC-Atoms], and the company [Atom Computing]. The development of the original version of the software started at the [5th Institute of Physics] of the University of Stuttgart.
[![University of Stuttgart][stuttgart-jpg]][stuttgart-link]
[![Federal Ministry of Education and Research][bmbf-jpg]][bmbf-link]
[![Atom Computing][atom-jpg]][atom-link]
[stuttgart-jpg]: https://github.com/pairinteraction/pairinteraction/raw/master/docs/_static/logos/uni_stuttgart.svg
[stuttgart-link]: https://www.uni-stuttgart.de/en/
[bmbf-jpg]: https://github.com/pairinteraction/pairinteraction/raw/master/docs/_static/logos/bmbf.svg
[bmbf-link]: https://www.bmbf.de/EN/
[atom-jpg]: https://github.com/pairinteraction/pairinteraction/raw/master/docs/_static/logos/atom_computing.svg
[atom-link]: https://atom-computing.com/
[Institute for Theoretical Physics III]: https://www.itp3.uni-stuttgart.de/
[QRydDemo]: https://www.quantentechnologien.de/forschung/foerderung/quantenprozessoren-und-technologien-fuer-quantencomputer/qryddemo.html
[MUNIQC-Atoms]: https://www.quantentechnologien.de/forschung/foerderung/quantencomputer-demonstrationsaufbauten/muniqc-atoms.html
[Atom Computing]: https://atom-computing.com/
[5th Institute of Physics]: https://www.pi5.uni-stuttgart.de/
[Sebastian Weber]: https://github.com/seweber
[Johannes Mögerle]: https://github.com/johannes-moegerle
[Henri Menke]: https://github.com/hmenke
[Frederic Hummel]: https://github.com/frederic-atom
[Eduard J. Braun]: https://github.com/EduardJBraun
[Nicolas Zuber]: https://github.com/tripiti
[Johannes Block]: https://github.com/johblock
[Simon Hollerith]: https://github.com/SimonHollerith
[contributor-link]: https://www.pairinteraction.org/pairinteraction/sphinx/html/contribute/getting_started.html
## License
The pairinteraction software is licensed under [LGPL v3][license-lgpl-link]. For more information, see [LICENSE.txt](https://github.com/pairinteraction/pairinteraction/blob/master/LICENSE.txt).
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"description": "# Pairinteraction - A Rydberg Interaction Calculator\n\n[![PyPI Package][pypi-svg]][pypi-link]\n[![arXiv:1612.08053][arXiv-svg]][arXiv-link]\n[![License: LGPL v3][license-lgpl-svg]][license-lgpl-link]\n[![CI Workflow][gh-workflow-svg]][gh-workflow-link]\n[![Quality Gate Status][sonarcloud-svg]][sonarcloud-link]\n[![C++ Coverage - ctest][coverage-cpp-ctest-svg]][coverage-cpp-ctest-link]\n[![C++ Coverage - pytest][coverage-cpp-pytest-svg]][coverage-cpp-pytest-link]\n[![Python Coverage - pytest][coverage-python-pytest-svg]][coverage-python-pytest-link]\n[![Documentation][docs-svg]][docs-link]\n\n[pypi-svg]: https://img.shields.io/pypi/v/pairinteraction.svg?style=flat\n[pypi-link]: https://pypi.org/project/pairinteraction/\n[arXiv-svg]: https://img.shields.io/badge/arXiv-1612.08053-b31b1b.svg?style=flat\n[arXiv-link]: https://arxiv.org/abs/1612.08053\n[license-lgpl-svg]: https://img.shields.io/badge/License-LGPL_v3-blue.svg?style=flat\n[license-lgpl-link]: https://www.gnu.org/licenses/lgpl-3.0.html\n[gh-workflow-svg]: https://github.com/pairinteraction/pairinteraction/actions/workflows/python-wheel.yml/badge.svg\n[gh-workflow-link]: https://github.com/pairinteraction/pairinteraction/actions/workflows/python-wheel.yml\n[sonarcloud-svg]: https://sonarcloud.io/api/project_badges/measure?project=pairinteraction_pairinteraction&metric=alert_status\n[sonarcloud-link]: https://sonarcloud.io/dashboard?id=pairinteraction_pairinteraction\n[coverage-cpp-ctest-svg]: https://img.shields.io/badge/C%2B%2B_coverage-ctest-blue.svg?style=flat\n[coverage-cpp-ctest-link]: https://www.pairinteraction.org/pairinteraction/coverage/cpp-ctest/html/index.html\n[coverage-cpp-pytest-svg]: https://img.shields.io/badge/C%2B%2B_coverage-pytest-blue.svg?style=flat\n[coverage-cpp-pytest-link]: https://www.pairinteraction.org/pairinteraction/coverage/cpp-pytest/html/index.html\n[coverage-python-pytest-svg]: https://img.shields.io/badge/Python_coverage-pytest-blue.svg?style=flat\n[coverage-python-pytest-link]: https://www.pairinteraction.org/pairinteraction/coverage/python-pytest/html/index.html\n[docs-svg]: https://img.shields.io/badge/Documentation-pairinteraction.org-blue.svg?style=flat\n[docs-link]: https://www.pairinteraction.org/pairinteraction/sphinx/html/\n\n**Note: This is a completely new version of the pairinteraction software that is not backward compatible to versions below v1.0.