Electric-dipole transitions

[thanasis]

I am trying to introduce a perturbation that will simulate electric-dipole transitions from the E1 component of the MW radiation.

As suggested by Stefan:
1) I first need to define the interaction of the E₁ field as H₁ = E₁ * n_E1 * He, where E₁ is the E-field intensity, n_E1 the E-field direction vector and He the rest of the Hamiltonian term depending on the spin degrees of freedom.
2) Then, I need to calculate intensities abs(V(:,i2)'*H1*V(:,i1))^2 to get the transition rate between eigenstates i1 and i2, assuming [V,E] = eig(H0) where H0 is the static Hamiltonian

Questions:
A) For typical perpendicular-mode EPR transition probabilities, in a general case we would calculate those in the following manner:

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H = sham(Sys,[0,0,0.001]);
[V,E]=eig(H);
[Sx,Sy,Sz] = sop(Sys,'x','y','z');
u = V(:,1); 
v = V(:,2); 
element12x = u'*Sx*v; 
element12y = u'*Sy*v; 
ampl12x = abs(element12x); 
ampl12y = abs(element12y); 
prob12x = ampl12x^2; 
prob12y = ampl12y^2; 
prob12 = (prob12x + prob12y)/2;

And by extension, I guess that for parallel-mode EPR we should calculate instead:

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element12z = u'*Sz*v;

and change the consecutive ones accordingly.

If I understand correctly, the (time-dependent?) H1 defined in (1) is the light-matter interaction Hamiltonian. As per (2) it should be of the same dimensions (n x n) as the Hilbert size of the problem, therefore, it should be constructed from the Sx, Sy, Sz operators that sop constructs in its turn? Should I just replace one with another by considering the particular geometry of the experiment? E.g. in a beam experiment, would that mean swap Sx for Sy (and vice versa) in a Faraday geometry, and change Sx/Sy for Sz in Voigt geometry?

B) To calculate the magnitude E₁, simple electromagnetics show that E₁ = c*B₁. Typically, we do not know either in absolute terms (we just scale simulated to experimental spectra), so should I just multiply by c in calculating the transition probability amplitudes of electric-dipole transitions?

Thanks for all your help!