Appendix
Density Matrix Methods
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Density matrix formulation
Excitation hamiltonian
Port Lawrence and Vistula Meadows
Entanglement
Preferential excitation with a beam
Preferential decay with a magnetic field
Expectation values
Trace
Ensemble average
Example: angular momentum
Eigenvectors and eigenvalues
Raising and lowering operators
Matrix representations
Matrix product and trace
Lx, Ly, Lz
Squared operators
Compare with L2
LxLy, LxLz, LyLz
Stokes parameters
Background
Definitions
Mueller Matrices
Linear polarizer
(continued)
Matrix
Retarding plate
Combined optical elements
(continued)
Circular polarization analyzer
Decay and detection
Decay operator
Relationship to density matrix
Symmetries
Detection operator
Application
Tilted foil geometry
Data reduction
Computation of angular momenta
Squared and cross terms
Summary
Landscape of measurements
Time dependence
Liouville equations
Commutators
Transfer of alignment
Polarization, orientation, and alignment
Cascade induced alignment
Decay of polarization
Quantum beats
Quantum beats
Two spectrometer measurements
Measured results
Tilted foil hfs measurements
Optical pumping and level crossing
Pi and sigma patterns
Optical pumping
Double optical resonance
Measurements
Level crossing
Measurements
Angular polarization
E1 radiation pattern
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Linear dipole representation
Angular distribution
Plot
Magic angles
Instrumental polarizations
Multiplet mixing
Multiplet mixing
E1 decay
Quantum beats
Detector function
Individual parts
Component transition intensities
Angular distribution from incoherent source
Polarization intensities
Relative efficiencies
Comments
Component transition probabilities
Pi transitions
Sigma transitions
Resonance fluorescence
E1 radiation pattern
Angular polarization
Decay processes
p
and
s
intensity distributions
Optical pumping
Optical double resonance
Measured spectra
Level crossing
Measured spectra