Time-Resolved Studies of Ultracold Ionizing Collisions

This paper is the third of the articles I wrote when I was a grad student, and the first one where I was the lead author. It's also probably my favorite of the lot, not just because of the role it played in my career, but because it packs a lot of science into four pages.

The whole thing is summarized in this figure from the old NIST web page, which is a simplified version of Figure 2 from the paper itself:

This shows the collision rate as a function of time after we hit a cold sample of atoms with a 40ns pulse of laser light tuned near the atomic resonance frequency. As discussed in the optical control of collisions paper, applying light to a sample of cold colliding atoms can modify the collision rate by exciting the atoms to attractive or repulsive molecular states. In the previous paper, we applied the light for a long period, and measured the change in the collision rate; here, we applied the light for a very short time, and watched the collisions happen in real time.

The red points show the result of applying light tuned to excite colliding pairs of atoms to a state where they are attracted together, and shows an increase in the collision rate for a short time. The blue points show the result of applying light tuned to excite colliding pairs to a state where they are repelled from one another, and prevented from colliding, which leads to a decrease in the collision rate for a short time.

The obvious question to ask here is "Why are there two peaks in the red curve?" That threw us at first, but it's a happy result of our detection set-up that allows us to extract a huge amount of information. Our detector was an ion detector placed several centimeters above the trapped atoms, which drew charged particles in with a large electric field. We had it set to draw in the positive ions produced in collisions between metastable atoms, and it turns out that there are two different processes that create a positive ion: "Penning ionization" (PI) in which two atoms collide and one loses an electron while the other goes to the ground state; and "associative ionization" (AI)in which the two atoms stick together to form an ionized molecule.

The ionized molecules from associative ionization have twice the mass of the atomic ions, and thus take longer to be drawn into the detector. The time of flight from the trap to the detector depends on the square root of the mass, and we measured the time of flight for a single atomic ion by sending in an intense pulse of green light that could directly ionize atoms from the trap, which is the green curve in the figure. The two peaks in the red signal represent the two different ionization processes, and the arrival time for the second peak is roughly 1.4 times that for the first peak, meaning that it consists of ionized molecules.

This lets us sort out associative ionization from Penning ionization, something that we weren't able to do in the past, so right there, that's exciting new physics. There's another key piece of information in this graph, which shows up as a curious feature of the blue data set: the blue points only show one dip. There's no decrease in the blue curve corresponding to the ionized molecules.

That happens because there are two different things going on when we excite the atoms for the red data set: the atoms can be excited to an attractive state, and rush together and collide while still in that state (we call these "S+P" collisions); or they can start to rush together, but decay back to the original metastable state before the collision (we call these "S+S" collisions). The collision rate for S+S collisions is still higher than in the absence of the light pulse, because the atoms were pulled together during the time they were excited. This process is known as "flux enhancement," and had been investigated by Phil Gould's group at UConn before we did these experiments.

So, we really have four collision processes going on in our sample: PI from S+S collisions, AI from S+S collisions, PI from S+P collisions, and AI from S+P collisions. That's a lot to disentangle, but a happy coincidence lets us sort it out.

The absence of a second dip in the blue data set tells us that there is no measurable associative ionization due to S+S collisions. The only collisions occurring in the blue data set are S+S, because any atom pairs excited by the laser are forced apart, and can never collide in the excited state. That means that all of the ionized molecules in the second red peak come from excited-state collisions.

This lets us sort out all sorts of different things, by measuring the collision enhancement for different laser detunings. The frequency of the laser pulse determines the separation between atoms when they are excited, and because the pulse is short, we only get atoms from right around the excitation region. As we go farther from resonance, we excite pairs of atoms at smaller separations, and the chances of the atoms surviving long enough to have an S+P collision approach 100%. At large detuning, the ratio of collisions in the first peak to collisions in the second peak tells us the ratio of Penning to associative ionization in S+P collisions, which turns out to be about 4:1 (this is Figure 3 in the paper).

That, in turn, allows us to measure the "flux enhancement" effect at small detunings. Since we know that the second peak is all S+P collisions, and there are four PI collisions for every AI collision, we can figure out how many of the ions in the PI peak are due to S+P collisions. The remainder must be S+S collisions through the flux enhancement process, and that turns out to be about 60% of the total collision rate (also Figure 3 in the paper).

The last thing we can do is to look at the time required for collisions. We know the flight time for ions created through direct photoionization (the green curve), so we can attribute any delay beyond that to the collision process itself. It's a little tricky to predict the time required for collision enhancement (though it can be done for the S+P collisions), but for S+S shielding (blue data points), the time dependence is really simple-- the time required for a collision to occur is just the distance at which the atoms were excited divided by the relative velocity in the collision.

Of course, it's not really that simple-- there are no two-level atoms, and metastale xenon is certainly not one of them, so it turns out that there are 20 different excited states that we need to worry about. We can sort of average all those together, though, and use the thermal distribution of velocities in our sample to predict the time at which we would expect to find the shielding peak. The model agrees beautifully with the data (Figure 4). The enhancement data also match the predicted functional form pretty well, especially for the associative ionization signal, which is all S+P. The Penning ionization signal diverges from the theory a little, probably due to the flux enhancement process.

So, it turns out that you can learn a lot about collisions by hitting a cold sample of atoms with short pulses of light.

Orzel, C., Bergeson, S.D., Kulin, S., Rolston, S.L. (1998). Time-Resolved Studies of Ultracold Ionizing Collisions. Physical Review Letters, 80(23), 5093-5096. DOI: 10.1103/PhysRevLett.80.5093