Calibrating Images of Laser Cooling
An undergraduate thesis in Physics
The goal of the Goodsell Lab is to laser-cool rubidium atoms in a vacuum chamber in order to document and study nearly stationary atoms and their interaction with solid surfaces and external electric fields. Early on in the lab's research - before laser-cooled atoms were achieved - I worked on methods of capturing and calibrating images of room-temperature fluorescing atoms and outlined their application to laser-cooled atoms.
When:
Spring and Fall 2012
Where:
Middlebury College
For:
Fig. 1. Hand-drawn diagram of vacuum chamber set-up for laser cooling.
Laser-cooling is a process by which atoms in a cloud are slowed and trapped at the intersection of multiple laser beams, tuned to resonance with an energy transition within the target atom. In laser-cooling experiments, imaging can be used to gain information about this cloud of atoms cooled to near absolute zero. Some of these imaging methods are tested in this paper on room-temperature fluorescing 85Rb atoms and outlined for application to laser-cooled atoms. A power meter and calibrated photos from a digital camera were used in two methods to determine the spatial distribution of room-temperature fluorescing atoms. A photodiode was used to determine the number of fluorescing warm atoms. Methods for capturing and calibrating digital imagery of laser-cooled 85Rb atoms are outlined to determine the number of atoms in the cloud, the dimensions of the cloud and the temperature of the cloud. The loss of kinetic energy that results in the slowing and thus cooling of the cloud is accounted for through calculations on conservation of energy and Doppler-shifted frequencies.
Abstract
Process
Because of the timing and resources available for undergraduate theses, my thesis topic was externally determined while the work I conducted within that topic was self-directed. I was asked to determine the diameter and temperature of a beam of fluorescing atoms. I used two methods to determine the diameter of the beam: the line cut method and the razor blade method.
The Line-Cut Method
The linecut method used a infrared photo of a laser beam passing through a slanted vessel of rubidium vapor, creating fluorescence. In the same photo, at the same distance away from the camera as the fluorescence, is a ruler used to calibrate the pixels of the photo.
A vertical and horizontal 'linecut' of pixel values from the photo are extracted and plotted in Mathematica.
The Razorblade Method
The razorblade method used a razorblade to interrupt the path of a laser beam incident on a powermeter. The incremental height of the razorblade was plotted against the power output at each increment. From this plot, the height, or diameter of the laser beam, was detected.
My favorite part of this project was a spontaneous addition to end end of my thesis in which I derived the energy calculation for how doppler-shifted photons actually cool rubidium atoms. For most of my thesis work, a question lingered in the back of my mind as to why adding energy to a system through lasers - usually used to heat and burn objects - cools a cloud of atoms. The answer lies in the finer details of the energy transition of a rubidium atom incident upon a photon of a very specific frequency. The result is a new photon output and a tiny loss of kinetic energy - which happens many times over to create a slowed cloud of atoms. I took myself step-by-step through this calculation and the result was an additional chapter.
Products
If you feel so inspired, a link to my 69-page thesis is available to the left.
I made an effort to write it in such a way that a non-laser-cooling expert would be able to understand its contents. Additionally, my final assessment was to defend this thesis in front of a panel of my previous professors.
Calibrating Images of Laser Cooling
by Ali Andrews
Why is this important?
For me:
I was able to combine the skills I developed over the course of my Physics degree, including computation, lab experiments and formal science writing. It was a good opportunity to hone my skills in presenting my findings formally and needing to defend them in front of an audience of physicists.
For others:
Laser cooling is a fascinating branch of science because it offers the opportunity to observe atoms at a near stand-still. It has has few practical applications yet - but has implications for atomic clocks, production of the Bose-Einstein condensate and precision of atomic energy levels.