Modeling and analyzing a photo-driven molecular motor system: Ratchet dynamics and non-linear optical spectra

A light-driven molecular motor system is investigated using a multi-state Brownian ratchet model described by a single effective coordinate with multiple electronic states in a dissipative environment. The rotational motion of the motor system is investigated on the basis of wavepacket dynamics. A current determined from the interplay between a fast photochemical isomerization (photoisomerization) process triggered by pulses and a slow thermal isomerization (thermalization) process arising from an overdamped environment is numerically evaluated. For this purpose, we employ the multi-state low-temperature quantum Smoluchowski equations that allow us to simulate the fast quantum electronic dynamics in the overdamped environment, where conventional approaches, such as the Zusman equation approach, fail to apply due to the positivity problem. We analyze the motor efficiency by numerically integrating the equations of motion for a rotator system driven by repeatedly impulsive excitations. When the time scales of the pulse repetition, photoisomerization, and thermalization processes are separated, the average rotational speed of the motor is determined by the time scale of thermalization. In this regime, the average rotational current can be described by a simple equation derived from a rate equation for the thermalization process. When laser pulses are applied repeatedly and the time scales of the photoisomerization and pulse repetition are close, the details of the photoisomerization process become important to analyze the entire rotational process. We examine the possibility of observing the photoisomerization and the thermalization processes associated with stationary rotating dynamics of the motor system by spectroscopic means, e.g., pump-probe, transient absorption, and two-dimensional electronic spectroscopy techniques.