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.

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. |

**Final Presentations: **

Poster: Computational Light-Matter Interactions - Daniel Keylon.pdf

Presentation: Computational L-M Interactions_1 (2).pptx

**About Me:**** ** I will receive my
bachelor’s degree in physics and mathematics from Union
University in the spring of 2016.

Besides Physics and Math, I participate in the local chapter of the Society of Physics Students in which I have held the positions

of senator and president over the years. I also participate in my school’s debate team as both a debater and a judge. In my

spare time, I read quite a lot.

Through this REU program, I have learned:

· How to estimate changing population levels for atomic systems.

· A deeper understanding of programming.

· What research is.

· About ethical considerations for researchers.

· Networking skills.

· How to canoe.

Introduction to Coherent Excitation:

Introduction to calculating Decay Rates: