AtomicDensityMatrix Package
AtomicDensityMatrix is a package for Mathematica version 6+ that facilitates density-matrix calculations in atomic and related systems.
Note: The documentation is incomplete. The symbols listed below are the only ones that have their own reference pages. Look at the tutorials to get started. Documentation is currently an active part of package development.
Atomic Systems
AtomicState expression representing an atomic state
Sublevels generate the hyperfine and Zeeman sublevels for a list of atomic states
J  ▪ L  ▪ S  ▪ M  ▪ NuclearSpin  ▪ F  ▪ Energy  ▪ HyperfineA  ▪ HyperfineB  ▪ NaturalWidth  ▪ GFactor  ▪ StateLabel  ▪ BranchingRatio  ▪ Parity  ▪ AtomicSystemQ  ▪ AtomicSystemType
Density Matrices
DensityMatrix create density matrix for a list of atomic states
OpticalField generate the expression for an optical field
Hamiltonian the Hamiltonian for an atomic system subject to external classical fields
RotatingWaveApproximation perform the rotating-wave approximation on a Hamiltonian
Relaxation and Repopulation
IntrinsicRelaxation relaxation matrix for spontaneous decay
Light Propagation
Observables the change in optical parameters upon propagation through an optically thin medium
LinearAbsorption formula for absorption of weak light
LevelDiagram draw a level diagram for an atomic system, Hamiltonian, and density matrix
AMPSPlot draw the angular-momentum probability surface for a density matrix
Tensor Algebra
ToCartesian convert a spherical tensor into the Cartesian basis
Decomposition decompose a reducible operator into a sum of polarization moments
Basic Examples
Advanced Examples
Copyright and License:
Copyright (C) 2004—2017 Simon M. Rochester <>
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program. If not, see