AtomicDensityMatrix`
AtomicDensityMatrix`
Hamiltonian
Hamiltonian[sys]
returns the matrix Hamiltonian for atomic system sys assuming the absence of external fields.
Hamiltonian[sys,MagneticField{bx,by,bz},ElectricField{ex,ey,ez}]
returns the matrix Hamiltonian including interaction terms with external classical magnetic and/or electric fields.
Details and Options
 The atomic system sys is specified as a list of AtomicState objects.
 Hamiltonian calls WignerEckart to evaluate the matrix elements for the necessary operators.
 Hamiltonian[sys] returns a diagonal Hamiltonian with diagonal terms determined by the Energy parameters (and the HyperfineA and HyperfineB parameters for hyperfineZeeman systems) of the corresponding atomic states.
 Different options applying to different fields can be specified using the form Hamiltonian[sys,{{MagneticField…,opts},{MagneticField…,…}},…].
 The following options can be given:

ElectricField 0 external electric field MagneticField 0 external magnetic field Interaction Automatic which types of interactions to include AllowedCouplings All which transitions to allow nonzero coupling on  The setting for the Interaction option may be given as a list of one or more of the following interaction types:

"Internal" eigenenergies due to internal interactions "MagneticDipole" magnetic dipole interaction with external field "ElectricDipole" electric dipole interaction with external field "Polarizability" effective Hamiltonian due to atomic polarizability  Additional possible settings are Automatic, which is equivalent to {"Internal","MagneticDipole","ElectricDipole"}, and All, meaning all interactions.
 The magneticdipole Hamiltonian is given by , where is the electronic magnetic moment operator and is the magnetic field.
 The electricdipole Hamiltonian is given by , where is the electric dipole operator and is the electric field.
 Under the coupling approximation, employed in the AtomicDensityMatrix package, magnetic coupling is allowed between two different states only if they are components of the fine structure of one term. This can be specified by labeling the two states {term, lab_{1}} and {term, lab_{2}}, where term, lab_{1}, and lab_{2} are arbitrary labels.
 For a toytype atomic system (no angular momentum), the magnetic field is disregarded, and the electric field is converted to a scalar by taking the norm, if there is more than one nonzero Cartesian component, or by taking the nonzero Cartesian component, if there is only one.
Examples
open allclose allBasic Examples (6)
Internal and electricfieldinteraction Hamiltonian for a toy system:
Magneticfieldinteraction Hamiltonian for a Zeeman system subject to an arbitrarily directed magnetic field:
Starkpolarizability Hamiltonian for a Zeeman system subject to an xdirected electric field:
Hamiltonian for a toy system subject to an optical field:
Hamiltonian for a Zeeman system subject to a linearly (x)polarized optical field and static magnetic field: