# Melting Simulated Insulators

The Joerg Heber post that provided one of the two papers for yesterday’s Hanbury Brown Twiss-travaganza also included a write-up of a new paper in Nature on Mott insulators, which was also written up in Physics World.

Most of the experimental details are quite similar to a paper by Markus Greiner’s group I wrote up in June: They make a Bose-Einstein Condensate, load it into an optical lattice, and use a fancy lens system to detect individual atoms at sites of the lattice. This lattice can be prepared in a “Mott insulator” state, where each site is occupied by a definite number of atoms. As the total number of atoms in the BEC increases, the number per site increases, and forms a set of “shells” with, say, exactly two atoms per site in the center, surrounded by a shell of one or two atoms per site, surrounded by a shell of exactly one atom per site, and so on.

The thing that sets this paper apart is a temperature-dependent effect, which appears as Figure 5, which I reproduce here:

So, what’s this figure, besides really complicated and orange-y? It is pretty orange, isn’t it? SteelyKid came downstairs while I was reading it, looked at the image on screen, and said “Fire, hot! Careful!”

This picture shows the “melting” of the Mott insulator as the temperature is increased. The three images at the top are pictures of the trapped atoms at different temperatures, increasing from left to right. You can see that the shells get less regular as the temperature increases– there’s still a clear shell structure in part c, but it’s not as distinct as part a.

Wait, I thought this was a BEC? Isn’t that as close to absolute zero as you can get? Yes and no. The way the cooling method works, you selectively remove the most energetic atoms from the trap, using the fact that they tend to be found around the outside edge of the atom cloud. This “evaporative cooling” is essentially the same as what happend to a cup of coffee or tea left sitting on your desk– the hot atoms evaporate away, and what’s left behind is colder.

Eventually, you reach a point where the atoms condense into a BEC, with most of the atoms occupying a single quantum state, the lowest-energy state of the trap. This doesn’t mean it’s at absolute zero, though, because even in the best experiments you still have a small fraction of the atoms existing in energy states above the lowest energy. And you still have fluctuations in the number of atoms in the BEC– they can occasionally pop out into higher energy states, then fall back into the condensate.

This means that even after the formation of the BEC, there’s still a temperature associated with the sample. You can continue evaporative cooling after the formation of the BEC, and you will continue to lower the temperature of the sample.

(They’re a little vague about how the temperature variation is obtained, but I think they’re varying the amount of evaporative cooling below the BEC point. At least, I can’t really think of another way they would be doing it in a controlled manner.)

So, this temperature acts to melt the insulator? Right. Because the atoms have a temperature, there’s a little bit of random extra energy floating around, that can be used to move atoms from one site to another. As you increase the temperature, more and more atoms will hop out of where they’re supposed to be, making your “shells” less distinct.

And the graphs at the bottom show this in some way? Right. The key thing to compare to is the grey points and line, which are data from a “zero temperature” cloud (evaporated far enough that there’s very little effect of fluctuations) that’s not one of the pictures in the figure. The upper graph shows the average number of atoms per site, and the lower graph the variance in the atoms per site, plotted as a function of the “local chemical potential” which is a measure of the distance from the center of the cloud and the number of atoms at that distance (to account for the fact that the density of atoms drops off as you go out).

The grey line shows exactly the behavior you expect for a Mott insulator. There’s a flat bit at the start where the average occupation is zero, then a region where it shoots up to one atom per site, then it drops back down. The variance in the number of atoms per site is zero at the beginning, and zero in the region where the average number is flat, and shows two peaks in the region where the average number is changing rapidly.

Then the orangey lines are the pictures at the top? Right. The nearly invisible yellow is the lowest temperature (part a), the orange is the middle (part b) and the red is the highest temperature (part c). You can see that the signal gets less distinct as the temperature increases. The peak occupation number goes down, while the variance goes up. The lines are fits to the data, used to extract the temperature and other parameters.

That doesn’t look like much variation. Couldn’t they have gotten some data in the big empty space between the grey and yellow lines? In principle, probably. In practice, this is a damnably difficult thing to control, as the number of atoms changes really dramatically when you try to increase the temperature. These are almost certainly the best images they were able to get that have the right number of atoms at non-“zero” temperatures.

So, how does this help us make flying cars, again? It’s not something that’s going to immediately give you a technological breakthrough– we’re talking thousands of atoms here, not anything close to a macroscopic object. This sort of imaging does give you a really nice probe of the behavior of the atoms in a system where they mimic the behavior of electrons in a superconductor, though, and lets you look at details that are really difficult to observe in a more traditional condensed matter system. The direct measurements of variance and thermal effects also give you a neat way to play with the thermodynamics and statistical physics of the system, looking at things like the movement of entropy through different parts of the system.

It’s not going to get you a flying car or a perpetual motion machine, but it’s a cool tool for looking at condensed matter type problems in a way that you couldn’t do before. And new experimental tools are always a good thing.

Sherson, J., Weitenberg, C., Endres, M., Cheneau, M., Bloch, I., & Kuhr, S. (2010). Single-atom-resolved fluorescence imaging of an atomic Mott insulator Nature DOI: 10.1038/nature09378

1. #1 Eric Lund
August 25, 2010

SteelyKid came downstairs while I was reading it, looked at the image on screen, and said “Fire, hot! Careful!”

Sounds like you’re not the only scientist living at Chateau Steelypips. I’ll grant that she doesn’t fully understand this result, but she seems to have noticed a correlation between fire/heat and certain things melting, as is happening here.

2. #2 Grep Agni
August 25, 2010

Why do the gray data points not continue as far to the right as the orange/red ones?

3. #3 Joerg Heber
August 25, 2010