Phenomenological modelling for Time-Resolved Electron Paramagnetic Resonance in radical-triplet system

The spin dynamics of radical-triplet system (RTS) has been calculated by using the Lindblad formalism within the theory of open quantum system. The single-radical-triplet system (SRTS) is considered here for single-qubit quantum gate operations while double-radical-triplet system (DRTS) for two-qubit operations. The environment effects taken into account include the spin-lattice relaxation of the triplet exciton and radical spin-$\frac{1}{2}$, the inter-system crossing process that induces the transition from singlet excited state to the triplet ground state, and the rather slow relaxation process from the triplet ground state back down to the singlet ground state. These calculations shown that the line shape broadening is strongly related to the exchange interaction between triplet and exciton, which can be understood as a spontaneous magnetic field created by the triplet renormalises the original spin-$\frac{1}{2}$ electron spin resonance spectra. This work will provide key information about the spin dynamics for building optically-controlled molecular quantum gate out of radical-bearing molecules. Moreover, this has generated the further theoretical question on how the mixture of fermion and boson behaves.