A shorter introduction to the ACME EDM experiment can be found here.

In the first introductory post of this series I outlined the immense precision of the ACME experiment in measuring the electron’s “shape.” A natural followup question is, how did we do that? In this post I will outline the basic measurement scheme in our experiment in the most general way possible, avoiding most of the technical physics jargon. The next post after this will get into the more gory technical details, but this one should hopefully be an understandable, but still mostly accurate and insightful explanation on how we do what we do. I will refer to the incarnation of the experimental apparatus which was used in the 2014 measurement as ACME I, whereas the current incarnation (with various improvements) is called ACME II. I will explain mostly the features of the ACME I experiment, although at this level the two generations are not very different.

Electron Shapes and Asymmetry

So far I’ve been saying that we’re measuring the electron’s “shape.”¹ But really, what we’re measuring is the electron’s electric dipole moment. I will not go into detail of what a dipole moment here is here. For now, it’s sufficient to just think of this as a vector quantity having a magnitude and direction, $\bf{d_e}$ . In our extended (and admittedly imperfect) analogy about the electron’s “shape,” if that shape had a slight bulge or asymmetry, it would manifest itself in a non-zero value of $\bf{d_e}$ . If we put our asymmetric electron in an electric field $\bf{E}$ , then that would result in an energy shift, which is nice because physicists like to think of things in terms of energies:

$H' = \bf{d_e} \cdot \bf{E}$ .

$\bf{d_e}$ is typically measured in units of $e \cdot \textrm{cm}$ , and electric fields are in units of $V/cm$ , so $H'$ has units electron volts (eV), which is an energy unit,² so this makes sense. In other words, to look for this asymmetry, we want to put an electron in an electric field and observe its behavior: we want to see if there’s an energy shift $H'$ which would come from this asymmetry, as expressed in the quantity $\bf{d_e}$ . Notice that if we increase the strength of the electric field $\bf{E}$ , then the overall energy shift $H'$ also gets bigger and easier to find.

This is literally what we do in our experiment: we are taking electrons and putting them in an electric field. Crudely speaking, we prepare our electrons using lasers and other contraptions, launch them through the field, and then interrogate them after they’ve passed through the field, observing how much they’ve “changed” as a result of this field. We can then narrow down to see whether they’ve changed more than we expected them to. If that’s the case, then that would be evidence that $\bf{d_e} \neq 0$ and thus the electron is asymmetric. In a nutshell, that is what we do in the ACME EDM experiment.

Riding a Molecule

However, it turns out that it’s not that easy to physically realize $H' = \bf{d_e} \cdot \bf{E}$ in the real world. The $\bf{E}$ part is easy: we can produce a relatively uniform electric field by putting two flat parallel plates a set distance from each other.

Two flat plats at opposite voltages, creating a uniform electric field between them - this is literally how we produce our electric field in the lab. It is the same as the common problems you encounter in high-school level electromagnetism physics problems. — Two flat plats at opposite voltages, creating a uniform electric field between them – this is literally how we produce our electric field in the lab. It is the same as the common problems you encounter in high-school level electromagnetism physics problems.

The $\bf{d_e}$ part is the hard one: it’s hard to put a single electron in an electric field. They’re so small (as we mentioned last time, at least a billion times smaller than a human hair) and typically we find them as part of other atoms and molecules, orbiting the nucleus.³ Even if you could get a lone electron, putting them between a pair of field plates like the figure above will only result in them crashing into the plates, because an electron has charge. So instead of trying to take lone electrons, we take a molecule which has some electrons (two to be exact) in its outermost shell, and put that in an electric field. See the figure:

A cartoon of thorium monoxide (ThO), a two-atom molecule with an electron orbiting around it that we can use to measure the deformation of the electron in general.

(The green lines with arrows depict the powerful internal electric field that that the electron experiences when ThO is subjected to an external electric field in our lab.) By some theoretical calculations by theoretical atomic physicists, we are able to deduce $\bf{d_e}$ from our observations of $\bf{d_{ThO}}$ , the electric dipole moment of our molecule (in this case thorium monoxide, or ThO).

