Research Interests

I am a PhD student in the mathematical physics and analysis research groups. My research is focused around a mathematical justification to rotating wave approximations, an important method in quantum optics, quantum computing, and atomic physics.

The idea of the rotating wave approximation is to take a Hamiltonian of a quantum system and rotate it into a rotating frame. We can then approximate the Hamiltonian with a simpler one by disregarding highly oscillatory counter-rotating terms. A classic example is the Quantum Rabi model, where we have a time-independent Hamiltonian describing the interaction between a laser and a two-level atom. We can rotate the Quantum Rabi Hamiltonian with respect to the laser, which gives us a time-dependent Hamiltonian, before discarding any highly oscillating counter-rotating terms. Rotating back into our original frame gives us a rotating wave approximation known as the Jaynes-Cummings model.

My research is focused on trying to mathematically justify approximations like the Jaynes-Cummings model for more general quantum systems by employing principles from operator theory and partial differential equations.