(This is the first in a planned series of posts writing up each of the scientific papers on which I am an author. A short description and a link to a PDF of the paper can be found at the archived Optical Control page.)
The essence of the optical control paper is contained in this one figure:
“Very pretty,” you’re thinking, “But what does it mean?”
The graph shows the increase or decrease in the ionizing collision rate for a sample of xenon atoms (well, two different samples, of different isotopes, but they behave exactly the same) at a temperature of 100 microkelvin or so due to the influence of a “control” laser tuned near the atomic resonance (zero on the horizontal axis). Positive numbers indicate an increase in the collision rate, and negative numbers indicate a decrease in the collision rate. The base collision rate is about 0.6 in the units of the vertical axis, so the maximum enhancement (at a frequency just below the resonance) of the rate is about a factor of five, while the maximum suppression (at a frequency just above the resonance) is about a factor of two.
How does it all work? Why does shining in a laser increase and decrease the rate of collisions between atoms?
The key to the whole experiment is the fact that you can think of a pair of atoms that are about to collide as a diatomic molecule. It’s an extremely large molecule– the atoms are typically separated by hundreds of atomic radii, rather than the ten or less of what we think of as a typical molecule– but any pair of interacting atoms can be thought of as a molecule.
When we think of the two colliding atoms as a molecule, we need to consider the interaction between them in terms of molecular states. For some arrangements of atoms, the molecular state will be such that the two atoms are drawn together, while for other arrangements, the two will be forced apart. In the basic configuration for this experiment, we had a sample of xenon atoms all in their lowest excited state (which is a metastable state with a lifetime of 43 seconds), and any randomly chosen pair of atoms would be weakly attracted to one another. If they get close enough (within 25 atomic radii or so), the two atoms will undergo an ionizing collision (which I’ll refer to as “colliding” in what follows– technically, any interaction between the two is a collision, but the only collisions we care about are ionizing collisions).
These atoms were cooled to very low temperatures, though, corresponding to speeds of only 10 cm/s or so. That means that it took a very long time for any given pair of atoms to collide with each other– a microsecond or more. In that case, it’s possible for one of the two atoms to absorb a photon, or, in the molecular language, for the colliding pair to be excited to a higher-energy molecular state, which could be either attractive or repulsive.
This excitation changes the collision rate. If the pair is excited to an attractive state, the interaction pulls the atoms together, making them more likely to collide, and the collision rate goes up. If the pair is excited to a repulsive state, the interaction forces the atoms apart, preventing them from colliding, and the rate will go down.
Which case you end up in depends on the detuning of the laser. If the attraction between atoms is repulsive, that means that they have a higher energy when they’re closer together than when they’re apart. That means that the energy needed to excite the pair to the repulsive state is greater than the energy needed to excite two separate atoms, and thus we see a reduction in the collision rate at positive detunings (namely, control laser frequencies above the atomic resonance).
Similarly, if the interaction is attractive, the energy for two atoms close together is lower than the energy for two atoms that are far apart, so we see an increase in the collision rate at negative detunings. The characteristic shape of the curve comes about because for any given laser detuning, the colliding pair will be excited to the higher energy state only at a particular separation between the atoms, known as the “Condon Radius.” The larger the detuning, the smaller the radius, and the fewer pairs available to be excited; on the other hand, the smaller the detuning, the larger the radius, and the smaller the effect of the excitation.
We did this experiment by loading a trap with as many xenon atoms as we could, and then turning the trapping laser off for a short time (about 50 ms). We measured the ionization rate during a 20 microsecond window when the atoms were in the dark. Then we repeated the cycle of loading and switching off the light, but flashed on a “control” laser for 50 microseconds during the “dark” period, and measured the ionization rate during a 20 microsecond window with the control laser on. The ratio of the ionization rate with the control laser to the ionization rate in he dark gave us the change in the rate, and we multiplied by the rate in the dark (which we measured by a different technique, measuring the number and density of trapped atoms directly and using those to extract the collision rate) to get the absolute change.
The point of this was to avoid contamination by other factors– the laser cooling and trapping mechanism uses lasers tuned slightly below the resonance frequency for separated atoms, so the collision rate with the trap lasers on is about 20 times higher than the rate in the dark. We also worried about whether the control laser would perturb the trap– ionizing collisions limited the maximum number of atoms in the trap, so a dramatic increase or decrease in the collision rate would potentially change the number of atoms loaded– and the ratio procedure accounted for this.
Of course, if suppressing the collision rate increases the loading, that could be a good thing, so we repeated the experiment with the trap lasers left on all the time, producing the graph at left. This is basically the reciprocal of the previous graph– the rate with just the trap laser divided by the rate with the trap laser plus the control laser– so higher numbers indicate larger suppression of the collision rate. Very close to resonance, the control laser visibly distorted the trap to such a degree that we really didn’t trust the results, but even outside that range, the suppression factor is close to 30.
Since the trap laser increases the rate by a factor of 20, that means that the rate with both lasers was actually lower than the rate in the dark, which is pretty cool. We can understand this as a two-step process: the trap laser close to resonance excites pairs of atoms at very large separations, which start to be drawn together. They decay after about 34 ns, though, returning to the lower state but continuing to approach, and then get excited a second time, by the control laser, which sends them to a repulsive state and blocks the collision.
At the time, everybody was looking for ways to increase the number and density of atoms in a trap, and this looked promising, so we tried it out, turning both lasers on all the time, and using the total amount of light scattered to measure the number of trapped atoms. From the decay in this number after we cut off the supply of atoms to be loaded into the trap, we determined the collision rate (this is figure 3 in the paper), and showed that we did, indeed, improve the trap performance. We managed to make a 50% improvement in the trap density, and doubled the total number of atoms, albeit at the cost of almost doubling the average velocity of the atoms (quadrupling the temperature). That’s why this never caught on as a trap enhancement.
This is a frequently cited paper– the Smithsonian abstract data service lists 59 citations– because it came right before the peak of cold-collision experiments in the mid-to-late 90′s, and also because it was one of the first times that absorptive imaging was used to make temperature and density measurements for these experiments. This is old hat, now, but used to require a fair bit of explaining. A very similar experiment was done around the same time by Katori and Shimizu, who will come up again, later.
So, the take-home message, here: We demonstrated the ability to change the rate of collisions between metastable xenon atoms by hitting them with light during the collision process. With the right choice of laser frequencies, we can shine two lasers on the atoms at the same time, and make the collision rate lower than that with no light at all. This could be used to improve the performance of our atom trap, but at the cost of heating the atoms like crazy.
This has gotten long, so I’ll spin the personal accounts of what it was like to do this off into a separate post.
Walhout, M., Sterr, U., Orzel, C., Hoogerland, M., Rolston, S.L. (1995). Optical Control of Ultracold Collisions in Metastable Xenon. Physical Review Letters, 74(4), 506-509. DOI: 10.1103/PhysRevLett.74.506