Saturday, May 18, 2013

Some Quantized Flux History

In  1961, William Fairbank and Bascomb Deaver experimentally verified that magnetic flux can be quantized.  This week I read an excellent paper on the history of the experiment[1].  For those who aren't close to a library with access to the journal, (and for my own notes), here are a few of the highlights.  For more info on the Fairbank/Deaver experiment see[4] .


The Other Experiment
The first interesting thing you should know is that there was a similar experiment  performed in Southern Germany by Robert Doll and Martin Näbauer in the same year, (1961)[2].  Their apparatus was different,  instead of  vibrating a superconducting cylinder to determine the value of the magnetic field at had trapped as Deaver and Fairbank did, they used a superconducting cylinder attached to a torsion pendulum (picture 1).  By measuring the amount of time it took the oscillations of the pendulum to die off they were able to determine the strength of the trapped magnetic field.  Their results showed the same stepping of trapped flux that the Deaver/Fairbank experiment did.


The two experimental groups knew nothing about each others efforts until the representatives of each experiment met at the IBM meeting on superconductivity in  Yorktown Heights, NY.

The Theory Connection
Nina Byers and Chen Yang, (of Yang-Mills fame), were working down the hall from Deaver and Fairbank while they were working on their experiment.  The two theorists studied the results of the experiment and wrote up the theoretical explanation in an article that immediately followed Deaver and Fairbank article in PRL[3].  When Fairbank showed preliminary data of the quantized flux plateaus to Chen he thought the data set was jut linear in the manner that might be expected if flux wasn't quantized.  Fairbank explained to him that having taken the data he felt the experimenter could attach a sort of personality to each data point and almost subconsciously analyze the validity of each point.  The completed data set at the end of the experiment bore out Fairbank's initial impressions.  Byers and Yang are pictured below (picture 2).



The Cooper Pairs
Kind of surprisingly, from a modern perspective where Cooper pairs are a given, there was a contingent of physicists that felt the results didn't show quantized flux because the flux steps were twice as big as predicted by London.  What Byers and Yang had already pointed out and others were quick to reinforce was that the result made perfect sence because the charge carriers in the superconductors were Cooper pairs.  The BCS theory of superconductivity, (C stands for Cooper), published in 1957 had predicted that the charge carriers in superconductors were actually pairs of electrons, (Cooper pairs). In addition to verifying that magnetic flux could be quantized, the two experiments had also provided evidence of the hypothetical Cooper pairs.


References:
1.
http://dx.doi.org/10.1007%2Fs10909-011-0349-x
Einzel D. (2011). 50 Years of Fluxoid Quantization: 2e or Not 2e, Journal of Low Temperature Physics, 163 (5-6) 215-237. DOI:

2.  Doll and Näbauer experiment
http://dx.doi.org/10.1103%2FPhysRevLett.7.51
Doll R. & Näbauer M. (1961). Experimental Proof of Magnetic Flux Quantization in a Superconducting Ring, Physical Review Letters, 7 (2) 51-52. DOI:

3.  Bauer and Yang
http://dx.doi.org/10.1103%2FPhysRevLett.7.46
Byers N. & Yang C. (1961). Theoretical Considerations Concerning Quantized Magnetic Flux in Superconducting Cylinders, Physical Review Letters, 7 (2) 46-49. DOI:

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