**\n\nThe *pairinteraction* software calculates properties of Rydberg atoms. The software consists of a Python library and a graphical user interface for obtaining single-atom properties and calculating pair potentials, making use of a high-performance C++ backend. For a more detailed description of the software that is written to be accessible also to non-specialists, see the [About page][about-link] of the project. The software can be installed via pip (requires Python >= 3.9, for tips see our [extended installation instructions][installation-link]):\n\n```bash\npip install pairinteraction\n```\n\nYou can use the pairinteraction software as a Python library, see our [quick start guide to get started in 5 minutes][tutorial-link], or you can launch its graphical user interface from the command line:\n\n```bash\npairinteraction gui\n```\n\n[about-link]: https://www.pairinteraction.org/pairinteraction/sphinx/html/about.html\n[installation-link]: https://www.pairinteraction.org/pairinteraction/sphinx/html/installation/installation.html\n[tutorial-link]: https://www.pairinteraction.org/pairinteraction/sphinx/html/tutorials/examples_python/quick_start.html\n\n## Highlights\n\n* For calculating Rydberg pair potentials, the software uses a similar approach as the [old version of pairinteraction](https://github.com/pairinteraction/pairinteraction/tree/v0.9.10), the [Alkali.ne Rydberg Calculator](https://github.com/nikolasibalic/ARC-Alkali-Rydberg-Calculator), and the [rydcalc library](https://github.com/ThompsonLabPrinceton/rydcalc). We optimized the construction and diagonalization of Hamiltonians, typically achieving a **speedup of 5-20x** compared to other implementations.\n\n ![benchmarking results][benchmark-results-link]\n\n *Figure: Benchmarking the construction and diagonalization of a Hamiltonian of a pair of Rb 60S atoms for 100 different internuclear distances on an AMD Ryzen 7 5700G CPU using Windows 11. The Hilbert space comprises pair states that differ at most by 4 in n, l and 25GHz in energy. When supported, symmetries where used to reduce the Hilbert space size. See the [benchmarking tool][benchmark-tool].*\n\n* The software uses single-channel quantum defect theory (SQDT) and also **multi-channel quantum defect theory (MQDT)** for the accurate description of atoms.\n\n The construction of Hamiltonians is accelerated by using pre-calculated matrix elements, which are stored in database tables. These tables are automatically downloaded from GitHub \\[[1],[2]\\] and cached locally when needed.\n\n[1]: https://github.com/pairinteraction/database-sqdt/releases\n[2]: https://github.com/pairinteraction/database-mqdt/releases\n[benchmark-tool]: https://github.com/pairinteraction/pairinteraction/tree/master/tools/benchmarking\n\n* **Electric and magnetic fields in arbitrary directions** can be included in the calculations. Diamagnetism is supported.\n\n[benchmark-results-link]: https://github.com/pairinteraction/pairinteraction/raw/master/data/benchmarking_results/0845d67063_1.4.2-cp313-win_amd-ryzen-7-5700g-with-radeon-graphics_reps4.png\n\n## How to Cite\n\nIf you use pairinteraction in your research, please cite our tutorial paper:\n\n> Sebastian Weber, Christoph Tresp, Henri Menke, Alban Urvoy, Ofer Firstenberg, Hans Peter B\u00fcchler, Sebastian Hofferberth, *Tutorial: Calculation of Rydberg interaction potentials*, [J. Phys. B: At. Mol. Opt. Phys. 50, 133001 (2017)][journal-link], [arXiv:1612.08053][arXiv-link]\n\n**Quantum Defects**\n<a id=\"quantum-defects\"></a>\n\nPairinteraction relies on quantum defects provided by the community. Consider citing relevant publications for your atomic species alongside pairinteraction.