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Observables[sys, , a] returns the differential change in optical parameters of probe light with frequency and amplitude a upon propagation through a medium described by atomic system sys in terms of the rotatingframe densitymatrix elements, assuming default light polarization and rotatingwave transform. 
Observables[sys, , a, pol] returns the change in optical parameters for probe light of polarization specified by parameters pol. 
Observables[sys, , (a, }, pol] returns the change in optical parameters for probe light with phase . 
Observables[sys, , a, pol, TransformMatrix→u] returns the change in optical parameters in terms of rotatingframe densitymatrix elements assuming the rotatingwave transform described by the matrix u. 
PolarizationVector  Automatic  reference polarization vector  
PropagationVector  Automatic  unit wave vector  
Parameterization  Automatic  parameterization scheme for polarization  
TimeVariable  Automatic  symbol used to represent time variable 
TimeDependence  Automatic  whether density matrix elements should have explicit time dependence  
Representation  Automatic  Zeeman or polarization moment representation  
DMSymbol  Automatic  symbol to use for density matrix elements  
DMLabel  Automatic  additional label for density matrix elements  
ComplexExpandVariables  Automatic  whether to express density matrix elements in terms of real and imaginary parts 
ExpandDipoleRME  True  whether to write the reduced dipole matrix element in terms of of the natural line width and other parameters  
TransformMatrix  Automatic  the unitary matrix used to transform from the laboratory frame to the rotating frame 
Expressions proportional to the fractional change in electric field amplitude, change of phase, change in polarization angle, and change in ellipticity of a field of frequency and amplitude a, in terms of the rotatingframe densitymatrix elements. The field is assumed to have the default polarization (linear, along x) and propagation direction (along z), and a standard method is used to generate the rotatingwave transform.
We can simplify the expressions somewhat by assuming that the light frequency is approximately equal to the transition frequency Energy[2], by writing the electricfield amplitude a in terms of the Rabi frequency R=ad, and by writing the transition frequency in terms of the transition wavelength =2/Energy[2]:
In the above form, we can see that the expressions have the units of length squared (the units of the frequencies and R cancel, and the densitymatrix elements are dimensionless). Thus by multiplying by a path length and the atomic density we obtain the changes in the dimensionless optical parameters.
In order to obtain correct results from a given calculation, it is vital that the light polarization and rotatingwave transformation used by Observables matches those used to produce the Hamiltonian used to generate the densitymatrix evolution equations.
Define an elliptically polarized optical field with reference polarization vector along z, propagating along x.
