## Light Doesn’t Stop – “Stopped Light and Image Storage by Electromagnetically Induced Transparency up to the Regime of One Minute”

I still remember the group meeting in grad school when someone brought up a news article stating that a researcher had slowed light down to the speed of a bicycle. We got a good laugh at the inaccuracies and clear misunderstandings in the news article. It was a little disturbing, then, to see similar articles pop up all over the web. The main problem with the articles was they claimed that scientists were slowing light down, when in fact they were slowing light pulses down. What’s the difference, you ask? Stick around and I’ll show you. When I recently saw a news article claiming that scientists had brought light to a complete stop, I felt the veins in my head start to throb again, and I couldn’t let it go without saying something. Hence this post. So what did they actually do$^1$? They were able to store the quantum properties of a light pulse for up to a second and then retrieve the information in a new pulse that was identical to the original. Storing the pulse and how then maintained the integrity of the information was the exciting aspect of this experiment. How do you go about storing the information from a pulse of light? You first need to compress the pulse so it is small enough to fit inside your apparatus. Since light moves so fast ($3\times10^8 \frac{m}{s}$), a pulse that is 1\micro s will be 1 km long! It is rather difficult fitting that into a lab room, let along a small crystal used for storage. The way you spacially compress the pulse is to slow it down as it enters the medium (in this case a silicate crystal of yttrium doped with Praseodymium (I’m not even sure where that is on the periodic table). Using something called electromagnetically induced transparency (EIT) the group velocity of light slows down, so that as the light pulse hits the crystal it is just like traffic hitting construction, the kilometer long pulse piles up into a centimeter long pulse. It is important to note that it is the group velocity that slows down to around 1 km/s and not the phase velocity. What is the difference? I’m glad you asked because this is at the heart of my complaint about the claims of “slowing light down to the speed of a bicycle”.

## Phase Velocity and Group Velocity

Classically speaking, light is an electromagnetic wave which means that the magnitude of the electric and magnetic fields vary sinusoidally. The phase velocity is how fast a particular peak or valley of the light wave moves in space.

Figure showing group velocity and phase velocity. Red dots move with phase velocity (following a peak of the wave) and green dots move with group velocity (following the nodes between pulses)

The red dot in the image above is moving with the phase velocity of the waves. However, to have a wave pulse, you must have many different waves of different frequencies. When you combine multiple frequencies of a wave you end up with interference between the waves that results in a phenomena called beating, which yields a slowly varying envelope superimposed on a rapidly varying wave. In the figure above you can see that the green dots are in between each of the larger envelope pulses and that the green dots are traveling slower than the red dots (notice how the red dots catch up to the green dots and pass them). This happens because, in some media, the phase velocity of light depends on the frequency. By introducing a very slight difference in phase velocity can result in a huge change in the group velocity. The light pulses in the experiment are the envelop you see in the figure and move at the group velocity. So the key here is to somehow have a medium where the phase velocity changes as the light frequency changes, so the pulse group velocity can be very slow. This is where electromagnetically induced transparency (EIT) comes in.

## EIT

Atomic level configurations for electromagnetically induced transparency. I will only talk about the Lambda configuration

This image shows a couple of different energy level configurations but I’ll focus on the lambda configuration (so named because it is shaped like the Greek letter lambda $\Lambda$). An energy level is possible state that an electron bonded to an atom can occupy. Electrons that are orbiting closer to the nucleus of the atom have lower energies than electrons that have orbitals that are farther away. On this diagram, states with higher energies are above states with lower energies, and the vertical distance between states represents the energy it would take to go from one state to the other (Don’t worry about what the horizontal displacement means, all we care about now is the vertical arrangement). If an atom is in one energy level, it can be encouraged to transition to a different energy level by absorbing or emitting light. The experimenters used laser light to encourage transitions between differing energy levels. The medium you shine your light through (in this case the silicate crystal of Yttrium) consists of millions and millions of atoms with similar energy level configurations. This means that if you shine a light pulse through that has an energy (which depends on frequency) that corresponds to any of the transitions between two levels (say between the |1> and |3> states), the light pulse is going to get absorbed by the atoms and not make its way through. However, if you shine a strong control laser (shown in red in the figure and with frequency $\omega_c$) and a weaker probe beam (shown by the black arrow and denoted to have frequency $\omega_p$), and you tweak the lasers just right, you can get interference between the states that prevents light from getting absorbed on the transition between states |1> and |3> (let’s call that frequency $\omega_x$). This is EIT; the medium is now transparent to light with an energy corresponding to $\omega_x$ because that light is no longer absorbed. One interesting result of EIT is that right around frequency $\omega_x$ is that the phase velocity of light varies significantly with frequency.

