Multistep Quantum Master Equation Theory for Response Functions in Four Wave Mixing Electronic Spectroscopy of Multichromophoric Macromolecules

Abstract

This work provides an alternative derivation of third order response functions in four wave mixing spectroscopy of multichromophoric macromolecular systems considering only single exciton states. For the case of harmonic oscillator bath linearly and diagonally coupled to exciton states, closed form expressions showing all the explicit time dependences are derived. These expressions can provide more solid physical basis for understanding 2-dimensional electronic spectroscopy signals. For more general cases of system-bath coupling, the quantum master equation (QME) approach is employed for the derivation of multistep time evolution equations for Green function-like operators. Solution of these equations is feasible at the level of 2nd order non-Markovian QME, and the new approach can account for inter-exciton coupling, dephasing, relaxation, and non-Markovian effects in a consistent manner. Key Words : Four wave mixing, Response function, Multichromophoric macromolecule IntroductionElectronic excitation is the outcome of correlated motion of electrons and is fundamentally quantum mechanical. When they are put together at nanometer length scale, each excitation loses its individuality and coherent superposition of those excitations, excitons, can be formed. This is possible even without physical contacts between chromophores because of long range characteristics of Coulomb interactions in particular. Thus, the energetics and the dynamics of delocalized excitons in so called multichromophoric macromolecule (MCMM) often result in optical properties that are distinctively different from those of individual chromophores. Well known examples of such MCMMs are photosynthetic light harvesting complexes, 1-4 conjugated polymers, 5-10 and dendrimers. 11-15Excitons in these MCMMs are tunable but fragile, which are being utilized positively for efficient and robust collection/ transfer of excitons in natural photosynthetic light harvesting complexes. [16][17][18][19] Similar utilization in synthetic MCMMs, if possible, can lead to novel mechanisms of solar energy conversion 20,21 and sensor development. Detailed spectroscopic studies of MCMM are needed to explore these possibilities.In general, spectroscopic study of MCMM is difficult because of broad range of dynamical time scales and the large number of structural/energetic degrees of freedom. In understanding how their optical properties reflect the molecular level structural and dynamical details, conventional linear spectroscopy is severely limited. Nonlinear spectroscopy of MCMM has an important role to play in this regard. [22][23][24][25] Indeed, recent progress in 2-dimensional electronic spectroscopy (2DES) [26][27][28][29] made it possible to identify quantum coherence lasting up to 500 fs in photosynthetic light harvesting complexes despite significant amount of disorder and fluctuations. Theoretical modelings of these 2DES signals have been made, 30-34 but clear understanding of the origins and effects of the coherent quantum beating is not available yet. This mo...