Time Dependent Hamiltonian: Visualizing Magnetic Resonance (read description for more detail)

In this animation, I iterate over many values of the drive frequency of the magnetic field (how fast it processes around the z axis). As the drive frequency approaches the Larmor frequency of the z component of the magnetic field, the path of the spin vector approaches the south pole of the Bloch sphere, indicating a high probability of a spin flip.

I enjoy creating computer animations of topics in math and physics that I use to help my peers and I visualize complicated concepts in unconventional ways. Earlier this year, my quantum mechanics teacher introduced Schrodinger time evolution, an important principle that describes how quantum spin is affected by a changing magnetic field. Using python, I successfully simulated and animated the path of a spin vector along the Bloch sphere in a way that, to my knowledge, has never been done before. With these animations, I’ve been able to visualize quantum magnetic resonance and the chaotic oscillations caused by varying both magnetic field position and strength with time.

Nothing compares to the butterfly-in-your-stomach feeling of discovery, the pure giddiness and awe that I felt while exploring this topic. My unconventional visual perspective of the concept revealed intricate patterns that my class and I have started to investigate. By varying the drive frequency of the magnetic field, the spin vector sometimes repeats its path periodically and sometimes never retraces its path. What conditions give rise to specific periods, or the lack of a period? When the spin vector never retraces its path, will it reach every point on the Bloch sphere in an infinite amount of time, or is there some bound to where it can reach? I’m working on these questions with several college physics professors, who are currently using my animations as teaching tools in their courses.