RydState - A Rydberg State Calculator

The RydState software calculates properties of Rydberg states of alkali and alkaline-earth-like atoms. Rydberg states are described by single-channel (SQDT) or multi-channel quantum defect theory (MQDT). Based on this, the software calculates the radial wavefunctions via the Numerov method, as well as energies and matrix elements of Rydberg states. The software can be installed via pip (requires Python >= 3.10):

pip install rydstate

To install the latest development version from github, use:

pip install git+https://github.com/pairinteraction/rydstate

How to Cite

This package relies on quantum defects provided by the community. Consider citing relevant publications for your atomic species.

Element	Model	Identifier	References
H	SQDT	H	Schrödinger equation for hydrogen
Li	SQDT	Li	10.1017/CBO9780511524530 (1994) 10.1103/PhysRevA.34.2889 (1986)
Na	SQDT	Na	10.1088/0953-4075/30/10/009 (1997) 10.1070/QE1995v025n09ABEH000501 (1995) 10.1103/PhysRevA.45.4720 (1992)
K	SQDT	K	10.1088/0031-8949/27/4/012 (1983) 10.1016/0030-4018(81)90225-X (1981)
Rb	SQDT	Rb	10.1103/PhysRevA.83.052515 (2011) 10.1103/PhysRevA.74.054502 (2006) 10.1103/PhysRevA.74.062712 (2006) 10.1103/PhysRevA.67.052502 (2003)
Cs	SQDT	Cs	10.1103/PhysRevA.93.013424 (2016) 10.1103/PhysRevA.35.4650 (1987) 10.1103/PhysRevA.26.2733 (1982)
Sr88	SQDT	Sr88_sqdt	10.1103/PhysRevA.108.022815 (2023) 10.17169/refubium-34581 (2022) 10.1016/j.cpc.2020.107814 (2021)
Sr87	MQDT	Sr87_mqdt (tag robicheaux2019)	10.1088/1361-6455/ab4c22 (2019)
Sr88	MQDT	Sr88_mqdt (tag robicheaux2019)	10.1088/1361-6455/ab4c22 (2019)
Sr88	MQDT	Sr88_mqdt (tag vaillant2024)	10.1088/1361-6455/ad76f0 (2024) 10.1088/0953-4075/47/15/155001 (2014) 10.1016/j.cpc.2020.107814 (2021)
Sr88+	SQDT	Sr88_ion	urn:nbn:se:su:diva-184811 (2020) 10.1007/978-3-030-33770-4 (2019) 10.1007/BF01426593 (1991)
Yb171	MQDT	Yb171_mqdt	10.1103/PhysRevX.15.011009 (2025) 10.1103/mzsv-rckx (2025)
Yb173	MQDT	Yb173_mqdt	MQDT model formulated by Frederic Hummel
Yb174	MQDT	Yb174_mqdt	10.1103/PhysRevX.15.011009 (2025) 10.1103/mzsv-rckx (2025)

Documentation

User Guide

• Tutorials - Examples of how to use the RydState library.

• API Reference - Documentation of classes and functions of the RydState Python library.

Contributors

This software is currently maintained by:

• Johannes Mögerle

The following people have made significant contributions:

• Frederic Hummel - Supported the development of the MQDT implementation. Author of the MQDT.jl Julia package, on which this package’s Python implementation of the MQDT calculations is based.
• Sebastian Weber - Provided substantial input on the physics and software architecture of this package.

We warmly welcome new contributions!

License

The rydstate software is licensed under LGPL v3. For more information, see LICENSE.txt.