Single-Photon Cooling: Making Maxwell's Demon

As mentioned previously, I've been reading Sean Carroll's Wheel arrow of time book, which necessarily includes a good bit of discussion of "Maxwell's Demon," a thought experiment famously proposed by James Clerk Maxwell as something that would allow you to cool a gas without obviously increasing entropy. The "demon" mans a trapdoor between a sample of gas and an initially empty space, and allows only slow-moving gas atoms to pass through. After some time, the empty volume is filled with a gas at lower temperature than the initial sample, while the gas in the original volume is hotter than when it started.

Purely by coincidence, I also recently read a paper by Mark Raizen's group at Texas with the exciting title "Single-photon cooling at the limit of trap dynamics: Maxwell's demon near maximum efficiency." It also figures this great figure showing both the original Maxwell demon set-up and a schematic view of their experimental arrangement. You have to love any figure involving a stick-figure demon:

(It's also discussed in this review article in Science, but without the charming little demon.)

In this paper, they demonstrate a technique for cooling a gas of atoms that is directly analogous to the Maxwell demon idea. It takes a gas of atoms held in a trap, and selectively transfers slow-moving atoms into a different trap, through scattering a single photon (hence, "single-photon cooling"). As a result, the second trap ends up filled with atoms at a significantly lower temperature than the original sample.

So, how does this work?

The key to the scheme is the picture of an atom trap in terms of energy. They start with atoms in a magnetic trap, represented by the shaded area marked "B" in the right-hand picture. The trap is described in terms of the potential energy an atom in the trap would have if it were placed at a given point at rest, shown by the two straight lines forming the bottom of the trap. The potential energy increases as you move out from the center of the trap, due to the interaction between the atoms and the magnetic field. The two slopes are slightly different due to the effect of gravity, which makes the potential energy on the high side of the trap (to the right in the figure) higher than the potential energy on the low side of the trap (to the left in the figure).

"Big deal," you say. "So they have some potential energy. The important thing here is the kinetic energy due to the atomic motion." And that's true. But here's the cool thing: the potential energy graph constrains the kinetic energy the atoms can have. If you put an atom in the center of the trap with some kinetic energy, it will move out from the center at some high speed. As it moves, though, its potential energy increases due to the trap, and since energy needs to be conserved, that means its kinetic energy decreases. At some point, the kinetic energy will go to zero, and the atom will come to a complete stop for just an instant, then turn around.

This is the same basic process that happens with a ball tossed up into the air. As it rises, its gravitational potential energy increases, and its kinetic energy decreases. At the highest point of the ball's flight, its "turning point," it has zero kinetic energy, and thus zero velocity for an instant.

The atoms in the trap behave just like the ball thrown into the air, only they lose kinetic energy whether they go up or down. There's a turning point for every atom above the center of the trap, and a turning point for every atom below the trap. The exact location of the turning point depends on the kinetic energy the atom started with-- the more kinetic energy it has, the farther out the turning point-- but every atoms near its turning point has a very low velocity.

The Raizen group cools atoms with a single photon by exploiting this fact. Their second trap is an arrangement of three laser beams to form a trough, and their "demon" is a laser beam placed just above the trough, with its frequency tuned so that atoms in the trapped state can absorb one photon to move into the excited state, and then emit one photon and drop into a state that is not affected by the magnetic trap, but will be caught by the laser trap.

The key to their scheme is the position of the "demon," which is right along the outer edge of the trap. The only atoms that get far enough out to encounter the demon are necessarily very close to their turning point, and thus moving very slowly. When they drop into the laser trap, they have almost no kinetic energy, and thus a very low temperature. This is exactly the cooling effect you get with Maxwell's demon.

The experiment described in the paper is basically a proof-of-principle demonstration of the technique. They only loaded a small fraction of the atoms into their laser trap (their highest claimed efficiency was about 2%), and only really cooled the atoms in one dimension. Still, they were able to select out a sample of a few hundred thousand atoms at 4.3μK, starting with a sample at 53μK. This also increased the "phase space density," which is a combination of position and momentum used as the figure of merit for attempts to get Bose-Einstein Condensation, by a factor of 350.

As you can tell from the starting temperature, they were working with laser-cooled atoms for this demonstration. The really attractive feature of the scheme, though, is that it could work for any atom, not just the ones that can easily be laser cooled (which are a small fraction of the Periodic Table). This could even work for molecules-- put it together with one of the beam-slowing techniques discussed last week, and you could use it to cool anything that you can hold in a magnetic trap. Their stated goal is to use this to trap and cool hydrogen isotopes, including tritium and maybe even anti-hydrogen, which would enable all sorts of cool fundamental physics tests.

To this point, I haven't answered the key question that goes with any invocation of Maxwell's demon: What happens to the entropy? In the classic thought experiment, the decrease in entropy caused by sorting the atoms into hot and cold samples is offset by the informational entropy increase the demon creates while keeping track of the positions and velocities of the atoms. So, where does that come from here?

In this case, the entropy increase comes from the photons. When an atom makes the transition from one trap to another, it absorbs one photon from the laser beam, which is an extremely low entropy state, and emits a second photon in a random direction. This scattering of low-entropy photons into higher-entropy states is enough to compensate for the decrease in entropy from the cooling.

Even when you do make a Maxwell demon in the lab, there's still no such thing as a free lunch.

Travis Bannerman, S., Price, G., Viering, K., & Raizen, M. (2009). Single-photon cooling at the limit of trap dynamics: Maxwell's demon near maximum efficiency New Journal of Physics, 11 (6) DOI: 10.1088/1367-2630/11/6/063044

Raizen, M. (2009). Comprehensive Control of Atomic Motion Science, 324 (5933), 1403-1406 DOI: 10.1126/science.1171506