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mathematica package

about : download : installation : laser guide stars : images : movies : release notes : feedback

AtomicDensityMatrix is a package for Mathematica version 6 that facilitates analytic and numerical density-matrix calculations in atomic and related systems. It is intended to be both general and user-friendly, and to be useful to the working physicist as well as to students.

Note: The ADM package has been checked for correctness in a large variety of circumstances, but there are certainly many cases that have not been checked. Please send bug reports to

The package documentation is growing, but far from complete. It is available in the Mathematica Documentation Center when the package is installed. Future package updates will include expanded documentation.

The images and animations below are from the ADM documentation, and were generated with the package.

  1. Download
  2. Unzip into the "Applications" subdirectory of the Mathematica base directory. You can find this directory by evaluating ToFileName[{$BaseDirectory, "Applications"}] or ToFileName[{$UserBaseDirectory, "Applications"}] in Mathematica
  3. After restarting Mathematica, the beginnings of a help file and demos should be available in the Mathematica Documentation Center under "Installed Add-Ons" (lower right-hand corner)
  4. The package can be loaded into Mathematica by evaluating <<AtomicDensityMatrix`
Laser Guide Stars:

The LGSBloch package is an extension to the Atomic Density Matrix package that contains routines for calculating the return flux from optically excited alkali atoms, specifically designed for Na atoms in the mesosphere.

This software has been developed and tested under Mathematica 7.1, and we believe it should run under version 6.x as well.

LGSBloch installation instructions

State vector plot Population plot Hexacontatetrapole moment Breit-Rabi diagram Nonlinear magneto-optical effects: absorption Nonlinear magneto-optical effects: phase shift Nonlinear magneto-optical effects: optical rotation Nonlinear magneto-optical effects: change of ellipticity Quadratic Stark shift 3D Stark-shift plot
Pumping hexadecapole, 2->1 transition Pumping hexadecapole, 2->2 transition Nonlinear Zeeman effect Comparing EIT and nonlinear magneto-optical effects Fig. 4(c) from RF NMOR paper. Fig. 5 from RF NMOR paper. Fig. 6 from RF NMOR paper.
Release notes:
Please send questions, suggestions, and bug reports to Simon Rochester at