Dimeric Perylene-Bisimide Organic Molecules: Fractional-Time Control of Quantum Resources

In this work, we explore the dynamics of quantum correlations, namely coherence, entanglement, and nonlocality associated with a Bell state, in a dimeric arrangement of organic PBI molecules, mediated by dipole-dipole interactions, under time-fractional dynamics. Within the framework of the time-fractional Schr\"odinger equation (TFSE) with Caputo fractional derivatives, we explore system dynamics for different values of the fractional order $\tau$, transition energies, interaction strength, and purity $p$. We employ the relative entropy of coherence, logarithmic entanglement entropy and concurrence, and CHSH inequality to estimate system dynamics associated with coherence, entanglement, and nonlocality, respectively. These findings highlight the role of the fractional order $\tau$ in system dynamics, including memory effects and relaxation, and thereby bring together ideas from fractional calculus and quantum information theory perspectives and discuss methodologies to control and utilize these molecular quantum correlations.