Order of transitions from Opt.Transitions

[thanasis]

Hello,

resfields and resfreqs give a series of transitions, by taking in an optional Opt.Transitions array field which defines which transitions are to be selected.

Is the order of these transitions in Pos, Amp,... etc outputs the same as the order of the transitions in Opt.Transitions array? Or is it some other ordering convention?

Thanks in advance.

[thanasis]

By running the calculation, it is clear that transitions are always sorted alphabetically.
E.g. fo four levels:

Code: Select all

1 2
1 3
1 4
2 3
2 4
3 4

This is OK for frequency-swept experiments, where we are likely to get each resonance once. However, for field-swept experiments, we may have several transitions with the same label.
E.g. in the example below, all resonances are labeled [1 2].

Code: Select all

cm=100*clight/1e6; % Conversion constant from cm-1 to MHz
Sys.S = 3/2;
Sys.D = [0.11 0]*cm;
Sys.g = [2.07 2.24];
Exp.Range = [0 400];
Exp.mwFreq = 2.5;

Params.mwFreq = Exp.mwFreq; Params.Range = [0 1000];
[PosPar,Amp,Wid,Trans] = resfields(Sys,Params)

Ori = 'z'; Par.Units = 'cm^-1'; FieldRange = Exp.Range; Par.nPoints=1000;
Freq=Exp.mwFreq;
levelsplot(Sys,Ori,FieldRange,Freq,Par);

Can anyone suggest a useful way of labeling them so that they can then be assigned to the same level pairs when the field sweep takes place at higher frequencies?

[Stefan Stoll]

Can you be more specific what you are looking for? The level pair is the transition label, and it is unambiguous.

For example, the transition label [1 2] always refers to the transition(s) between the first and the second level, ordered by energy, no matter whether there are multiple resonance fields for that transition or only one.

[thanasis]

I am trying to plot roadmaps of transitions as a function of frequency. The B0//z case is the most tricky, as there are several level crossings.

So, in the above example (D > 0), as we increase the frequency, the label of the transition between e.g. Ms = -1/2 and Ms = +1/2 will start off from [1 2] before the first level crossing, will become [1 3] between the two level crossings and finally [2 3] beyond the second level crossing.

Seen from the opposite side, for a fixed 2.5 GHz frequency there are three [1 2]-labeled transitions, which need to be identified by the natures of the two states (one is Ms = +1/2 --> -1/2, the other two are both Ms = -3/2 --> -1/2).

So, as labeling does not have a 1-to-1 correspondence to the level nature (i.e. the S,Ms numbers) but is related to their relative energy, I am finding it difficult to easily create these roadmaps in a coherent manner.

[Stefan Stoll]

Indeed, levels in EasySpin are not labelled by their eigenvector character, but by their place in the energy order. The reason for this is that it is not possible to come up with a unique labeling based on eigenvector characters.

Think about a sharp anticrossing. The lower level always stays the lower level, and the upper stays the upper. However, the character of the two state vectors changes very rapidly over a narrow field range around that anticrossing. It makes no sense to swap the labels before and after the anticrossing. Now, a crossings is basically an infinitely sharp anticrossings, so not fundamentally different from a sharp anticrossing.