Watching Individual Atoms Make a Phase Transition

A press release from Harvard caught my eye last week, announcing results from Markus Greiner’s group that were, according to the release, published in Science. The press release seems to have gotten the date wrong, though– the article didn’t appear in Science last week. It is, however, available on the arxiv, so you get the ResearchBlogging for the free version a few days before you can pay an exorbitant amount to read it in the journal.

The title of the paper is “Probing the Superfluid to Mott Insulator Transition at the Single Atom Level,” which is kind of a lot of jargon. The key image is this:

Those by themselves probably don’t clear things up all that much, though, so let’s unpack that a little in Q&A format.

What’s this about? Greiner’s group has an apparatus that can detect the positions of individual atoms from a BEC in an optical lattice, which they have used to watch what happens to the distribution of atoms when they take the system from a “superconducting” state to an “insulating” state.

So, these atoms are conducting electricity? No, the atoms are playing the role of electrons. They’re placed in an optical lattice, which plays the role of the atoms making up a solid. The transition in question is a transition from a state in which atoms move freely from one site to another to a state in which atoms are fixed in place at definite sites.

So what’s an “optical lattice,” again? An optical lattice is a periodic pattern of light that acts to trap atoms at specific points– either spots where the light intensity is a maximum, or spots where the light intensity is a minimum, depending on the arrangement. The set-up Greiner is using is a two-dimensional square array of lattice sites, produced by projecting a predetermined pattern onto a BEC using a lens system that extends into the vacuum system, mounted just nine microns (0.000009 m, about a tenth the thickness of a human hair) away from the atoms.

How do they take pictures of the atoms, then? They use the same lens system that projects the lattice pattern, as described in an earlier paper (Nature, arxiv). It’s a nice bit of engineering, but nothing all that unusual, optics-wise. They just put a really big lens right up next to their atoms.

So what’s the big deal with that picture, then? OK, the top row of pictures in that figure are the actual images from their optical system. The bright green squares are producing a lot of light; the dark squares are producing very little light.

Those squares, which are 680nm on a side, correspond to different sites in the lattice where atoms can be trapped. The only way to get a lot of light from one of these sites is to have an atom sitting their absorbing and emitting photons, so the second row of pictures shows the output of an atom-spotting algorithm run on their images, which uses a threshold to assign either 1 or 0 atoms to the site .

As you go from left to right in the figure, the pictures correspond to samples prepared in optical lattices of different “depths.” The deeper the lattice site, the lower the probability of atoms moving from one site to another, so the leftmost column of images corresponds to a “superconducting” state in which atoms move about freely, while the rightmost column of images corresponds to an “insulating” state where the atoms cannot move.

So, basically, you have more atoms in the insulating state? It looks that way, but only because of a detail of their imaging system. When they take their pictures, any sites containing two atoms get emptied out very quickly, thanks to an optical enhancement of the collision rate which knocks both atoms out of the trap. So the bright spots don’t indicate sites with atoms as opposed to sites without atoms, but sites with an odd number of atoms– a bright spot is a site that ended up with a single atom in it after all the possible pairs collided and went away.

So, the patchy-looking pictures on the left in that figure don’t show just occupied and unoccupied sites, but sites with odd or even numbers of atoms. Some of those dark spots are sites that originally contained two atoms, and some of the bright spots are sites that originally contained three atoms. The picture all the way on the right shows the same overall number of atoms, but they’re distributed more uniformly– every lattice site has a single atom in it.

This is the difference between a superconducting state and an insulating one. In the superconducting phase, atoms can move from place to place, and thus the atom number per lattice site can fluctuate, even when it’s in the lowest possible energy state. In the insulating phase, the atoms can’t move from one site to another, so the lowest-energy state of the system has exactly one atom per site. What you see in the pictures is exactly what you expect to see on the microscopic level during this sort of phase transition.

Yeah, but how do you know that they’re really uniformly distributed, and you didn’t just get really unlucky with the distribution of pairs? That’s the point of the third row of pictures. These are images of the atom cloud some time after it was released from the lattice. The distinct bright spots in the leftmost picture are an interference pattern resulting from atoms expanding out from different lattice sites, which is a signature of the superconducting phase. When you move to the insulating phase, the reduction in the fluctuation in the number of atoms per site leads to a random phase shift for the wavefunction at various sites, wiping out the interference pattern and producing the indistinct blob on the right. This provides confirmation of the phase transition.

That’s pretty cool. What else can they do? Well, if they bump up the number of atoms, they see pictures like the ones at right. The atoms are confined to a limited range in two dimensions, so as they increase the atom number, at some point, they start to pile up in the center, and you get a dark region in the center where each site has exactly two atoms in it, and a bright ring where each site has exactly one atom. Keep going, and you get a bright central region with three atoms per site, then a dark region with four, and so on.