Rabi frequency ratio does not agree with the result of published papers

[wu-michelle]

I was trying to calculate the Rabi frequency ratio of Cs atom excitation (6S{1/2} -->nP{1/2}) to (6S{1/2} -->nP{3/2}) By running the following code:

rabiFreq = cs.getRabiFrequency(n1=6, l1=0, j1=0.5, mj1=0.5, n2=84, l2=1, j2=1.5, q= +1, 
                                       laserPower=1000.e-3, laserWaist= 50.e-6)
rabiFreq_2 = cs.getRabiFrequency(n1=6, l1=0, j1=0.5, mj1=0.5, n2=84, l2=1, j2=0.5, q= 0, 
                                       laserPower=1000.e-3, laserWaist= 50.e-6)
print(rabiFreq/rabiFreq_2)

I got the ratio = 3.4056. However, the following papers say that the oscillator strength for excitation to P{1/2} states is orders of magnitude weaker than for excitation to P{3/2} states: • https://journals.aps.org/pra/abstract/10.1103/PhysRevA.89.033416 • https://arxiv.org/pdf/1706.06237.pdf The oscillator strengths are proportional to the square of the Rabi frequency: 3.4^2 = 11.56 but this still can't get us 4 orders of magnitude as the paper say .... I wonder if there is something wrong with getDipoleMatrixElement? By the way, I also made this plot:

[nikolasibalic]

HI @MinHsuanWu , thank you for pointing this out.

This might have to do with spin-orbit interaction ( #14 ) and core modification of dipole operator, that seem to together make a difference for nP_1/2 states in Cs. I will have a more detailed look into this and let you know.

[wu-michelle]

Seems like it is more of a fundamental problem? So it will not only affect Cs but also other atoms?

[nikolasibalic]

It seems to be effect that is significant particularly for Cs. https://iopscience.iop.org/article/10.1088/0022-3700/11/24/004 I was delayed with some other things, will check this now.

[wu-michelle]

Hi, I just want to check if there is an update.

Also, this problem seems to suggest that the Rabi frequency given by getRabiFrequency for 6S{1/2} -->nP{1/2} or P_{3/2} for high n, Cs, might not be correct?

One example in this notebook: https://arc-alkali-rydberg-calculator.readthedocs.io/en/latest/Rydberg_atoms_a_primer.html is talking about reaching highly excited states by multiple-step excitation instead of direct excitation can save us from using high power laser. And the reason is the weak overlap between the ground and highly excited Rydberg states require large intensities. Does this problem suggest that this statement might not be true if we use the 6S{1/2} -->nP{3/2} for Cs?

Thanks

[nikolasibalic]

HI @MinHsuanWu ,

I had to go on holiday before I could test all changes. Should be able to continue this weekend with this. Just to clarify few points:

• low-lying to high-lying transition DME are the hardest to get because some approximations that are used for numerically obtaining wave functions in model potential break for low lying states. Thus low-lying wave functions are not as accurately estimated as high lying ones. For transitions between low lying states ARC uses than literature vales obtained by other more precise methods or measurements, but for low- to high- lying states we have to use wave functions. The 6S_{1/2} -->nP series in Cs in particular seem to have strong contribution of additional effects. Goal for version 4. of ARC is to introduce new calculations that would give more accurate wave functions for low-lying states too. In the meantime, I will try to implement and test some corrections that would effectively take care of it.

• the focus is not getRabiFrequency, which is correct calculation, but in fact calculations of DME used for low to high lying transitions of Cs.

• Overlap between high and low lying states is always weak, and this does not suggest that the statement in primer is not true. In fact, these corrections go in direction of further reducing DME of 6S_{1/2} -->nP in Cs.

Will write for weekend on final result regarding this.

[wu-michelle]

Hi Nikola,

Have you been able to test the changes you mentioned?

Thanks, Min-Hsuan

On Wed, Jul 15, 2020 at 2:37 AM Nikola Šibalić notifications@github.com wrote:

HI @MinHsuanWu https://github.com/MinHsuanWu ,

I had to go on holiday before I could test all changes. Should be able to continue this weekend with this. Just to clarify few points:

-

low-lying to high-lying states are the hardest to get because some approximation that are used for integrating wave functions in model potential break for low lying states. Thus low-lying wave functions are not as accurately estimated as high lying ones. For transitions between low lying states ARC uses than literature vales obtained by other more precise methods or measurements, but for low- to high- lying states we have to use wave functions. The 6S_{1/2} -->nP series in Cs in particular seem to have strong contribution additional effects. Goal for version 4. of ARC is to introduce new calculations that would give more accurate wave functions for low-lying states too. In the meantime, I will try to implement and test some corrections that would effectively take care of it.

the focus is not getRabiFrequency, which is correct calculation, but in fact calculations of DME used for low to high lying transitions of Cs.

Overlap between high and low lying states is always weak, and this does not suggest that the statement in primer is not true. In fact, these corrections go in direction of further reducing DME of 6S_{1/2} -->nP in Cs.

Will write for weekend on final result regarding this.

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[m-schleier]

Hi @nikolasibalic,

I noticed that @MinHsuanWu's request has still not been resolved and am wondering whether we might be able to help with this. I use a modified version of the getRadialMatrixElement function that accounts for the core polarizability effect in cesium to obtain oscillator strengths that match spectroscopic data (and that could readily be extended to other alkali atoms). I've posted a Python notebook here that demonstrates this functionality and includes some notes on what it would take to more fully integrate the improved calculation into ARC. I would be happy to explain further and discuss what is needed to implement properly.

--Monika

[nikolasibalic]

Dear Monika @m-schleier ,

Many thanks for this well documented and benchmarked contribution. As I can see, this crucially includes Eq. 19 from M. Marinescu, H. R. Sadeghpour, and A. Dalgarno, PRA 49, 982 (1994), with value of corePolRc better estimated thanks to fits to recent measurements. I guess that is the dominant contribution, with smaller correction of lower-bound for integration. Very nice.

Would you like to submit a pull request on branch that I have just opened (core_polarisability) so that we can keep track of your contribution on GitHub page?

I would try then to do some cleanup and integrate this smoothly into master branch.

Would it be fine with you also if we include this very useful notebook verbatim in ARC documentation? I was thinking to add link somewhere in documentation of getRadialMatrixElement that would open notebook then, explaining this. Let me know.

Once again, many thanks for reaching out and resolving this! Best wishes, Nikola

[m-schleier]

Hi @nikolasibalic,

I just submitted the pull request. It definitely does need some cleanup, so I appreciate your willingness to take this on!

And yes, feel free to include the notebook in the ARC documentation. (That said, I should probably look over it one more time, and I'll let you know if I notice any edits that are needed.)