This act of using a molecule has an additional great benefit: it turns out that an electron orbiting a nucleus experiences an amplification of the electric field we apply in the lab. We call this $\bf{E}_{eff}$ , or the effective electric field. So we would be measuring

$H' = \bf{d_e} \cdot \bf{E}_{eff}$ ,

and a larger $\bf{E}_{eff}$ results in a larger energy shift $H'$ = easier measurement and better precision. It turns out that the larger the atomic or molecular nucleus that the electron is orbiting, the stronger the amplification of the electric field. In our case, we use thorium monoxide: thorium has an atomic number of 90, one of the highest of all stable elements in the periodic table. This results in an $\bf{E}_{eff}$ that is a billion times larger than the electric field we apply in the lab. This is very convenient as there are practical limits on how strong of an electric field one can generate in a laboratory without complications – typically on the order of a few thousand kilovolts per centimeter. In comparison, to get a bolt of lightning to strike you need a potential difference of several hundred million volts between the sky and the ground – about 10 kV/cm. (In other words, if you try to generate a field that strong in a room without vacuum isolation, it will likely result in arcs of lightning between the field plates, which is bad.)

Thus by using ThO, we only generate an electric field of a few tens of V/cm for our experiment, yet the effective field experienced by the electron in the molecule is a billion times stronger. That’s a very large gain for our precision. Indeed, historically speaking, finding good molecules that have a large $\bf{E}_{eff}$ has been a critical first step in designing an experiment finding the electron EDM. There are other equally important reasons why we chose ThO as opposed to other molecules (which I shall get into eventually), but this large effective field is one of the most basic and important criteria.

A Beam of Molecules and an Electric Field

So we start our experiment by producing our thorium monoxide (ThO) molecules. This is done inside a vacuum-sealed box or cell, where a solid target of ThO₂ sits inside. A high-powered laser (an Nd:YAG laser outputting about 10 watts of 1064 nm light) blasts the target in short pulses, almost magically creating molecules of just ThO (with one oxygen), a process called ablation. The cell has a small hole through which the molecules spray out as a beam into the rest of the experiment.

Besides ThO, we also put in neon gas inside the cell, and the whole cell is cooled to a very low, cryogenic temperature of 16 K (-257 degrees Celcius). This neon gas is a buffer gas – it helps to cool down the ThO molecules in the cell, lowering the speed of the molecules as they come out of the cell. The result is a relatively well-controlled beam of molecules with an average velocity of about 185 m/s (666 km/h). This is “slow” by atomic physics standards, although it takes the molecules only several tenths of a second to traverse through the entire experiment! These molecules progress from the hole through the stem, which is what we call the airtight cylindrical pipe that provides a path for the molecules through the rest of the experiment.

However, one thing to remember is that like light coming out from a hole, the molecules are diffracted outwards – they “fan out” with a non-zero solid angle. The further away the beam travels, the molecules are further away from each other. This is not ideal, as many of them start crashing into the walls of the stem, rendering them useless. In fact, in the first generation of the experiment only about 1 in 20,000 molecules ultimately reach the interaction region where the actual measurement itself is performed. As our sensitivity is proportional to the square root of the number of molecules, this directly affects the precision of our experiment. The more molecules you have, the more times you can repeat the measurement, and the more precise the result is.

After the cell, the molecules go through the rotational cooling stage which I will explain in more detail in a future post. Essentially, to make it possible to use the molecules for a measurement, we have to get them to a specific quantum state. This is done by using laser light of specific colors,⁴ but the process is limited by some natural restrictions that make it less efficient. Rotational cooling manipulates the atoms using lasers to make it possible to later transfer more of them into the state we want. The actual transfer into the desired state for the measurement is done in the state preparation stage, where a different technique⁵ is performed to get as many molecules as possible from the ground state (the natural, default state of the molecules which we call the $X$ state), into something we call the H excited state of ThO, which is the quantum state the molecules need to be in to perform the measurement.⁶ State preparation is also important in that it immediately transforms an incoherent jumble of molecules in various different states into a smaller but more uniform population that we can examine as a unified body.

The Actual Measurement: Spin Precession

The molecules are now ready to be put into the interaction region, where the measurement happens. There, we apply an electric field to them using a pair of parallel flat metal plates which are held at a distance of several cm from each other (see the first figure in this post). If $\bf{d_e}$ is really non-zero, then here it will do its work and leave its mark.⁷ What happens to the molecule as it goes through this region is something called a spin precession. You can imagine this as similar to the precession of a top, only instead of a top, there is a similar vector quantity in the molecule called spin that precesses (rotates in orientation) as you keep applying an electric field to it.

A cartoon diagram of what roughly happens in the interaction region, where a pair of field plates apply an electric field that causes spin precession as the ThO molecules go through it.

are ready to be interrogated, again using a different set of lasers – the probe lasers. The probe lasers stimulate the molecules to get into a different, higher excited state – we call it the $C$ state.⁸ This state is naturally more unstable, such that after a very brief period the molecules decay back into the ground $X$ state. As they do this, they release energy in the form of green, 512 nm light as they do so. This is the light we detect using photo-multiplier tubes (PMTs), which are essentially black-and-white cameras. The input from the PMTs are sent to a computer as data to be processed and analyzed. Having finished their use, the molecules continue their journey out of the interaction into the “beyond” – they eventually crash against the other end of the stem, never to be seen from again.

