The transition between classical physics and quantum physics is always fascinating. How does an object go from behaving in a deterministic manner to occupying the quantum world, where its activities are a matter of probability? At the boundary between the two, we cannot behave as if something is entirely classical or entirely quantum—rather, we need to treat it as a mixture of the two.

In a paper published in Physical Review Letters, researchers show that they can manipulate both the classical and quantum parts of a Rydberg atom with a microwave field. In the process, they get an electron to orbit in an almost predictable manner.

A group of researchers has been studying how to manipulate the states of Rydberg atoms. These are atoms with one electron excited to a very highly energetic state (see sidebar). In this state, an electron still has some wave-like properties, but it is also very much like a particle, in that it can really be thought of as orbiting the nucleus in a circular or elliptical orbit. So, you can think of a little cigar-shaped wave of "electron-ness" whipping around the nucleus of the atom at a fairly high rate.

Going down the rabbit hole of quantum mechanics An atom consists of a positively charged nucleus surrounded by electrons that are trapped by their attraction to the nucleus. In school, we often learn to picture this as a tiny solar system, with the electrons in fixed circular orbits around the nucleus. Such a picture is useful, but almost entirely wrong. Instead, you need to think of each electron as a wave that is spread out around the nucleus. It is, literally, everywhere around the atom once. And, as we add electrons to our atom, the shape of the waves the new electrons take on are different. Some are spherical in nature, meaning that the wave is evenly spread around the nucleus; while others are lobed so that the wave is more concentrated in some spatial locations and not in others. If we were to try and find an electron, we could; it would appear as a particle at some specific location. That would seem to contradict what I have just written, but there's a link between the two: the amplitude of the wave at a location dictates the probability of finding the electron-as-a-particle at that location. These electrons are also stacked in terms of energy. If you consider Neon, it has ten electrons. Two are paired up in the lowest energy, a spherically shaped shell, and two more are in the next shell. The final six are at higher energy, paired up and divided among three lobed shells. But the ten protons have sufficient attractive force to hold on to electrons at higher energies than those in the outermost shell. Indeed, every atom has empty energy levels hanging around like family members at the death of a rich uncle. Because the energy gap between each energy level gets smaller with each step up in energy, there are, in principle, an infinite number of energy levels—though the energy required for an electron to escape the atom remains finite. It is possible to excite an electron into these upper levels, creating a Rydberg atom. When they are excited to these higher energy levels, electrons are rather interesting. They are still confined, so they have wave-like properties. But the wave isn't initially spread out around the entire shell—instead, it is localized in a wave packet that orbits the nucleus rather like a planet.

But this nice, clean situation doesn't last very long. In less than 100ns, the electron will either be gone from the orbit, or, if it's still in the orbit, the wave packet will have spread out, so the electron is effectively everywhere around the nucleus again.

What the researchers wanted to do is to see if they could keep the electron wave packet together to create an indefinitely predictable orbit. To do this, they illuminated the atom with microwaves with a frequency that coincided with the expected orbital frequency. In slightly more detail, the researchers create the Rydberg atom and shine a microwave on it for a fixed period of time, then kick the electron out of orbit and see where it hits a detector. By back-tracking, they could figure out where the electron was when it was kicked out. By running this experiment multiple times, they could figure out how predictable the electron's orbit is.

The experimental results show that, over the short term (about 50ns) the microwave field makes very little difference, and may even make things slightly worse. However, by 100ns, the electron wave packet is orbiting in a highly predictable fashion. And this continues indefinitely—the researchers stopped at a microsecond, inadvertently showing that scientists have an extremely limited attention span.

The explanation for this time dependence appears to be the due to the starting conditions. When the electron is kicked out of its normal state and into the very high energy state, it ends up at a random location, so the phase difference between the electron and the microwave field differs between experiments. Some time is then spent gently bringing the electron into phase with the microwave field, after which it stays locked to the microwave field and orbits the atom quite happily.

The researchers also showed that this locking process can be used to smoothly shift an electron from one energy level to another. They did this by first locking the electron to the microwave and then slowly changing the microwave frequency. This speeds up or slows down the electron wave packet (depending on whether you increase or decrease the frequency), shifting the electron from one energy level to the other without the loss of phase information. This process, called an adiabatic passage, is quite a common theoretical technique, but is often difficult to pull off experimentally.

This is really a paper about control rather than anything else. Rydberg atoms are a simple model system for testing quantum mechanics over a range of energy scales. With this research, we have gained an extra knob via which we can tune interactions between Rydberg atoms. It may then be possible to translate findings from these experiments to more applied systems.

Physical Review Letters, 2012, DOI: 10.1103/PhysRevLett.108.043001