# Research

Below are brief descriptions of some of my research projects. For further details, visit the links or see my CV.

## • Lévy processes and Extreme Events

Lévy processes are the continuous-time analog of random walks, and include the well-known Wiener process (i.e. Brownian motion) as well as the $\alpha$-stable processes, where the stochastic increment is drawn from a power-law distribution. These $\alpha$-stable Lévy processes are important for modeling a variety of extreme events (geologic processes, market crashes), as well as systems exhibiting anomalous diffusion (laser-cooled atoms, certain animal foraging behavior). My recent research has focused on conditioned Lévy processes, or Lévy bridges, which are a powerful tool for analyzing the history of a Lévy process. One of my recent results shows that by considering Lévy bridges, it is possible to derive a useful length scale which has applications for the detection of extreme events, as well as giving insight into the behavior of Lévy processes.

## • Anomalous Diffusion and Laser Cooled Atoms

Laser-cooled atoms are essential for a variety of high precision experiments, such as the development of Bose-Einstein condensates, atomic clocks, and a variety of precision metrology. Beyond direct applications, cold atoms themselves are an interesting testing ground for stochastic transport, as they are isolated systems with well defined forces. For part of my graduate research, I studied anomalous diffusion in Sisyphus cooling, and how certain boundary crossing statistics can have strong signatures indicating the presence of anomalous diffusion and Lévy flights.

## • Experiments with a Single Neutral Atom

As part of my graduate research, I performed a number of experiments and simulations with a single trapped rubidium atom. These included developing control systems for automatically trapping, manipulating, and monitoring single atoms (e.g. real-time imaging of a single trapped atom), as well as temperature measurements through release-recapture experiments (some of these results are included in Richard Wagner's PhD dissertation).

## • Electromagnetically Induced Transparency (undergraduate thesis)

For my undergraduate thesis at Reed College I designed and constructed an optical system to measure and analyze Electromagnetically Induced Transparency in thermal rubidium vapor.

In summer of 2010 I participated in an NSF Research Experience for Undergraduates program at University of Arkansas. My project involved measuring high time-resolution blinking statistics of colloidal CdSe quantum dots. I developed a LabVIEW control system for driving a nanometer precision scan of quantum dot samples, so that a single quantum emitter could be identified through $g^{(2)}$ measurements. Additionally, a full-field camera system allowed for the collection of low-time resolution blinking statistics of many quantum dots simultaneously. For this system I developed a tool in C to automatically extract blinking statistics from images many quantum dots.