A Brief History of the Electron’s Shape – Part 2: The First “Golden Age”

Last week, we talked about how the pioneering papers in the 1950s and 60s of Purcell, Ramsey, and Sandars started off the decades-long search for imperfection in the electron’s shape, or the electron electric dipole moment (eEDM). This week, we’re going to cover some of the early beam experiments dedicated to measuring the electron EDM.

First, let’s get back to the plot of electron EDM measurement results versus time:

Now let’s focus on some of those red markers in the 1960s. Most of the experiments done in the 1960s used a beam of cesium (Cs) atoms.1 They were mainly performed by Sandars himself at Oxford and some competitors/collaborators at Brandeis University under the direction of Edgar Lipworth. We will focus a little bit more on this experiment in this post.

How to measure an EDM with cesium

Most experiments attempting to measuring an EDM in an atom try to do it by measuring the effect of an EDM on the energy levels of an atom. (I’ve covered the energy levels of an atom/molecule in a little bit more in detail in the past.) To put it bluntly, due to quantum mechanics, an atom can only absorb certain pre-determined, fixed amounts of energy. These levels reflect different ways in which the components of an atom can line up with one another. The components of an atom include electrons. If the electron is slightly non-spherical (meaning that it has a nonzero EDM), then this will cause a peculiar, tiny shift in the energy levels. Therefore, an experiment looking for an electron EDM in an atom only needs to measure the energy levels of an atom very, very precisely, since this shift is believed to be very small.

The experiment Sandars and Lipworth performed in 1964 consisted of a atomic beam of cesium, probably made by heating solid cesium in a vacuum-sealed oven and then making a small hole to let some of the gaseous cesium out. They then performed what is now known as Ramsey interferometry, an ingenious technique developed by Ramsey in the 1950s to measure small shifts in atomic energy levels. Such techniques are still the basis for cesium beam clocks today (which defines the second as a unit of time) and countless experiments in atomic physics. There isn’t space here to fully explain this technique, especially without assuming quantum mechanics. In a nutshell, Ramsey interferometry allows us to observe the effects of a tiny shift in the atom’s energy structure (induced by a tiny electron EDM). It works by applying the right sequence of a series of radio wave pulses tuned at the right frequency, allowing the atom to evolve in magnetic and electric fields in a way that magnifies the effect of the tiny EDM-induced shifts.

In his experiment, Sandars applied a mix of oscillating (AC) and constant (DC) electric fields. His team sampled a variety of different strengths of these fields. While the details of his detection scheme are pretty technical2 the detected signal was expected to have a linear (straight line) relationship with the value of the DC field. The signature of an electron EDM would be, among other things, a non-zero signal when the DC field was reduced to zero. If the EDM was zero, then the straight line would intercept the origin.

The first non-zero result?

So what did they find? The following is a plot of signal against DC electric field strength that Sandars and Lipworth obtained:

Plot of experimental results from Sandars’ 1964 cesium beam experiment.

We can see here the expected linear relationship between the signal and the DC electric field strength. As we can see (and I circled in red), the result was NOT zero! As the authors remark, the above is consistent with an electron EDM value of (2.2 \pm 0.1) \times 10^{-21}~e\cdot cm. 3 So did we actually already discover an electron EDM back in the 1960s?

The answer unfortunately, is no. Sandars and Lipworth, as good experimental physicists, were astute enough to notice that the frequency shift they saw could have been caused by imperfections in the experiment masquerading as an electron EDM. Thus began the history of systematic error detection, the hated old friend of precision measurement experimenters across all time! In this case, they cleverly saw that if the electric and magnetic fields applied to their experiment were slightly non-parallel to each other by even just half a degree, this would create an additional “motional” magnetic field that would result in a tiny energy shift large enough to explain the non-zero intercept in the above plot. The effect would depend on how fast the atoms were moving in the beam, but at the time they did not have the equipment to precisely pin this down.

Finally, to be conservative and staying on the safe side (a null result being less sensational than a non-null result), Sandars and Lipworth simply concluded that even if the electron EDM really was non-zero, it was no larger than (2.2 \pm 0.1) \times 10^{-21}~e\cdot cm. This became the new upper limit for the electron EDM, which was a massive improvement of 100,000 times compared to the previous experiments to measure it using scattering of helium.

The quest continues

Three years afterwards, Sandars and his group repeated the experiment, this time building an apparatus which was capable of sending beams of atoms in opposite directions. The idea was that if the detected non-zero result was due to some physical effect dependent on the atoms’ velocities, by comparing the results in one direction verses another, one could subtract out this effect. Sure enough, after this upgrade (as well as some other technical refinements to their detection method), they concluded that there was no significant remaining electron EDM, improving on their previous limit by an order of magnitude.

The rest of the 1960s was pretty eventful in terms of the electron EDM, seeing a series of similar cesium beam experiments by different groups (including at MIT) with increasing precision. Here is a list of the experiments which improved the upper limit on the eEDM on previous ones:

Year Location of experiment Upper limit on the electron EDM (e\cdot cm) Improvement factor over previous experiment
1964 Brandeis (Lipworth & Sandars) 2 \times 10^{-21} 100,000 (compared to non-beam experiments)
1966 MIT (Thornburg & King) 8.8\times 10^{-22} 25
1967 Oxford (Sandars et al.) 1 \times 10^{-22} 9
1967 Brandeis (Lipworth et al.) 2 \times 10^{-23} 5
1968 Brandeis (Lipworth et al.) 3 \times 10^{-24} 7

Thus, by the end of the 1960s, compared to Sandars and Lipworth’s initial 1964 experiment, the eEDM community had managed to improve the sensitivity of their experiments by 25 \times 9 \times 5 \times 7 = 8000 times within a decade! No EDM was found; the electron was still round. In the meantime, the real world saw the Civil Rights Movements and the ascent of the Beatles, among other things.

The drought

In 1970, the results of two new experiments using thallium and xenon were performed by Gould and Sandars respectively. While they were probably groundbreaking in using new species of atoms other than cesium to look for the electron EDM, they did not manage to improve on 1968 limit established using cesium beams. In fact, for the next two decades, no experiment would manage to improve upon this limit, showing that progress in precision measurement shouldn’t be taken for granted. Perhaps it was not simply a question of the experimental technology not being available, but also the fact that theoretical interest may have waned. Part of the impetus to look for the electron EDM (which would violate time-reversal symmetry) was driven by the 1964 discovery of charge-parity (CP) violation. But until the 1990s (and arguably to today), no more groundbreaking discoveries of violations of nature’s symmetries happened.4

The first substantial improvement would only occur in the new cesium experiment performed at Amherst College by my former professor Larry Hunter in 1989. Stay tuned for more details on this experiment and the “resurrection” of the electron EDM next time!

  1. The first beam experiment to measure the eEDM was technically done with rubidium (Rb) in 1962 by Earl Ensberg (a former graduate student of Hans Dehmelt) – see p. 577 of Dehmelt’s 1989 Nobel lecture here. However, no paper was published was for this result before 1967.
  2. Some more technical-minded people could have guessed (correctly) that the AC electric fields were applied in order to implement phase-sensitive or lock-in detection.
  3. Assuming a conversion factor of R \approx 100 between the electron and cesium EDMs, which we briefly covered last week. The actual factor is closer to 121, calculated more precisely a few years later.
  4. That being said, the Standard Model of particle physics did enjoy some great triumphs in this period, such as the discovery of the J/psi meson in 1974.

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