\n\n<p><details>\n<summary><b>Click to expand for quantum defect references</b></summary>\n\n| Element | Model | Identifier | References |\n|---------|-----------------------|----------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------|\n| H | SQDT | `H` | Schr\u00f6dinger equation for hydrogen |\n| Li | SQDT | `Li` | [10.1017/CBO9780511524530] (1994)<br>[10.1103/PhysRevA.34.2889] (1986) |\n| Na | SQDT | `Na` | [10.1088/0953-4075/30/10/009] (1997)<br>[10.1070/QE1995v025n09ABEH000501] (1995)<br>[10.1103/PhysRevA.45.4720] (1992) |\n| K | SQDT | `K` | [10.1088/0031-8949/27/4/012] (1983)<br>[10.1016/0030-4018(81)90225-X] (1981) |\n| Rb | SQDT | `Rb` | [10.1103/PhysRevA.83.052515] (2011)<br>[10.1103/PhysRevA.74.054502] (2006)<br>[10.1103/PhysRevA.74.062712] (2006)<br>[10.1103/PhysRevA.67.052502] (2003) |\n| Cs | SQDT | `Cs` | [10.1103/PhysRevA.93.013424] (2016)<br>[10.1103/PhysRevA.35.4650] (1987)<br>[10.1103/PhysRevA.26.2733] (1982) |\n| Sr88 | SQDT, singlet sector | `Sr88_singlet` | [10.1103/PhysRevA.108.022815] (2023)<br>[10.17169/refubium-34581] (2022) |\n| Sr88 | SQDT, triplet sector | `Sr88_triplet` | [10.1016/j.cpc.2020.107814] (2021) |\n| Sr87 | MQDT | `Sr87_mqdt` | [10.1088/1361-6455/ab4c22] (2019) |\n| Sr88 | MQDT | `Sr88_mqdt` | [10.1088/1361-6455/ab4c22] (2019) |\n| Yb171 | MQDT | `Yb171_mqdt` | [10.48550/arXiv.2406.01482] (2024) |\n| Yb173 | MQDT | `Yb173_mqdt` | MQDT model formulated by us |\n| Yb174 | MQDT | `Yb174_mqdt` | [10.48550/arXiv.2406.01482] (2024) |\n\nThe identifier can be used to specify an atomic species in the pairinteraction software.\n\n\n</details></p>\n\n[journal-link]: https://doi.org/10.1088/1361-6455/aa743a\n[10.1103/PhysRevA.34.2889]: https://doi.org/10.1103/PhysRevA.34.2889\n[10.1017/CBO9780511524530]: https://doi.org/10.1017/CBO9780511524530\n[10.1103/PhysRevA.45.4720]: https://doi.org/10.1103/PhysRevA.45.4720\n[10.1070/QE1995v025n09ABEH000501]: https://doi.org/10.1070/QE1995v025n09ABEH000501\n[10.1088/0953-4075/30/10/009]: https://doi.org/10.1088/0953-4075/30/10/009\n[10.1088/0031-8949/27/4/012]: https://doi.org/10.1088/0031-8949/27/4/012\n[10.1016/0030-4018(81)90225-X]: https://doi.org/10.1016/0030-4018(81)90225-X\n[10.1103/PhysRevA.83.052515]: https://doi.org/10.1103/PhysRevA.83.052515\n[10.1103/PhysRevA.67.052502]: https://doi.org/10.1103/PhysRevA.67.052502\n[10.1103/PhysRevA.74.054502]: https://doi.org/10.1103/PhysRevA.74.054502\n[10.1103/PhysRevA.74.062712]: https://doi.org/10.1103/PhysRevA.74.062712\n[10.1103/PhysRevA.93.013424]: https://doi.org/10.1103/PhysRevA.93.013424\n[10.1103/PhysRevA.26.2733]: https://doi.org/10.1103/PhysRevA.26.2733\n[10.1103/PhysRevA.35.4650]: https://doi.org/10.1103/PhysRevA.35.4650\n[10.1103/PhysRevA.108.022815]: https://doi.org/10.1103/PhysRevA.108.022815\n[10.17169/refubium-34581]: https://doi.org/10.17169/refubium-34581\n[10.1016/j.cpc.2020.107814]: https://doi.org/10.1016/j.cpc.2020.107814\n[10.1088/1361-6455/ab4c22]: https://doi.org/10.1088/1361-6455/ab4c22\n[10.48550/arXiv.2406.01482]: https://doi.org/10.48550/arXiv.2406.01482\n\n## Documentation\n\n**User Guide**\n\n- [Installation] - Whether you prefer an installation via pip or compiling from source, we've got all the information you need.\n\n- [Tutorials] - Covering both the graphical user interface and the Python library,\nthese tutorials enable you to leverage pairinteraction for your projects.\n\n- [API Reference] - Documentation of classes and functions of pairinteraction's Python library.\n\n- [Publications] - Find out more about the theory behind pairinteraction and how to cite it and the quantum defects you use.\n\n**Contributor Guide**\n\n- [Getting Started as a Contributor] - Discover the many ways you can help improve pairinteraction, from contributing to the repository to providing quantum defects.\n\n- [Overview About pairinteraction's Architecture] - Find out how pairinteraction is structured.\n\n- [Style Guide] - Learn about the coding style used in pairinteraction.\n\n- [Database Format] - Explore the database for storing atomic states and matrix elements.\n\n**Utility Tools [External Links]**\n\n- [MQDT.jl] - Learn how to calculate states and matrix elements using multi-channel quantum defect theory with our tool written in Julia.\n\n- [ryd-numerov] - Learn how to calculate states and matrix elements using single quantum defect theory with our tool written in Python.\n\n[Installation]: https://www.pairinteraction.org/pairinteraction/sphinx/html/installation/installation.html\n[Tutorials]: https://www.pairinteraction.org/pairinteraction/sphinx/html/tutorials/tutorials.html\n[API Reference]: https://www.pairinteraction.org/pairinteraction/sphinx/html/api_reference.html\n[Publications]: https://www.pairinteraction.org/pairinteraction/sphinx/html/publications/publications.html\n[Getting Started as a Contributor]: https://www.pairinteraction.org/pairinteraction/sphinx/html/contribute/getting_started.html\n[Overview About pairinteraction's Architecture]: https://www.pairinteraction.org/pairinteraction/sphinx/html/contribute/architecture.html\n[Style Guide]: https://www.pairinteraction.org/pairinteraction/sphinx/html/contribute/style_guide.html\n[Database Format]: https://www.pairinteraction.org/pairinteraction/sphinx/html/contribute/database.html\n[MQDT.jl]: https://github.com/pairinteraction/MQDT.jl\n[ryd-numerov]: https://github.com/pairinteraction/ryd-numerov/\n\n## Contributors\n\nThe software is maintained by:\n* [Sebastian Weber]\n* [Johannes M\u00f6gerle]\n\nIn addition, the following people contributed significantly to the current and/or previous versions of the software:\n* [Henri Menke]\n* [Frederic Hummel] - Julia package for multi-channel quantum defect theory, matrix elements\n* [Eduard J. Braun] - Perturbative calculations, installation instructions for Windows\n* [Johannes Block] - Calculation of Rydberg pair potentials near surfaces *(not yet in new version)*\n* [Nicolas Zuber] - Tutorial on Rydberg-ion interaction\n* [Simon Hollerith] - Documentation of the graphical user interface *(not yet in new version)*\n\nWe warmly welcome new contributions! Please see our [contributor guide][contributor-link] for more information!\n\nThe development of the pairinteraction software has been supported by the [Institute for Theoretical Physics III] of the University of Stuttgart, the Federal Ministry of Education and Research under the Grants [QRydDemo] and [MUNIQC-Atoms], and the company [Atom Computing]. The development of the original version of the software started at the [5th Institute of Physics] of the University of Stuttgart.\n\n[![University of Stuttgart][stuttgart-jpg]][stuttgart-link]\n[![Federal Ministry of Education and Research][bmbf-jpg]][bmbf-link]\n[![Atom Computing][atom-jpg]][atom-link]\n\n[stuttgart-jpg]: https://github.com/pairinteraction/pairinteraction/raw/master/docs/_static/logos/uni_stuttgart.svg\n[stuttgart-link]: https://www.uni-stuttgart.de/en/\n[bmbf-jpg]: https://github.com/pairinteraction/pairinteraction/raw/master/docs/_static/logos/bmbf.svg\n[bmbf-link]: https://www.bmbf.de/EN/\n[atom-jpg]: https://github.com/pairinteraction/pairinteraction/raw/master/docs/_static/logos/atom_computing.svg\n[atom-link]: https://atom-computing.com/\n\n[Institute for Theoretical Physics III]: https://www.itp3.uni-stuttgart.de/\n[QRydDemo]: https://www.quantentechnologien.de/forschung/foerderung/quantenprozessoren-und-technologien-fuer-quantencomputer/qryddemo.html\n[MUNIQC-Atoms]: https://www.quantentechnologien.de/forschung/foerderung/quantencomputer-demonstrationsaufbauten/muniqc-atoms.html\n[Atom Computing]: https://atom-computing.com/\n[5th Institute of Physics]: https://www.pi5.uni-stuttgart.de/\n[Sebastian Weber]: https://github.com/seweber\n[Johannes M\u00f6gerle]: https://github.com/johannes-moegerle\n[Henri Menke]: https://github.com/hmenke\n[Frederic Hummel]: https://github.com/frederic-atom\n[Eduard J. Braun]: https://github.com/EduardJBraun\n[Nicolas Zuber]: https://github.com/tripiti\n[Johannes Block]: https://github.com/johblock\n[Simon Hollerith]: https://github.com/SimonHollerith\n[contributor-link]: https://www.pairinteraction.org/pairinteraction/sphinx/html/contribute/getting_started.html\n\n## License\n\nThe pairinteraction software is licensed under [LGPL v3][license-lgpl-link]. For more information, see [LICENSE.txt](https://github.com/pairinteraction/pairinteraction/blob/master/LICENSE.txt).\n",
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