Semi-Automatic Retrieval of Temperature and Density in a Magneto-Optical Trap
This summer I am working to design, construct, and test an apparatus to measure the temperature and density of Rubidium vapor in a magneto-optical trap (MOT). MOTRIMS uses a MOT to run experiments on photo-association of molecules. They do not at this time have a way to measure the density of atoms in the MOT, or a way to measure the temperature of atoms in the MOT. That is where my project comes in.
What is a Magneto-Optical Trap?
A MOT is an apparatus used to cool and trap atoms. The MOTRIMS MOT works using six orthogonal laser beams of identical frequency, along with a magnetic field gradient created by a pair of anti-Helmholtz coils. The laser beams are set at a frequency just below a transition frequency of the Rubidium atoms that we use. So when an atom moves away from where the six beams meet, it will “see” a Doppler shifted frequency of the light and absorb a photon from the direction that the atom is heading. When the atom de-excites, a photon is released isotropically and, due to conservation of momentum, that atom will, on average, have net change in velocity opposite to its direction of motion. Therefore, the atoms eventually collect at the center of the trap, where they have very low velocities, hence very low temperatures.
The MOTRIMS MOT
What is photo-association of molecules?
We start with a collection of Rubidium atoms, but it is easier to think about if we consider just two such atoms. In general, these two atoms will not interact much, especially in low density situations. When they do interact, the atoms will undergo a collision and due to conservation of momentum they will simply bounce off each other. In order for a molecule to form, a third particle is needed, due, once again, to conservation of momentum. This is because when a molecule is formed, and the two atoms drop into a lower energy state together, the third particle can carry away the extra energy and momentum.
In photo-association, one of the atoms becomes excited by absorbing a photon, which acts as the “third body” described above. So now two atoms collide, one of them excited, and an unbound molecule exists. This quasi-molecule then decays into a lower energy and one of two things can happen: 1. A photon of energy equal to the original photon is emitted and we are left with an atom pair, or 2. The photon emitted is of greater energy, and we are left with a bound molecule.
Now this is fun and all, but what happens in MOTRIMS is a little bit different…
In MOTRIMS, we look at what happens when the molecule is further excited before any photons have been emitted. This means that the molecule will be excited above its ionization level, but will eventually autoionize, and we are left with an ionized Rubidium molecule.
You may be asking yourself, why would we want to do this? And so I will tell you. When we form these molecular ions, they follow a path, jumping from potential curve to potential curve. We are trying to study the path that Rubidium takes to get to the molecular ion potential curve. This way, it will be possible to look for the optimum path for creating molecules.
These are some of the potential curves that the “molecule” follows in being formed. There is quite a few.
So why do we want to know the density and temperature?
In order to study this process and somewhat the goal, we want to make as many molecules as possible. That is where temperature and density can play a part. In a high density gas, the atoms will interact more often than in a low density gas because, on average, the atoms are closer together. And since temperature is related to velocity, atoms at high temperatures will interact more often than atoms at low temperatures, but the interaction energy will be higher and more energy will need to somehow be dissipated. So what is the best density and temperature to work with? We don’t know. That’s why I’m here.
How do we plan on doing this?
I’m glad you asked. There are different ways of measuring this out there, but they can be quite expensive and tricky. I am working on cheap way to do this using a cheap and simple CCD camera. Density will be measured by sending a light pulse, near resonance, through the trapped Rubidium cloud to a CCD camera. On the image, we will see a “shadow” caused by the Rubidium absorbing/scattering some of the light. By looking at how “bright” and “dark” this shadow is, it will be possible to reconstruct the density of the MOT. Measuring temperature is slightly trickier. We will do the same process, but we will have to compare images of the MOT expanding once the MOT lasers are turned off. The rate at which the Rubidium vapor expands is related to the temperature so it will be possible to trace back what the original temperature was.
The apparatus that I am using.
Thank you for reading through my research, I hope it was enlightening.