Method to calculate absolute transition frequency

[cjbe]

It would be useful to have a method that calculates the absolute transition frequency between any pair of states

[hartytp]

Out of curiosity, what's the use-case? Does the splitting of the magnetic/hyperfine subleves make a noticeable difference to the overall transition frequency?

Anyway, yes, that's a good idea. I don't like the ion.delta method. Maybe the way to go here is to have a method like ion.transition_frequency(lower_state, upper_state, absolute=True) (bikeshed names and default values) to replace the delta method.

[cjbe]

This would allow a Stark shift solver to just sum over all levels, and one does not have to think (all levels being S-P1/2, S-P3/2, or D-P1/2, D-P3/2).

Similarly, a Raman matrix element calculation can just sum over all coupled levels, rather than require extra manual work, meaning it works for all ions and all wavelengths for free

[hartytp]

So you want to do something like this calculation, summing over transitions: https://github.com/OxfordIonTrapGroup/ion_phys/blob/8a4fc96e531332391a871617ed102166d9b5323b/ion_phys/rate_equations.py#L76-L77 ?

The way I like to write code is to keep things as matricies which I can multiple. AFAICT the way you're suggesting you'd be iterating over pairs of states (since I assume get_frequency or whatever would return a number)? Or would you want something that actually returns an absolute energy matrix?

[hartytp]

Following: #27 (comment) I think the best bet here is:

• replace delta with get_energy(ind, absolute=True) and get_frequency(lower, upper, absolute=True) accessors.

[cjbe]

So you want to do something like this calculation...

Yes, but in more complex situations, e.g. for a Raman coupling:
Omega = \sum_{all e} g1g2pol1(q1)*pol2(q2)*matrix_element(dn,e)*matrix_element(e,up) / (frequency(dn,up,e)-omega0)

[hartytp]

Ok. Are you happy with my proposed solution? If so, it's quick to implement so I'll aim to do it soon...

[cjbe]

Yes - LGTM
(nit pick: I feel a "relative" kwarg is better than "absolute", as it is not clear to me what the opposite of "absolute" is as an API user)