Laser Cooling and the Anti-Murphy's Law

Laser Cooling follows some kind of Anti-Murphy's law. While normally, something you expect to work doesn't work as well. Like, a kilogram of petrol (or gasoline) in your car has 47 MJ of energy, it gives you less than 18 MJ to run your car. With laser cooling, things which were not expected to work have worked, while things which were expected to work have exceeded their limits.

One of the most fascinating stories I've heard from the history of laser cooling is that of sub-doppler cooling. It is one of the few times in science when experiments beat the theoretical limit.

A brief background of laser cooling. The idea came in the 1970s. For a gas of atoms, all the energy is in its motion. If you can slow the atoms down, their temperature will fall significantly. You do that by shining the proper laser light from the proper direction and using the photon momentum to slow the atoms down. Here is an instructive picture. In the quantum picture, light consists of miniscule, finite particles, called photons, which have a certain energy and momentum, like ordinary particles (for the record, photons differ from ordinary particles in that they have no mass and that they travel at the speed of light). Imagine a truck free-rolling (for eg. putting it on neutral gear at some speed) on a road. Now, if you stood in front of it and threw many balls (probably thousands) at it, it would slow down significantly. The atom is like the truck and the balls you throw are the photons.

What if the truck was moving away from you? If you threw balls at it, wouldn't it move faster? That's when the key concept of doppler shift comes in. When an atom is moving towards a laser beam, it sees the light at a higher frequency (referred to as blue-shifted. Blue light has a higher frequency than red light), the same effect as when you hear a train horn coming towards you at a higher pitch. Similarly, when an atom is moving away from a laser beam, it sees the light at a lower frequency (red-shifted), just like the train horn sounding at a lower pitch when the train has passed you and is moving away from you. The youtube video below is very instructive.



One of the key principles of quantum mechanics is discrete quantum energy states, which play a role when you consider tiny systems. If you consider an atom with 2 energy levels (simplest case; they typically have several), the atom can absorb (and later emit) light at a particular frequency which corresponds to the energy difference between the 2 states. It is referred to as a resonance, where atoms scatter light only if it is at the correct frequency. If you shone resonant laser light on an atom, it would see the light only if it was at rest. If you red-detuned (lowered the frequency) of the light, an atom moving towards the light would see it blue-shifted (increase the frequency). That would bring the light into resonance for that atom. The atom would scatter photons and be pushed back. An atom moving away would see the light red-shifted, which would move it further out of resonance. That atom will not be affected by that laser beam.

So, if you put "red-detuned" laser light from all directions, you'll get atoms trapped at the center. If any atom tries to move in any direction, it sees oncoming laser light on resonance, scatters photons and gets pushed back. One keeps a magnetic field gradient to enhance the effect of the laser beams (I'm skipping the details). This is called a Magneto-Optical Trap (MOT).

Below is a video of sodium atoms in a MOT. It is in a glass cell inside vacuum, so that other atoms and molecules, normally present in air do not destroy it. The bright spot you see is ball of trapped sodium atoms scattering the yellow laser light (same colour as sodium lamps) that is used to trap it. There are probably a billion atoms there.



Back to the story. Once the idea of laser cooling had been established, theorists (physicists who work on theory only) made a simple model for atoms and predicted that you could cool Sodium atoms down only to the doppler limit, 240 uK (microKelvin, 0.000240 degrees above absolute zero, much colder than liquid helium), which is the point at which the heating due to laser light prevents the atoms from getting colder. It was simple and straightforward enough and taken as the best you can possibly do.

When people started doing the experiment, they noticed something strange going on, where things were not behaving as expected. On taking a more careful look, they found out that the atoms were actually COLDER than the 240 uK! On playing around with the setup, they found they could cool the atoms down to 40 uK, 6 times colder than the doppler limit! To put this in perspective, the best solar cells have achieved 25% efficiency. Imagine if a scientist working on a solar cell found that she got more electrical energy from the cell than the total energy falling on it. That simply can't happen! So, how was it possible to beat the doppler limit?

It turned out that, in the simple model, the theorists had assumed a 2-level atom, which is quite reasonable considering that other levels don't participate in the cooling. However, it turned out that the other levels did in fact play a role and instead of preventing the atoms from being cooled to the theoretical limit, actually conspired to enable them to cool to a temperature 6 times lower! So, instead of being stopped at the doppler limit, we now have sub-doppler cooling and a sub-doppler limit.

Another story I've heard is from people who cool Erbium. Erbium is a more complicated atom with many more energy levels. The physicists had worked out the optimal parameters from theory and were making a MOT. They got some atoms trapped, and then decided to play around with the laser frequency. Trying out the laser frequency on the blue-detuned side of the resonance, they found that they were able to do better and got a bigger MOT. How is it possible that laser light which would push atoms away can even trap them? It turned out that the magnetic properties of Erbium played a role, and again conspired to make things work.

There are other such stories I've heard in laser cooling, where some kind of Anti-Murhpy's law seems to exist. While I'm sure that many people who work in the field face the usual frustrations and struggles of trying to make things work like they're expected to, it is amazing that there is are so many instances of Anti-Murphy's law where things have worked better than they should have.