# Controlling Light With Light

“Slow light” is in the news again. The popular descriptions of the process usually leave a lot to be desired, so let’s see if we can’t do a slightly better job of explaining what’s going on. The key idea is using one light beam to control the transmission of another.

Let’s say you have a bunch of atoms in a gas and a laser. The laser happens to be at exactly the right frequency to be absorbed by the atoms, meaning that if you try to shine the laser through the gas, it’ll be absorbed, and won’t make it out the other side. This is traditionally represented by a diagram like to one to the right, where the energy states of one atom (labeled |1>, |2>, and |3>, with state |1> having the lowest energy and state |2> the highest, with state |3> between them but close to |1>) are represented by the horizontal lines, and the blue line connecting states |1> and |2> represents the laser.

Now, let’s say you really want the laser to make it through the gas of atoms, but you can’t move them out of the way, or modify their energy levels so they don’t absorb the light any more. Let’s also say that what you want to send is a short, fairly weak pulse of light, containing a not terribly large number of photons, so you really can’t afford to lose any of them. What are your options?

Well, one thing you can do is to put the atoms in a state where they can’t absorb the light. With the energy level scheme illustrated above, there are two ways to do this. The simplest way is if the atoms happen to naturally decay from state |2> into state |3> at least part of the time. Then you just turn your laser on, and let the atoms absorb photons, exciting them to state |2>. Any atoms that happen to fall into state |3> won’t interact with the laser any more, while those that fall back into state |1> will just get excited again, and keep going back and forth until they eventually fall into |3>. This process is called “optical pumping.”

This works, but it’s not really the optimal solution. For one thing, you lose a whole bunch of your laser light in the process of pumping the atoms from state |1> into state |3>– the atoms keep absorbing photons from the laser, which is what you’re trying to avoid. It also takes some time to move the atoms between states, which doesn’t help you if you have a short pulse of light that you want to send– by the time the atoms are in a place where they can’t absorb, the pulse is over, and you’ve lost most of it. If there’s a way for atoms in state |3> to move back to state |1> (and there almost always is), then it’s really hopeless.

Another thing you can do is to send in a really strong “pump” beam of the same light you want to send through the gas. This will excite a bunch of the atoms to state |2>, and once they’re there, they can’t absorb another photon. This reduces the number of atoms that can absorb light, and increases the chance of your pulse making it through.

This “saturation” method works, but again, it’s not optimal. You get away from the short pulse problem– you can just leave the “pump” beam on all the time, so there’s no time required for the effect to kick in– but you can never get all of the atoms into state |2> this way (if you’re lucky, you can get about half of them there), so there’s always some absorption of you laser pulse.

Things get really interesting, though, if you have access to a second laser, at the frequency needed to move atoms from state |3> into state |2>.

In this “lambda” scheme, shown at right, you have not one but two laser fields interacting with the atoms. The blue arrow represents the “probe” pulse that you want to get through your collection of atoms, while the red arrow represents a “control” laser, at a very different frequency.

This might not seem like it would help, but it turns out to be exactly what you need to get your pulse through the medium. There are a couple of ways to think about it, but maybe the easiest is to think of the atoms in terms of waves. The state of an atom is described by a quantum wavefunction, and in the presence of both lasers, that wavefunction has pieces corresponding to some probability of the atom being in each of the three possible states. Each of those pieces acts a bit like a wave, oscillating up and down.

When you think about an atom that’s trying to absorb a photon from the blue probe laser, that atom needs to end up in state |2>. In order to figure out the probability of that happening, you need to consider all of the possible ways an atom could get there, which include not only the simple process of starting in |1> and absorbing one blue photon then emitting one red photon to move to |3>, then absorbing a red photon to move back to |2>.

If you arrange things properly, it turns out that you get an interference between those different paths. For a probe pulse tuned exactly to the frequency needed to go from |1> to |2>, the waves corresponding to the direct path add to the waves from the roundabout path, and exactly cancel each other out. It’s a little like those noise-cancelling headphones that eliminate loud noises by playing them back with a slight delay. The delayed waves show up with their peaks in the valleys of the original waves, and you end up with no sound at all.

For the right combination of lasers, at just the right frequencies, this interference means that the probability of finding an atom in state |2> is zero. Which means that the probability of that atom absorbing a blue photon is also zero (because the energy needed to put the atom there would have to come from the blue laser), so the probe pulse goes right through, even though it’s at exactly the right frequency to be absorbed.

This phenomenon is known as “Electromagnetically Induced Transparency,” (EIT) (there’s a good overview of the physics in a thesis chapter linked from this page at St. Andrews) and it has a lot of nice features. For one thing, it uses one laser (the red one) to control the transmission of the other. If the red laser is there, the blue laser passes through; turn off the red laser, and the blue laser gets absorbed. This is of interest to people who want to quickly and efficiently turn light beams on and off, which is of critical importance to telecommunications.

Another interesting feature of the EIT effect is what it does to the propagation of light. The transparency does not pass the probe pulse completely unchanged, but at a much reduced pulse speed. You can think about this in very rough terms as a consequence of the fact that both blue and red lasers are needed to make the effect work. The probe pulse gets through without absorption, but not without interaction, and the effect of the interaction ends up looking like a greatly reduced transmission speed. This is the origin of the “slow light” experiments that have popped up again recently. You can also “stop” the probe pulse by turning off the control laser pulse (red) while the probe laser pulse (blue) is inside the medium, which is a pretty neat trick. You can get the pulse back again at a later time by turning the control laser back on, so the gas of atoms can act as “storage” for the light pulse.

One thing to notice about the above description, though, is that at no point did I use the words “Bose-Einstein Condensate.” Nothing in this scheme requires the atoms to be in any particular collective state, or at low temperatures. Indeed, people have done “slow light” experiments in hot gases, and everything works just the same. The best-known experiments use a Bose condensate as the medium because it’s convenient to have the atoms moving as little as possible, but this can and does work in room-temperature vapors.

So, that’s how you can use light to slow light, or even stop it. Pretty cool, no?

1. #1 Brian H
January 5, 2010

Just jumped over to the blackboard to check it out for myself; very cool when I saw the cancellation occur. Thanks for this post!

2. #2 Chuk
January 5, 2010

Neat stuff, I’d heard vague pop-sci comments about “slowed light” but never had it explained so clearly. Thanks!

3. #3 Brian H
January 5, 2010

Oops, lots of mistakes in my work there. Tried again having mathematica do the heavy lifting and I found the result that the 1->2 transition occurs only at second order in the ratio of the blue beam intensity to the red beam intensity. Does this sound remotely right?