As you perhaps know, or recall from previous posts of mine, entanglement is a phenomenon which is at the heart of quantum physics and distinguishes it from our everyday world. Objects that are entangled behave, in a sense, as if they are a single entity even when separated and manipulated independently. Entanglement can improve measurement precision, e.g. the precision of atomic clocks, and it enables quantum computing.
Usually we talk about entanglement between two particles, considering some property that each particle has. For example, the energy state of an atom here might be correlated with the energy of an atom in another location, such that the two atoms are entangled. But there doesn't actually have to be two particles to create entanglement. One is enough.
If we shine light on a half-transparent mirror, half of it will go through, and half of it will be reflected. So we get two beams of light, going off in different directions. If we send a single photon (a particle of light) towards the mirror it can also get transmitted or reflected. So if we put some cameras in the path of the transmitted or reflected light, which measure whether the photon arrives, we will find a correlation: When a photon is detected in one camera, nothing is detected in the other, and vice versa. If we repeat the experiment, sometimes the photon arrives in one camera, sometimes in the other. We don't know in advance which one it is going to be, but always exactly one camera clicks. This looks like a simple correlation, but quantum mechanics tells us that it is actually something more intricate. When the photon hits the mirror, it doesn't simply either go through or get reflected. Instead, we get a so-called superposition of these two possibilities. Nature doesn't decide which possibility is realised until we make a measurement (for example with the cameras), even though this may happen much later than the photon hitting the mirror.
So, considering the two paths after the mirror, we have a superposition of two possibilities: There is a photon in the path on the right of the mirror and none on the left (say), or vice versa. This looks very similar to entanglement. Entanglement between two atoms happens, for example, when we have a superposition where the first atom has a high energy and the second a low one or vice versa. However, now there is just one particle, and it is not a property of the particle that changes (such as the energy), but instead whether the particle is there at all or not, in a given path. Is this entanglement?
This question was debated for quite a while in the past. By now, it is well established that in the case of photons (light), the answer is 'yes', and in fact this entanglement is useful for applications, for example ultra secure cryptography. We call this kind of entanglement 'mode entanglement'. In the example above, each path is a 'mode' which can contain different numbers of photons, and the two separate paths are the objects which are entangled. These are not two particles - instead the number of particles provides the degree of freedom in which the paths are entangled.
So the question is settled for light. What about other particles? What about electrons?
It turns out that for electrons, the question is more subtle and the debate is still ongoing. The thing is that to reveal the entanglement, it is not enough just to measure whether the particle is there or not in each path. One needs to also do 'in between' measurements, which require the creation of superpositions of zero or one particle locally in the path which is measured. This is ok for photons - it's not easy, but there is nothing in principle forbidding such superpositions, and we can do measurements which are not quite optimal but good enough. But for particles with electrical charge - such as electrons - the situation is different. As far as we know, superpositions of states with different total charge cannot exist (this is known as the superselection rule for charge). So in particular, superpositions of zero or one electrons are ruled out, and it is unclear if it is possible to do measurements which will reveal mode entanglement for charged particles.
In this paper, we argue that the answer for electrons is also 'yes'. We propose an experimental setup, which uses single electrons split on a kind of electronic mirror, in an analogue way to how a photon would be split on a mirror for light. In our setup, the entanglement created by the splitting is revealed without breaking any fundamental principles. We need to use two single photons at the same time, split on two separate mirrors. However, while two electrons are involved, we show that the result we obtain would be impossible unless each split single electron creates an entangled state. So, we conclude that single-electron entanglement indeed exists and is observable.
It will be interesting to see the reactions to this paper. Whether our colleagues will be convinced or not. And if they are, whether someone is up for doing the experiment :).