Rate-Equation Simulation of Molecular Quantum State Evolution
To guide experimental development, I wrote a Python simulation of the behavior of a molecule when irradiated with a spectrally broad laser source. This spectral breadth effectively mimics an array of dozens of monochromatic lasers, each of which potentially interacts with hundreds of molecular quantum states.
The problem is modeled as a system of first-order linear differential equations
where the D matrix is given explicitly in terms of the Einstein transition coefficients, which quantify the interaction of the molecule with the electromagnetic spectrum
The quadratic increase in computational cost with the number of basis states necessitated careful development of pruning methodology. A non-trivial set of self-consistency tests also needed to be developed in order to confirm the descriptive accuracy of the pruned set.
More detail may be found in Chapter 4 of my doctoral thesis.
Ion Trap Instability Analysis
In the field of ultracold trapped ions, minimization of ion micromotion has been a goal for decades. Quantification of the effect has proven particularly challenging, but between 2009 and 2012 I was able to develop an original methodology to further that goal.
More detail may be found in Appl. Phys. B. 107, 1097-1104 (2012).