Coherent Control of Population Transfer via Linear Chirp in Liquid Solution: The Role of Motional Narrowing.

Abstract

The conditions under which linear chirp can be used to control population transfer between the electronic states of a chromophore dissolved in liquid solution are investigated. To this end, we model the chromophore as a two-state system with shifted electronic potential energy surfaces and a fluctuating electronic transition frequency. The fluctuations are described as an exponentially correlated Gaussian stochastic process, which can be characterized by the average fluctuation amplitude, σ, and correlation time, τc. The time-dependent Schrödinger equation is solved numerically for an ensemble of stochastic histories, at different values of σ and τc, and under a wide range of pulse intensities and linear chirp coefficients. In the limit τc → ∞, we find that control diminishes rapidly as soon as σ exceeds the bandwidth of the pulse. However, we also find that control can be regained by reducing τc. We attribute this trend to motional narrowing, whereby decreasing τc narrows down the effective bandwidth of the solvent-induced fluctuations. The results suggest that the choice of methanol as a solvent in the actual experimental demonstration of chirp control by Cerullo et al. [ Chem. Phys. Lett. 1996 , 262 , 362 - 368 ] may have contributed to its success, due to the particularly short τc (∼20 fs) that the rapid librations of this hydrogen bonded liquid give rise to. The results also give rise to the rather surprising prediction that coherent control in liquid solution can be strongly dependent on the choice of solvent and be improved upon by choosing solvents that correspond to lower values of στc.