Single electron – single proton continuous solid effect

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I made this long time ago, did not posted or published anywhere.

I planned to made a more beautiful journal paper in near future, may be this year.

CW Solid effect

somethings need to be clean up and more detail is needed.

The calculation is based on Hartman-Hahn and Tim Wenckebach, the difference is, they use Fermi-Golden Rule to approximate the polarization transfer rate, but I solved it exactly with computer and also deduced the analytical solution for high-frequency truncated Hamiltonian. This reveal the validity on the frequency truncation. And I will add a comparison with experimental data in the planned-to-do paper.

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[Pol. p Target] resume experiment

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after a long summer break due to lab maintain.

we check the system to see weather it gives same results before.

the Hall probe reading is weird, so we calibrate it with water NMR signal.

and we redo the 30% laser duty, found that it is small, much smaller then expected.

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after discussion with my professor on my PhD topic.

i like to study the spin by nuclear scattering experiment. the polarized spin target is a good spin detector.

one possibility is on the EPR paradox and the Bell’s inequality. my professor gave me a PhD thesis on proton-neutron spin experiment on EPR.

another possibility is on the localized special relativity and quantum entanglement. since these two are strongly related by spin. my professor gave me a book on spin statistic about that.

another unclear way is through the study of spin group, Lorentz group and Mobius group. by some transformation, a 3D rotation can transform into a 2X2 matrix and then reveal that spin can have classical picture with the help of complex number. that is a suggestion that L, the orbital momentum, and S, the spin, may be the same thing. moreover, the mathematical structure of L and S are the same for s=1. can we find a counterpart of l=1/2???

[Pol. p target] laser duty 10%

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we did 10% laser duty. the result is no surprise.

since we employed Fourier Analysis, so, the Fourier spectrum has 2 peaks, separated by 60 kHz. the central frequency is 12.6 MHz.

[Pol. p Target] laser duty 5%

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my groupmate fixed the signal. it is probably the crystal angle.

thus, i continuous the laser duty 5% and done.

but before, i did not get large signal. and spent few hours on checking system. the problem is, the default FID area count from 1500 to 3000, not 800 to 3000.

the water resistivity of the laser is low. has a warning.

[Pol. p target] checking the Hall probe

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last week, we had measured the magnetic field against water NMR frequency. However, the magnetic field calculated from the Hall probe has 10% different from theoretical value. we think that it may be due to the position of the hall probe is not on the crystal site but lower, about 50mm. and the separation of the Helmholtz coil is 150mm.

thus, we take out the crystal, and replace it with another hall probe. we found that the magnetic field was much closer to the theoretical value. Although it is closer, and the different is 0.0038 Tesla to the theoretical value. which is 1% to 2% error. Thus, we think this error is due to the horizontal position.

[Pol. p target] Principle of magnetic field optimization

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the Hartmann-Hahn Condition is:

\sqrt{ (\gamma_e H - \omega_{\mu w})^2 + P_{\mu w} \gamma_e^2 } = \gamma_p H

since we fixed the microwave power and frequency, the only parameter to change is the magnetic field. the solution of the magnetic field.

since, changing the magnetic field will also change the Larmor frequency of the proton and affect the pulse frequency of the NMR system. Thus, when changing the magnetic field, we have to find out the corresponding Larmor frequency to determine the NMR pulse frequency.

we first, measure the proton in water, since the proton can be regarded as free proton, and the Larmor frequency can be measured in high precision. the method we are used,

  1. set the NMR frequency in 12.2MHz, 12.4 MHz, etc.
  2. change the magnetic field such that the NMR signal is pure decay without any oscillation.

after acquire the data, we set the magnetic field and NMR frequency on crystal sample polarization.   there is only 1 magnetic field satisfy the Hartmann-Hahn condition and get a maximum polarization and NMR signal.

Note, the crystal field will broaden the peak of Larmor frequency, but the broadening is not shifting the center.

 

[ Pol. p Target ] Finding 90 degrees pulse

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we believe the system is good and reliable now ( the error may about 40 units ). i first checked the signal by changing nothing. i obtains a similar signal strength. thus, i start to change the NMR pulse duration from 0.5µs to 9µs.

the result is good and agree with the fitting curve.

When I depolarize the 1.5 or 1.6us are the 90 degree pulse, the 1st depolarization (the 2nd
measurement) makes the signal go to BG. And 2nd depolarization also BG. Thus, All longitudinal
polarization rotated to traverse polarization.
The last thing is, I fit the curve during experiment and use the fitting curve to predict the FID
area. And the prediction is close to the result. :D

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