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

## TL;DR

This paper models a light-driven molecular motor using a multi-state Brownian ratchet approach, analyzing its dynamics and optical spectra, and explores how pulse timing affects efficiency and observable signals.

## Contribution

It introduces a multi-state quantum Smoluchowski model for photo-driven molecular motors and investigates the effects of pulse timing on motor efficiency and spectroscopic signatures.

## Key findings

- Average rotational speed depends on thermalization timescale.
- Efficiency is maximized when pulse repetition and photoisomerization timescales are separated.
- Spectroscopic techniques can observe the photoisomerization and thermalization processes.

## Abstract

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. We analyze the motor efficiency by numerically integrating the equations of motion for a rotator system driven by repeatedly impulsive excitations. When the timescales of the pulse repetition, photoisomerization, and thermalization processes are separated, the average rotational speed of the motor is determined by the timescale 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 timescales 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.