Suppression and Enhancement of Collisions in Optical Lattices

I announced my intention to do some research blogging a little while ago, and managed one pair of posts before the arrival of SteelyKid kind of distracted me. I’m still planning to complete the Metastable Xenon Project blog, though (despite the utter lack of response to the first two), and the second real paper I was an author on is “Suppression and Enhancement of Collisions in Optical Lattices,” a PRL from 1998, with a preprint version available here.

So, this is another paper about collisions, obviously, but what’s an optical lattice? An optical lattice is an arrangement of laser beams– four in our case– with their angles and polarizations chosen so that they create a three-dimensional interference pattern in a region of space. For the right choice of beam properties, the lasers interact with the atoms to produce an array of “wells” where the energy of the atoms is lower than outside the wells. If you load this lattice with very cold atoms, the atoms will collect where the energy is lowest, and form a pattern that looks very much like a salt crystal– a regular rectangular array of sites where you are likely to find atoms, and nothing in between.

So, what does this sort of structure do to the collision rate when you load a whole bunch of atoms into it? Well, you can argue that it ought to suppress the rate, because atoms in different wells are prevented from colliding with one another. You can also argue, though, that it ought to enhance the collision rate, because large regions of space are forbidden to the atoms, making them more likely to encounter other atoms, and thus experience a collision.

So, does putting atoms in an optical lattice enhance the probability of atoms colliding, or suppress the possibility of collisions? The answer turns out to be “yes,” and the key figure from the paper is here:

What the figure shows is the rate of ionizing collisions (that is, charged particles reaching our detector) as a function of time spent in the lattice. We turn the lattice on at time 0, and hold the atoms for 100 milliseconds, then drop the atoms.

The large initial drop in the collision rate happens because the atoms we put into the lattice were at too high a temperature for all of them to be trapped in the wells. When we turned the lattice on, only the least energetic atoms were caught, while the faster-moving atoms pinballed their way through the lattice for a while, and eventually just fell out entirely. As they left, they lowered the number of atoms available to undergo collisions, and that means that the collision rate dropped.

At 100 ms, the rate jumps up dramatically. That’s the instant when we turned off the lattice, and let the atoms held in the individual wells escape to collide with their neighbors. The collision rate jumps up dramatically, almost doubling, indicating that the lattice was, in fact, suppressing the rate of collisions once the hot atoms had left, and all we had in our sample was cold atoms at the bottom of the lattice wells (that is, once the sample was “thermalized” with the lattice, meaning that the temperature of the trapped atoms was consistent with what the lattice could hold).

So, we saw suppression for a fully thermalized lattice, but what about during the in-between times? Well, if the lattice isn’t given enough time to thermalize, it turns out that the rate is, in fact, enhanced. When there are hot atoms around, the rate is higher than we would expect if the lattice weren’t present– the atoms have enough energy to move around, but the lattice structure still steers them toward the “wells,” where they are more likely to collide with other atoms.

The inset to the figure above is also pretty cool: it shows a “zoomed in” view of the time right around when the lattice is switched off. We can see that the collision rate actually drops slightly before it spikes up. That happens because some of the wells contain more than one atom. The rate while the lattice is on is related to the number of two-atom wells, and when the lattice is switched off, those atoms either collide immediately, or fly apart, and the rate drops a little. Then it picks up again a few microseconds later, as the atoms move far enough from their starting points to encounter atoms from other wells, leading to the big spike up.

So, to boil it all down, we found that putting atoms in an optical lattice enhances the collision rate at first, and then suppresses the rate of collisions, once the atoms have thermalized. We also used the collision rate in the thermalized lattice to estimate how often atoms “hop” from one well to another, and found that they hop from site to site about once every four milliseconds (it says 8 in the paper, but I re-did it a couple of years later for my thesis, and there was a factor of two error somewhere).

J. Lawall, C. Orzel, S. L. Rolston (1998). Suppression and Enhancement of Collisions in Optical Lattices Physical Review Letters, 80 (3), 480-483 DOI: 10.1103/PhysRevLett.80.480