AtomicDensityMatrix Paclet Symbol

# 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.
• 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 hyperfine-Zeeman 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 RestrictCoupling 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 magnetic-dipole Hamiltonian is given by , where is the electronic magnetic moment operator and is the magnetic field.
• The electric-dipole 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 is specified by labeling the two states {term, lab1} and {term, lab2}, where term, lab1, and lab2 are arbitrary labels.
• For a toy-type atomic system (no angular momentum), the magnetic field is disregarded, and the electric field is converted to a scalar by taking the first nonzero Cartesian component.
Internal and electric-field-interaction Hamiltonian for a toy system:
 Out[3]//MatrixForm=

Magnetic-field-interaction Hamiltonian for a Zeeman system subject to an arbitrarily directed magnetic field:
 Out[2]=
 Out[3]//MatrixForm=

Stark-polarizability Hamiltonian for a Zeeman system subject to an x-directed electric field:
 Out[2]//TableForm=
 Out[3]//MatrixForm=

Hamiltonian for a toy system subject to an optical field:
 Out[2]=
 Out[3]//MatrixForm=

Hamiltonian for a Zeeman system subject to a linearly (x)-polarized optical field and static magnetic field:
 Out[2]=
 Out[3]//MatrixForm=

Internal Hamiltonian for a hyperfine-Zeeman system:
 Out[2]=
 Out[3]//MatrixForm=
 Scope   (1)
 Options   (7)
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