How can you tell a physicist from a normal person? If they ask "I wonder how small we can make a fridge?" instead of "Does that fridge hold enough beer," you're probably talking to a physicist. This is exactly the question posed in a recent Physical Review A paper. And the answer is about this big [holds thumb and finger really close together]. No seriously, it turns out that if you get it right, a fridge made from just a single quantum object, like an atom, is possible. Furthermore, while such a fridge can't get to absolute zero, it can get arbitrarily close.

So how do you make such a fridge? Let's imagine we have two atoms that are slightly different from one another, so that they have different excited state energies. Specifically, atom 1 (to be cooled) has an excited state with lower energy than atom 2. Now, at any given temperature, we are more likely to find atom 1 in an excited state than atom 2. So, what we do is apply a series of light pulses that swaps their states, no matter what state they are actually in. Thanks to the probabilities involved, we are more likely to have cooled atom 1. Atom 2, now excited, dissipates its energy by radiating into space. You have now cooled atom 1.

But all this playing with light and adding energy through light pulses just goes against the grain. And besides, if these sorts of refrigerators are to play any role in, say, nanotechnology or biology, then they must be able to work by using the energy that surrounds them rather than waiting for the right dude with the right laser to turn up and help things along.

Getting rid of the lasers

To investigate other options, Linden and coworkers, from the University of Bristol, changed the model so that it included three atoms that have slightly special properties. Atom 1 is to be cooled, atom 2, with slightly different energy levels, is sitting next to it. Atom 3 is connected to a thermal bath with a higher temperature than the bath that atom 2 and atom 1 are connected to.

The energy required to get to the excited state of atom 3 is equal the difference between the energy required to excite atoms 1 and 2. Now, we have two possible states with equal energy: exciting atoms 1 and 3 takes the same energy as exciting atom 2. And, because atom 3 is connected to a higher temperature bath, the most probable state is for atom 1 and atom 3 to be excited.

The cool (pun intended) part of this is that the operation to swap from atoms 1 and 3 being excited to atom 2 being excited is a natural interaction between quantum states, since the net energy difference is zero. In other words, the swap will spontaneously happen all the time. So, the system is most likely to start with atom 1 excited, but transfer that energy, along with some energy from atom 3 to atom 2. Now, atom 2 is free, and indeed likely, to radiate its energy out into space, leaving atom 1 cooler than it was before.

This is a fridge that runs on a natural temperature difference in a two-atom system—the higher temperature of atom 3 drives the system to cool atom 1 and heat atom 2—but it requires a three-body interaction. That is, atoms 1, 2, and 3 all have to swap states simultaneously, which is unlikely. So Linden and co-workers went further and tried to find a situation that would work with much more likely two-body interactions.

Getting rid of an atom

Again, we have atom 1, which is feeling the heat and needs cooling off. Atom 3 is identical to atom 1, but is in contact with a higher temperature bath. Atom 2 now has two energetic states; in the higher state it has the same energy as atom 1 and 3 in their excited states. So we have the possibility of energy exchange back and forth, where atom 2 absorbs two quanta of energy: one each from atom 1 and 3. This cools atom 1 and, because there is an intermediate state available, these can happen sequentially. That's much more likely than the two occurring simultaneously.

It also turns out to be possible to make atom 2 play the role of the entire refrigerator, as long as it is at a higher temperature than atom 1 and able to dissipate energy from its highest excited state into the environment. So, there you go: the smallest fridge consists of one quantum object with three states. And, inside it, are the world's smallest bottles of Grolsch.

What is required for this to work? First, atom 3 needs to have good coupling to the bath: it needs to regularly absorb quanta of energy to keep it in an excited state. Second, atom 2 also needs good coupling to a bath, as this is the atom that dissipates the heat from atom 1 and atom 3.

But there's more. Since I have published work that has involved "special" states, I will be the first to throw stones: THE THREE ATOMS ALL NEED SPECIAL STATES. That's really, really hard to arrange, so this example would seem to be confined to theory.

But let me a bit more specific about that, because it probably isn't that big a problem. I have used the example of atoms, but really, any quantum object will do. But these quantum objects need to have carefully matched energy states so that unidirectional energy flow is favored. In the atomic world, this is unlikely. However, anything that has discrete states and quantum goodness will do, so we can think about replacing the atoms with something like a protein that is folding up.

With proteins, you have a bunch of functional groups, many of which have the ability to rotate about their bonds. For the folding to stabilize, many of these rotational modes must be cooled, so that the hydrogen bonding can hold the structure in place.

In this case, one can imagine that small temperature differences could allow one rotating functional group to cool another via a third, provided that they are all identical (because rotational modes are nearly evenly spaced in terms of energy). Finally, in the case of nanotechnology, where we engineer quantum states, I can see that this might be possible to exploit. And that would be pretty awesome.

Physical Review A, 2010, DOI: 10.1103/PhysRevLett.105.130401