Numbering of separate transitions

[JuliaL]

Hello!

Using pepper, I'm simulating the separate transitions of one spin 1/2 and one spin 3/2:

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Sys.S = [1/2; 3/2]; Sys.g = [8; 2]; Sys.ee = 0;
Exp = struct('Range', [1, 1000], 'mwFreq', 9.7601, 'Harmonic', 0);
Opt.Output = 'separate';
[x,y,tr] = pepper(Sys,Exp,Opt);
 

There are 10 transitions shown in 'tr'. They are sorted by intensity, I guess.

Can the numbering of the levels somehow be correlated to the quantum numbers of the two spins, like (-1/2,-3/2) - (-1/2,-1/2) corresponding to 1-2 ?

I'm wondering because the numbers of some transitions are changing when I reduce the first spin g-value... Like 1-5 becoming 1-4 etc.


(The aim is to separate the (S=3/2: -1/2->1/2)-transition of a (1/2, 3/2, 1/2) system with J12, J23 and D. It's hard to keep track of the numbering beyond 30 transitions...)

[Stefan Stoll]

There is no particular guaranteed sort order for the transitions. It is best to assume they are in random order.

The best way to get projection numbers mS1 and mS2 for the individual spins is to calculate them, for each state, via the expectation values of S1z and S2z - that's how mS is defined in general. This will work for any situation, no matter how strong the mixing among the spins is, and not only in the limit of weak electron-electron coupling.

Here is a code snippet, assuming you have a two-spin system defined in Sys.

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[S1z,S2z] = sop(Sys,'ze','ez');

B0 = [0;0;300]; % mT
H = sham(Sys,B0);
[V,E] = eig(H);

for k = 1:length(E)
  v = V(:,k);
  mS1(k) = v'*S1z*v;
  mS2(k) = v'*S2z*v;
end

Instead of the for-loop, you could also use

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mS1 = diag(V'*S1z*V)
mS2 = diag(V'*S2z*V)