Professor Abdulla to Present at Massachusetts Institute of Technology

Title: Quantum Optimal Control for Coherent Spin Dynamics of Radical Pairs via Pontryagin Maximum Principle

Description: We consider the problem of devising the shape of the external electromagnetic field driving the spin dynamics of radical pairs to quantum coherent state, through maximization of the triplet-singlet yield in biochemical reactions. The model is a Schrödinger system with spin Hamiltonians given by the sum of Zeeman interaction and hyperfine coupling interaction terms. We introduce a one-parameter family of optimal control problems by coupling the Schrödinger system to a control field through filtering equations for the electromagnetic field. Fréchet differentiability and Pontryagin Maximum Principle in Hilbert space is proved and the bang-bang structure of the optimal control is established. A new iterative Pontryagin Maximum Principle (IPMP) method for the identification of the bang-bang optimal control is developed. Numerical simulations based on IPMP and the gradient projection method (GPM) in Hilbert spaces are pursued, and the convergence, stability and the regularization effect are demonstrated. Comparative analysis of filtering with regular optimal electromagnetic field versus non-filtering with a pure bang-bang optimal field (Abdulla et al, 2024 ) demonstrates the change of the maxima of the singlet yield is less than 1%, while yielding a smooth variation of the electromagnetic field. The results open a venue for a potential experimental work for the magnetoreception as a manifestation of quantum biological phenomena.

Joint research with Jose Rodrigues and Jean-Jacques Slotine.