Laser Cooling.

When I first heard the term ‘Laser cooling’, I was fully dumbstruck.
Till the time I started to understand laser cooling, whenever I hear laser the pictures that would come into my mind are Lightsaber from star wars, Hot x-ray vision of Superman and similarly powerful vision of Scott from X-men. In all these pictures Laser is trying to heat the parts where it hits but never have I seen laser in cooling. So I must say the Physicists who gave us this superb technique must be ingenious.

In this article, I will explain the basics of Laser Cooling. But before going any further one must know exactly what a Laser is? or some of the properties of Electromagnetic radiation or simply LIGHT.

Back in the days of Newton, Newton proposed corpuscular theory for light. It says light is made up of tiny corpuscles or particles. Later this theory was rejected after Thomas Young proved that Light behaves as a wave. Most of us know the famous Young experiment. Then later on Einstein came along and said Actually light is neither wave nor particle but both.
Wait! But why am I telling you all this? Am I crazy or what?

I am telling you all this because in Laser Cooling both the wave and particle nature acts together to cool atoms. Whenever I say Photon in this article I mean Laser, because laser is just Amplified(power increased) light.
Laser Cooling Is any technique in which we use Laser to slow down the atoms. What do I mean slow down the atoms? The name says cooling, right!

In high school, you might have studied this definition. That Kinetic energy is the energy by the virtue of its motion. Well, the heat energy is just some form of kinetic energy. The more the body is in motion the more the heat it has. To get a nice picture of this, try to stop a rotating bicycle tyre. Your hand gets hot after some time. You might say “oh! its the friction that is heating your hand.” Yeah, you are right. But the overall picture is the kinetic energy of the wheel decreased and your hands’ temperature increased. So simply putting You can say Heat energy in the form of kinetic energy which gets transferred from one body in motion to others.

More clearly looking, When you are trying to stop the tire, you are interacting with the surface atoms of the tire. They are in motion. They hit the atoms on your hand and they transfer a part of their momentum to the surface atoms on your hand setting them in motion. Since the momentum is received is only enough that they can’t rip all the atoms of the skin, these surface atoms just keep agitating and vibrating on the skin which you feel like an increase in temperature. That exact sensation is due to transfer of kinetic energy or we can simply call it as heat energy. Since the brain interprets it as heat, you couldn’t exactly feel the motion in the first place.

So if we slow down the atoms, we can cool them down.

How do we slow them then? Idea is that we hit the atoms with the particles of light, which are called Photons, in the direction opposite to the motion of atoms. And that will do it. Remember the time you play with small truck toys. To stop your siblings truck, you would send your truck in the opposite direction with almost the same speed. That would do it.

But what if you hit the truck with a bigger one at the same speed, it would send your brother’s truck back. To just stop your brother’s truck, you have to slow your truck’s speed. What if you hit with a smaller one. It would send your truck back. So you have to send your truck at a higher speed.
What is important is the right product of mass and speed of the truck, which can be otherwise called as momentum.
momentum P = mass M * velocity V

So the atoms we hit gets slowed down by the amount of momentum of Photon we are hitting it with. This Property that Light being a photon and having momentum is the particle nature of the photon. So what is the momentum of Photons?
The momentum of Photon P is given by E/c, where E is the energy of photon and C is the velocity of light, well the photon itself, in a vacuum.
Where E = hc/λ., h is Planck’s constant and λ is the wavelength of the photon. I said particle and now I am speaking of wavelengths. Wavelength because photon travels in the form of a wave. The whole basic idea of laser cooling in the below picture.

So the atoms get hit by the photons and slow down. This process repeats…

There are a few more things one must know. Atoms are not disturbed by all the photons. You need them to be to of particular wavelengths. Because atoms only absorb at certain energy levels.
Imagine the atom as a multi-storey building with 2 rooms on each floor. So you can rent each floor to only two people. Each person on the same floor has equal potential energy(since they are at an equal height from the ground). So Floor one guys have E1 amount of energy, floor two guys have E2 amount of energy and so on. And the floors are not of the same height, so the energy differences vary.
If a guy has to go to floor two from floor one he must gain extra energy which is equal to E2-E1, not less and not more. Not more because he has no other way to lose energy, he would get fat. And another condition is you can enter a floor only if at least one of its rooms are empty.
And you can’t stay on that floor for a long time if the rooms on the lower floor are empty. Everyone is interested in the floor nearer to ground.

Same is with atoms. They have energy levels with the energy of electrons in that level increases with the number of that level. Each level can only accommodate two electrons. If you give them enough energy, they jump into higher levels, but they don’t stay long. They lose the energy given to them and jump back to lower levels.

To gain energy electrons absorb photons because photons are one of the purest forms of energy carriers there is. To lose energy they emit photons, and this way of losing energy is called Spontaneous Emission. It is a random process. Electrons emit photons in all random directions. While emitting photons, Atoms get a recoil momentum, the type of momentum one gets while shooting. But because it is a random process, the overall change of momentum because of spontaneous emission gets to zero after a large number of such emissions.

So as I said they don’t absorb all the photons, Only the ones containing energy equal to that of the energy difference between two levels. And they slow down by the momentum of h/λ.

Here comes another problem. Have you heard of the Doppler effect?
If you have, then you might have heard the famous example of a train passing by. As the train approaches you, the frequency of sound is higher and as it leaves you the frequency drops. If you are moving opposite to train the frequency increases with the increase in the relative speed. Same goes with light.

