You may be familiar with matryoshka dolls: nested sets of painted figurines that fit within painted figurines. In the case of wooden dolls, the concept is pretty straightforward: hollow out a large bit and fit smaller bits in. You might think that doing the same thing with atoms is kind of tough. Yes, atoms are mostly space, but they are kind of difficult to hollow out. And, convincing another atom to enter the empty space (and make itself smaller) seems an impossible task.

Yet, this is kind of what a group of researchers has done. They created a crowd of very cold atoms; within that crowd, they took a single atom and convinced one of the electrons to orbit at a very large distance. Pairs of atoms kind of fell into the gap between that electron and its nucleus. And there they sat, trapped between an outer shell of a fast-orbiting electron and a hard wall of the inner electrons and nucleus. It's not quite a matryoshka doll—all of the trapped atoms sit together in the gap, not inside each other—but it's an impressive approximation.

So, how did the researchers manage this feat of atomic woodwork? To get a grip on that, we need to introduce three concepts: the Bose Einstein Condensate, which forms the crowd of very cold atoms; a polaron, which is the mechanism that traps the atoms inside the outer shell of the doll; and finally, Rydberg atoms, a way to make an atom very large and very empty.

I don’t know what a Rydberg atom is, but I’ll take two of ’em

To put the above in technical terms, the researchers took a nice, relaxed Bose Einstein Condensate, dropped a Rydberg atom in it, and watched the whole lot bounce around excitedly in response.

A Rydberg atom is an ordinary atom with one electron that has an awful lot of energy. Negatively charged electrons are held by an atom because they are attracted to the positively charged nucleus. The trapped electrons are all stacked in order of energy (I'm ignoring all the other properties, which make the stack more interesting). This stack is basically the same for all atoms: there are an infinite number of possible energies, all of which are still below zero, and an energy above zero indicates that the electron is no longer bound to the atom. The trick is that as the gap between each layer in the stack gets smaller and smaller the more energy you have.

A laser with exactly the right color can excite an electron from somewhere near the bottom (so, maybe around the fifth layer in the stack) up to something like the 30th through 150th layer in the stack. These electrons are barely bound to the atom. Their energy is so high that they have circular orbits, almost like planets, at a large distance from the nucleus. These Rydberg atoms can have a radius as large as a micrometer, about a thousand times larger than their normal size.

The space between that excited electron and the rest of the electrons is empty, but, normally, other atoms will not fall into the gap. They could pass through, or their passage might cause the electron to fall back to its normal position in the stack. They usually won't remain trapped inside with everything nice and stable, however. To get that, you need atoms in a special state, called a Bose Einstein Condensate.

Let’s stay on the same wavelength

A Bose Einstein Condensate is a special form of matter that relies on a peculiarity of quantum mechanics. In the quantum world, you can either be a boson or a fermion. Almost everything around us is made up of fermions: electrons, protons, and neutrons are all fermions. Particles like photons, on the other hand, are bosons. The important difference between fermions and bosons is how they behave when they are brought close together.

When you brace yourself and try to look into the mind of a physicist, what you will mostly find is "????" overlain with a patina of useful laziness.

To understand the difference between fermions and bosons, we need to think of the wave-like properties of particles. The wave holds the probability of finding a particle, and, as the particles approach each other, the waves of the two particles start to overlap. That means that the probability of finding both particles in the overlap region is proportional to the sum of the two waves there. For fermions, the size of the wave in the overlap region gets smaller as the particles approach each other; instead, the wave grows in the non-overlapping region. This means the two particles avoid each other.

For bosons, exactly the opposite happens: the sum of the waves in the overlapping region increases, and the particles seem to race together into a fierce embrace. When a large group of bosons gets together, they can, with some encouragement, all end up in exactly the same quantum state and behave as if they are one single particle. A nice analogy might be going to a concert. Once the music gets going and the crowd warms up, they form a single group: the concertgoers give up their individuality to lose themselves in the music.

When atoms are bosons (fermions, which make up atoms, can be combined to form a boson), they can cool down to a cloud of atoms that holds itself together. Although the atoms are not physically close to each other, they won't repel each other when they do get close.

These are atoms that can sit gently within the radius of a Rydberg atom without necessarily disrupting it. But that isn't enough to trap them within the Rydberg atom. To do that, we need to think about how the atoms from the condensate respond to the outermost electron. To understand that, we need to delve into the sordid world of quasiparticles.

Not all attractions are fatal

When you brace yourself and try to look into the mind of a physicist, what you will mostly find is "????" overlain with a patina of useful laziness. There is no better demonstration of that than the world of quasiparticles. Quasiparticles are not particles in the normal sense of the word, but they are groups of "stuff" that, together, behave like a single entity. Within this pantheon of pretend particles, we will find the polaron (the one with dark hair, just to the left of the angry exciton).

Imagine a solid crystal. All the atoms are spaced at regular intervals, and everything is electrically neutral. Now, we drop an electron into the crystal. The electrons around the atoms recoil from the intruder, leaving a slight positive charge surrounding it. This movement effectively screens the rest of the crystal from the new electron's intrusive negative charge.

Now, as the electron moves, the atoms that it leaves behind relax, while those in front start to distort themselves to maintain the screen. The relaxation and distortion generate sound waves that travel with the electron. So, we end up with an electron, traveling in a shell of sound waves, all of this behaving like a single entity that we call a polaron.

That is a free polaron. But there are also trapped polarons. Imagine the same situation: an electron is dropped into a neutral crystal. The electrons around the atoms recoil, surrounding the electron with positive charges. The electron slows until it can only vibrate back and forth in place. As it vibrates, the surrounding atoms also vibrate, emitting sound waves through the crystal. Again, it looks like a single particle consisting of a charge and sound waves but bound to some point in the crystal.

Unscrewing the bolts and examining the nuts

So the process involved in creating atoms-within-atoms looks a bit like this. The researchers take a gas of atoms and cool them down until they form a Bose Einstein Condensate. At this point, the atoms are so cold that they are basically not moving and are spaced about 80 nanometers apart. After that, the researchers shine a very short burst of ultraviolet light through the condensate. The color and intensity of this light is chosen so that, in all likelihood, a single Rydberg atom is formed.

To the surrounding atoms, the orbiting electron looks like a solitary electron. The largest Rydberg atoms have electron orbits with a diameter on the order of a micrometer, which means that something like 160 atoms are within the orbit when the Rydberg atom is formed. The trapped atoms rearrange their electrons so that a slightly positive charge is facing the electron and a slightly negative charge is facing the nucleus. As the electron orbits, these atoms physically vibrate, emitting sound waves into the rest of the Bose Einstein Condensate.

You've trapped a polaron inside a Rydberg atom. All within a Bose Einstein Condensate.

If that has not blown your mind, the researchers can also see how polarons form little groups with each other within the Rydberg atom. Since the size of the Rydberg atom can be controlled, the researchers can also control the number and manner of polarons that are trapped.

For small Rydberg atoms, it is possible to see how the polarons are bound to the atom. For instance, polarons form pairs: both polarons are bound to the Rydberg atom, but, at the same time, they push each other about, forming a single unit. This works for groups of three and five as well. But as the number of trapped polarons increases, these discrete groups smear out as all the polarons push each other around.

It is easy to be pretty underwhelmed and cynical when you read scientific papers on a daily basis. A lot of results are similar or are (useful) extensions to previous work. You can, with sufficient coffee, appreciate the skill and the new knowledge without it really getting the blood flowing. This research is exactly the opposite: the new knowledge and skill take second place to the "they did what?" factor. Now, I need to go lie down for a while.

Physical Review Letters, 2018, DOI: 10.1103/PhysRevLett.120.083401