Author: Eric Seglem | Major: Physics (Professional Concentration) and Mathematics (Applied Concentration) | Semester: Spring 2024
Presenting at the INBRE 2023 Conference. Credit: inbre.uark.edu
My name is Eric Seglem and I am an Honors College Fellow of 2020. I am a student of the J. William Fulbright College of Arts and Sciences and I am double majoring in Physics (Professional Concentration) and Mathematics (Applied Concentration). During the Spring of 2024, I defended my honors thesis in the study of quantum optics under Physics Professor Reeta Vyas. In the future, I plan to obtain a PhD in Physics with the intention of studying quantum information or mathematical physics.
For one year now, I have been performing research in quantum optics under Physics Professor Reeta Vyas. In this project, we explore the theory of certain superpositions of light. Specifically, we are analyzing superpositions of coherent states of light and squeezed states of light. The goal of the project is to determine if these states possess a nonclassical property known as photon antibunching. If a light source has antibunching, then the photons being emitted from the source have a low probability of being detected near each other. The reason why this is important is because antibunching is a signature characteristic of single-photon sources, which are capable of emitting singular photons on demand. Being able to manipulate the emission of photons has many implications for quantum information and technology, including quantum networks and quantum computers. Essentially, our research contributes to a larger effort to control photon emissions.
The work being performed in this project is mostly mathematical. To determine the necessary information about the quantum states, we must derive equations for the photon counting statistics. This allows us to analyze the emission of photons for each of our states from a statistical perspective, and we can use this perspective to determine if antibunching can be observed or not. What this means is we are not actually measuring anything in the physical world, but rather predicting the results through mathematical analysis. No lab equipment is necessary; we simply derive the equations by hand and analyze them using Wolfram Mathematica software.
What I like most about like about this project is the freedom it provides. Due to the theoretical nature of these topics, we are not limited by measurements or physical constraints. Not only does this mean that I can perform the necessary work at the comfort of my home, but also that I can use any tools which are mathematically feasible to do so. It was often the case that there were multiple different methods of accomplishing the same task, and each method offered a slightly different perspective on the problem. Of course, some methods are easier than others, but they all reveal unique insights into the nature of our light states.
During this semester, I set a goal for myself to find an interesting mathematical relationship which could be used to help simplify the calculations. This turned out to be a difficult task. My first attempt was to introduce matrix notation. My idea was to define matrices in a fashion which I would describe as being loosely inspired by the famous Pauli spin matrices. For around three weeks, I devoted myself to making this work, but eventually, I had to admit failure. I also tried programming a heatmap which would provide an easier way to find antibunched states, but the calculations required to generate the plots proved to be too much for even Wolfram Mathematica to handle.
Even though I had many unsuccessful attempts, I eventually found success in a place I did not expect. Throughout the duration of this project, I noticed a pattern which kept appearing in the derived equations. It was a term which was only slightly different from the Taylor series expansion of the familiar exponential function. For many months, I assumed that it could not be simplified any further and left it as it was. One day, however, my curiosity got the better of me, and I began searching online in hopes of finding some information about simplifying this mysterious term. Instead, I found an entire class of special functions defined by this exact term: these are the generalized hyperbolic functions. After integrating them into the equations, I found that not only did these functions simplify the expressions, but they also made the derivations much quicker. Within a single day, I was able to rederive all the equations and check them with the original results. I now believe that these functions may be used to inspire new research for these quantum states.
Over the past year, I have learned many things from this project. I learned how to plan effective presentations, read research papers, and write scientifically, among other skills. But perhaps the most important thing I learned this semester is not a skill, but rather a lesson: Sometimes, things just fail, but you cannot let yourself become discouraged. Research is often unpredictable, and we cannot expect everything to work out as planned. In my case, I tried many different approaches before I found something meaningful. Moreover, what I found was inspired by the patterns I had noticed for a long time; the real victory was in allowing my curiosity to take over. Even with my brief introduction to physics research, I am now certain that this what I wish to pursue in my future. I look forward to continuing this project and learning more about the fascinating world of physics.