The entire above journey of a molecule takes only about 3-5 thousandths of a second. Every time the ablation laser fires into the target, as many as 100 billion molecules are produced, but only about 100,000 (in ACME I) survive the journey to the interaction region. Many are lost by crashing into the walls of the stem, while others are simply not in the right quantum state for the measurement. Even in the case of those which successfully undergo spin precession and get interrogated by the probe beam, only 1% of the photons produced are detected due to ineffiencies in our detection scheme – resulting in only 1,000 photons detected per pulse of molecules.⁹ The ablation laser fires every 50 ms, or 20 times a second. Typically, we take and average data for about a week before we reach a precision good enough for a “result”. Technically, at this point one would be able to figure out if indeed $\bf{d_e}$ is zero or not – thus potentially making a discovery!

However, this is not the end of the story. It turns out that there are various stray effects in our experiment that can happen, causing additional spin precession that masquerades as a non-zero value of $\bf{d_e}$ . These are called systematic errors. The bulk of our time is actually spent testing and looking for these errors. We change various settings in our experiment, especially settings which we think shouldn’t have an impact on the measured value of $\bf{d_e}$ . For example, we can turn on additional magnetic fields, change the intensities of our lasers, or do even seemingly trivial changes such as moving our lasers to the opposite side of the room and shining them at the molecules from the other side. In many cases, we would not expect a change in the measured EDM value, yet sometimes we do. If that happens then we have to find out why that setting is causing the change, and possibly remedy the condition before releasing our result.

Closing Remarks

Thus is the entire process by which we perform a measurement of the electron’s shape, or $\bf{d_e}$ , as physicists call it. It is a complex, multi-stage process involving multiple lasers, computers, and various equipment to control pressures, temperatures, and voltages in the experiment. Three different experimental groups collaborate and are roughly responsible for different stages of the experiment. The ACME experiment is unique in that it’s an experiment small enough to be fitted in a single room, but is still many times more complex (and expensive) than the average atomic physics tabletop experiment. To become truly familiar with all aspects of the experiment, a graduate student would have to gain practical skills in building lasers, aligning optics, maintaining vacuum systems, assembling electronics, program computers, and configure data acquisition hardware and software, among other things. This is apart from the physics one has to know to truly understand the experiment: standard techniques in atomic physics with some additional complexities due to the fact that we have molecules, not atoms, plus a sprinkling of particle physics to be able to truly understand the theoretical context of the experiment.

For me, this is what makes the ACME experiment so exciting: we are building an extremely complex machine to measure just one quantity, but one which is so important that it can potentially unlock so many secrets about the nature of the universe! For more details on how exactly the shape of the electron is important and can do this, stay tuned!

This nomenclature was I believe first used by the Ed Hinds group in Imperial College when they first measured the electron EDM in 2011 and published their paper in Nature with that title. Incidentally, this is the measurement that we bettered 12 times in 2014. ↩
This is the same unit that is often used when describing the energy of collisions at the Large Hadron Collider or other large particle physics experiments, as well as the masses of new particles like the Higgs boson, which has mass of about 126 billion eVs. ↩
On the other hand, the Gabrielse lab where I work has as one of its greatest achievements in measuring the electron’s magnetic moment to unprecedented precision – the most precisely tested theory in all of physics, and perhaps all of science. This was done by trapping literally a single electron using a device called a Penning trap and observing its behavior. ↩
Color is determined by the wavelength of the light. Wavelength ( $\lambda$ ) is inversely proportional to frequency ( $\nu$ ) by the formula $\lambda \nu = c$ where $c$ is the speed of light, so they are interchangeable as terms. When I specify some color of light, I can immediately figure out what wavelength and frequency it is. ↩
In ACME I, the transfer was done using a standard atomic physics technique of optical pumping, whereas in ACME II we are using a different technique – STIRAP – which is over 10 times more efficient. ↩
Note that this is different from the $H'$ I used above for signifying the energy shift caused by the electron EDM, which is just short for Hamiltonian – a term synonymous with energy.) ↩
We apply a magnetic field as well, but strictly speaking this is not necessary for the measurement. ↩
In ACME II will be the $I$ state. But the mechanism is exactly the same otherwise. ↩
In ACME II, this number has been increased to over 300,000 photons per pulse. ↩