Think of yourself as an atom, the train as photon and wavelength of sound as the wavelength of light relative to you. As it approaches the atom i.e., you…the wavelength appears as increased ones. The difference between appeared frequency and the original frequency is called the Doppler shift.

So the problem here is you can’t send photons with energy equal to E2-E1 and frequency equal to ‘ν=E2-E1/c‘. Because Atoms perceive them as of higher frequency(>ν). The solution is to send photons of lower frequency, a little lower so that it is balanced by the doppler shift.

In general, if we consider atoms in the air they are spread with different velocities. In the below picture they are shown by the dotted line. And after hitting them with constant wavelength ( which is perfectly suited for absorption) photons, we slow them up to some velocity. After they reach that lower velocity, the doppler shift decreases, thus the atoms don’t absorb the photons anymore. This stage is reached when all the atoms above that velocity region reach that velocity. In the below picture you can see the peak in the dark curve. It shows all the atoms getting to that velocity, giving us peak density of atoms at that velocity.

But what if we are hitting the atoms from the backside? This will further increase the momentum. Well, this problem is already solved by the doppler effect. As I said Atoms perceive the wavelength to be higher when it hits in the opposite direction and lighter when hit in the same direction as motion. So the atom that is moving in the same direction is transparent to that photon.

There comes another problem. You see previously I said Atom is a multi-storey building, there is an additional picture too. There is not just a single level at each floor i.e., each Energy level is little widespread.

As you can see, E1 is one full level and E2 is another. They are spread into many other levels.
So the problem is now there are many other nearby energy levels, but we are just using photon which corresponds to one level. You can the problem clearly in the below picture of Sodium which is a two-level system, that is it has two energy levels.

a)Original pic to show problem
b)Solution
So we are using photons to send the electrons from F=2 to F’=3, shown by the dark line in (a). And what if the electron falls into F=1. Now it doesn’t respond to our photons and we can’t slow down the atom further.

This is the Optical Pumping problem. The solution to this is we can Use a secondary laser Which will repump the electron from F=1 to any of the upper levels. So this time it falls back to F=1. This is shown in (b) part of the above picture.

So we are finally ready with the basic Idea of Laser cooling.

• We hit the atoms with Photons of wavelengths which are slightly less than the wavelengths absorbed by the atoms.
• The atom absorbs it and slows down.
• Then it emits the photon.
• then again it absorbs the photon. and this continues…

Well after a certain we have to change the wavelengths of photons because as I said above these photons can only slow it down it to a certain velocity.

But how will we know the direction of motion of Atoms? Well, we don’t need to know.
What we can do is we send the laser in both directions ie., from the front and the back. So they only get hit by and absorbs the photons from the front because we will be sending laser of slightly lower wavelengths. So the Doppler shift in the front case will make it appear as the absorbable wavelengths and not the back ones.

As you can see from the Atom’s point of view on is red-shifted i.e., wavelength appears as increased. While the other is blue-shifted i.e., wavelength appears decreased.

There is this concept of Atomic traps called Optical Molasses.
We hit the atom from all the six directions i.e., from +z,-z,+x.-x,+y,-y. So whatever direction the atom is moving the opposite photon appears red-shifted and corrected to its wavelength. So it absorbs and slows down. It’s a trap. If it moves in any direction, it gets slowed down.

All the above technique which we understood till now is called Doppler laser cooling.

There is a slightly modified technique called Zeeman Cooling. I would call it an extended version of Doppler cooling.
In this what we do is instead of changing the wavelength of photons after a certain amount of time (remember after a certain time all the atoms go to a lower velocity where they don’t respond to the present photons), we change the E2-E1 values. That is we now play with atomic energy levels.

To understand this you need to know of something called Zeeman effect.

Imagine the orbitals of electrons revolving around the nucleus as a circular wire conducting current. We know that such wire has its magnetic field. We can call it a tiny magnet. So when this tiny wire interacts with the external magnetic field they get extra energy(kind of magnetic potential energy). And all the electrons have a different value of the magnetic moment. The magnetic moment is a direction oriented magnetic quantity, which is higher when the magnetic field due to orbital is higher. So based on this Zeeman effect there will slight rises and falls in the energy levels. These changes are called Zeeman shift.

So higher the external magnetic field higher the effect on the levels, so higher Zeeman effect. This increase the E2-E1 value for us.
The basic setup is as follows:

What you are looking in the first part is that we are sending the atomic beam through a tapered solenoid. A solenoid is just a cylinder wound with plastered wire whose ends can be connected across a voltage difference. Because of the current, this solenoid creates a magnetic field. So the solenoid is wound heavily at the beginning and the winding gradually decreases. That means the magnetic field is higher at the beginning and decreases as we go to the other end. This magnetic field B(z) is shown in the second part as to how it is varying along z.

So initially the magnetic field is higher so the Zeeman shift is higher, that means E2-E1 value is higher. That’s why we send photons of particular wavelength so that the doppler shift exactly matches up the wavelength for us. As we move along z, the atoms are slightly slowed down because of photon absorption. So the doppler shift decreases. Alongside the magnetic field decreased thus decreasing the Zeeman shift thus decreasing E2-E1. So the change is doppler shift is compensated by the change in Zeeman shift, thus enabling the atoms to absorb the photons even further.

Thus cooling the atoms.

There are many other techniques developed after this which work in different ways. But the above techniques give us the first developed ideas on Cooling Atoms using Lasers.

Please correct me if I am wrong. I will consider them and correct the article.
Comments are strongly encouraged.