A Brief History of the Electron’s Shape – Part 3: How My Small College Measured the Electron’s Shape

When we left off last time, we were in the middle of a drought: over two decades of no improvement in the upper limit of the electron EDM from that found by the last of the cesium beam experiments in 1968:

3 \times 10^{-24}~e\cdot cm

This was not a bad number at all. In fact, using the classical electron radius (3\times 10^{-15} m) for the “size” of the electron, if we blew up the electron to the size of the Earth (i.e. multiplying it by 10^{21}), we are looking for asymmetries with millimeter precision!

It’s quite interesting to ask why there was not much activity in this field from 1970-1990. During this time, the Standard Model of particle physics was still actively being solidified, both theoretically and experimentally; for example the J/psi meson, which gave vindication to the theory that quarks exist, was only discovered in 1974.  In the 1980s, experiments found the existence of the W and Z bosons, which are responsible for mediating the weak force. But nothing much happened for tabletop experiments looking for the electron EDM. (The search for the neutron EDM, on the other hand, looked pretty active throughout this era.) But there was one professor in a small college who would eventually restart this trend…

Amherst College resurrects the search for the electron EDM

Strictly speaking, the 1989 electron EDM result at Amherst was not the first result in 20 years. In 1987, an experiment at the University of Washington obtained an upper limit on the mercury EDM, which turned out to imply an upper limit on various fundamental particles such as the electron, proton and neutron. But it only improved on the 1968 limit by a factor of 2, to 1.5 \times 10^{-24}~e\cdot cm. On the other hand, Larry Hunter’s Amherst experiment improved on the 1968 result by a factor of over 40.

As a disclaimer of sorts, Larry Hunter was my research adviser and professor who first introduced me to precision measurement, research and even college-level physics in general (my first physics class at Amherst was taken under him). Although Amherst is an excellent liberal arts college, it does not have graduate students to power its research labs. College students stay on an experiment for at most one or two years, rarely acquiring truly in-depth expertise. Sometimes there were funds available to support a postdoc, but funding in general was also tight compared to a major university lab. Larry often described to me that his strategy was to find a niche which was not (yet) popular in the field, but still good science. Only then can you avoid being out-competed by labs at larger universities. And in this case the opportunity came for a new measurement of the electron EDM.

This measurement was also done using cesium. But instead of using a beam, it was done in glass cells filled with cesium. By using a cell, one is able to examine a larger number of cesium atoms at once, directly boosting the statistics. (It’s also practically much easier and more compact compared to a beam, as you don’t have to setup a vacuum chamber.) But this only works if the collisions of the atoms with the glass walls of the cell don’t scramble the spin orientation of atoms (we call this the relaxation time), severely degrading the quality of the data. So the cells need to be carefully made, often with special wax lining in the interior to prevent this scrambling.

An additional tidbit: during my time at Amherst, while my research had nothing to do with electron EDMs, I got to use the same magnetic shields that was originally used by the Cs electron EDM experiment, 25 years before:

My old test setup for my senior thesis at Amherst College. In the background are the cylindrical shields originally used to shield the Cs EDM experiment from the Earth’s and stray magnetic fields.

Differential measurements to the rescue…again

The way the experiment works is similar to that of a Cs beam experiment which we have already encountered many times in this series. A cell filled with cesium atoms is immersed in an electric field. Lasers, tuned to an energy transition of Cs, are shone onto the cell to make the spins of the atoms all pointing along one axis (x), while the electric field is pointing perpendicular to it (z). If the electron EDM exists, it will cause the atoms to precess a little bit away from x towards y. When one reverses the direction of the electric field, the direction additional precession will be reversed. Thus by subtracting the two results, we can isolate the contribution of the electron EDM (there could be other things causing precession as well).

A clever strategy to reduce noise is that the Hunter experiment used two cells instead of one, stacked on top of each other. Opposite electric fields were applied to the cells by holding the center electrode at a non-zero voltage and the two outer electrodes at ground (0 V). An assumption was made, that the two cells roughly experience the same stray magnetic fields, if there exist any (usually there are some residual fields from the Earth’s field, or various magnetic things around in the lab).

A diagram of the arrangement of cesium cells in the Amherst experiment.

The idea was that if there were stray residual magnetic fields, they would cause additional precession in the same direction in the two cells. But because the electron EDM is always aligned with the electric field, the precession caused by the electron EDM would be opposite to the direction of the magnetic field in one cell, and parallel to it in the other one:
\phi_{top} = \phi_{B} - \phi_{EDM}

phi_{bot} = \phi_{B} + \phi_{EDM}

Thus by subtracting the two, we can isolate \phi_{EDM}:

\frac{1}{2} \phi_{bot}-\phi_{top} = \phi_{EDM}

This is again, another example of differential measurements being used to eliminate noise in a precision measurement experiment, a topic that I have covered before with regards to the ACME experiment. Of course, the assumption that the magnetic field experienced by the two cells are the same (field homogeneity assumption) is not perfectly true, so it

Final results

The Amherst EDM experiment again found that the electron is perfectly round:

|d_e| \leq 7 \times 10^{-26}~e\cdot cm

It improved on the Washington bound by a factor of 21, or a factor of 42 on the 1968 Sandars bound. The experiment had several systematic limitations, the two major ones of which was that the electric field was not perfectly reversed (as I depicted in the above diagram), and stray current could leak between the top and bottom electrodes, causing the presence of a magnetic field that resulted in additional precession.

Only about a year later, this limit would be overcome by the Berkeley thallium experiment under the direction of the great Eugene Commins, Larry Hunter’s former PhD adviser. Alas, Amherst was never to become the world leader in the measurement of such a fundamental quantity. But for a brief moment over three decades ago, a small college in Western Massachusetts was the world leader in the measurement of a quantity which is today being measured independently by at least four different labs in major universities.1

  1. The four active electron EDM experiments are Harvard-Yale-Northwestern (ThO), JILA (Hf+, ThF+), Imperial College (YbF), University of Groningen (BaF), and Caltech (YbOH). Other groups in Penn State, University of Texas, Lawrence Berkeley National Lab, and YbOH have been or will be pursuing similar experiments.

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