Blue curve is index of refraction vs. frequency. Grey curve is absorption of light vs frequency

The blue line corresponds to the phase velocity (actually the index of refraction) and the horizontal axis is frequency. The grey curve shows the absorption of light so you can see the transparent window (the dip in the curve) where the light is not longer absorbed. Since the phase velocity varies, any pulse of light with frequency near the transparent window will have a very slow group velocity. By tweaking the properties of the system you are able to get light going 1 km/s in this experiment (in other experiments involved cold gases, researchers have achieved speeds of 17 m/s in an ultracold atomic gas$^2$).

## Storing the Pulse

Reading some of the popular articles, they make it sound like they actually slow the light down enough to stop it, but that isn’t how it works. While the pulse is moving much slower than it did in air, it is by no means standing still. What you need to do is get the medium to absorb the photons, but in a way that preserves the quantum properties of the light. This is done by switching off the control laser beam, which means that the medium is now able to absorb light with energies corresponding to the |1> to |3> transition. As the control beam is turned off, the transparent transition can now absorb light, and the quantum properties of the light are stored as spin excitation of the atoms. The important point here is that the energy from the electromagnetic field making up the light pulse is now transferred to the atoms, that the light gets absorbed, and there is no more light pulse. Now comes the hard part, making sure that the stored information is not lost, and this is where this experiment shines. By applying various magnetic fields and applying a microwave pulse, the experimenters were able to keep the atoms isolated from the effects that cause decoherence (basically, things get bumped and jiggled enough that the information is lost). What is even more amazing is that they used an adaptive algorithm to tweak the parameters of the magnetic fields and microwave pulse to maximize the storage lifetime. They did such a good job that they were able to get close to the theoretical maximum storage time for this particular type of crystal, but this technique can now be applied to other materials that might have longer possible storage times.

## So why is this experiment exciting?

Overall, the experiment is about storing and retrieving the quantum mechanical properties of a light pulse. This has applications to quantum computing and quantum cryptography, which rely on quantum entanglement. The big deal here is that they managed to store light pulses in a solid-state device, a doped silicate crystal. Most of the previous storage experiments had focused on using cold gases, but a lot of people feel that solid-state devices will be needed to scale up to larger projects involving hundreds or even thousands of light pulses. Solid-state devices are more difficult because of the strong interaction between atoms of the crystal, which makes it harder to isolate the atoms that are used to store the pulse. 1 Georg Heinze, Christian Hubrich, and Thomas Halfmann (2013). Stopped Light and Image Storage by Electromagnetically Induced Transparency up to the Regime of One Minute Physical Review LEtters DOI: 10.1103/PhysRevLett.111.033601 Note: The article is behind a paywall, but you can read a summary at http://physics.aps.org/articles/v6/80?from_TRM_site=Yttrium 2 Hau, L. V., Harris, S. E., Dutton, Z., & Behroozi, C. H. (1999). Light speed reduction to 17 metres per second in an ultracold atomic gas. Nature, 397(6720), 594-598.  http://www.nature.com/nature/journal/v397/n6720/abs/397594a0.html Sorry, this one is behind a paywall too.

Edit: I found a nice article by Chad Orzel talking about slowing light.  Check it out:  http://scienceblogs.com/principles/2010/01/05/controlling-light-with-light/