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Computational Light-Matter Interactions

By Daniel C. Keylon

Supervisor: Dr. Brett Depoala, Professor of Physics

Kansas State University Physics Department REU Program

This program is funded by the National Science Foundation through grant number PHYS-1461251. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Below, I describe the Project Overview, my Research Description, my Research Progress, and my Final Presentation . Scrolls all the way down to learn more About Me. Finally, I've included some Useful Links.

Project Overview: This is 1-2 paragraphs suitable for a congressperson.

The goal of my work this summer is to develop a computer program to automate the solution of equations relating to the population levels of atoms. Studying atoms and molecules often involves using lasers to figure out how many electrons reside in each energy level of the atomic structure and what processes contribute to changes in these population levels. However, setting up experiments to test different parameters tends to be time consuming and possibly expensive. Luckily, theoreticians have discovered equations that can be used to model the evolution of the atomic systems over time. These equations can be used to help predict what configuration of parameters would produce the most interesting experimental outcomes. Unfortunately, solving these equations by hand involves tedium, time, and a large margin for accidental error. Already existing software packages, such as Mathematica, can be used to accelerate this process, but as the complexity of the atomic system increases, the time it takes for these software packages to compute solutions increases dramatically. As far as Dr. Depaola and I are aware, no custom software exists to solve these equations, so we intend to write our own software which will remedy all above mentioned problems. This software will be published freely on the internet for the use of researchers.

Research Description:

This project heavily relied on knowledge of introductory quantum mechanics, a basic knowledge of laser physics, and a decent amount of coding experience in C or C++. The summer began with a review of energy level physics and associated notation. From there, I was introduced to the physics of coherent excitation by lasers which served as the foundation of the rest of the REU. After I gained experience with this basic material, work began on calculating numerical results for a specific example for use in checking the code. As work on the C++ code began and deepened, I learned about Vigner 3J and 6J symbols as well as related Clebsch-Gordon coefficients. These mathematical constructs were implemented into the code to account for spontaneous emission. Implementation of these features, debugging, and implementation of related human interface features, consumed the rest of the summer.

Research Progress: I have made progress! Here are some of my most recent actions.

Week 1	Introduction to program. Learn material on Coherent Excitation.
Week 2	Finished learning material on Coherent Excitation and began hand calculation of example case.
Week 3	Finished hand calculation. Programmed Mathematica to compute energy level populations for steady state, numeric constant solutions. Began working with code.
Week 4	Began learning vigner 3j and 6j material. Began working through common algorithms in the code.
Week 5	Learned material on Vigner 3j and 6j symbols and began implementation of makeGamma function.
Week 6	Finished implementation of makeGamma and related debugging.
Week 7	Debugging of laserQuery function and other related functions.
Week 8	Debugging of output
Week 9	Debugging of functions that create and use Gamma. Debugging of laser selection methods.
Week 10	Debugging of initialization methods. Correction of Wigner Calculations.