Simulating Two-Dimensional Coherent Spectroscopy with Arbitrary Inhomogeneity Beyond Gaussian Distributions

Line shape analysis in two-dimensional coherent spectroscopy (2DCS) is crucial for understanding complex dynamics, but traditional methods often assume Gaussian inhomogeneity [1,2], limiting accuracy. We present a computational approach that expands 2DCS simulations to accommodate arbitrary inhomogeneous distributions and correlations. This method addresses challenges in systems like quantum dots and localized emitters in monolayer transition metal dichalcogenides, where Gaussian-based techniques might be less accurate. The technique reinterprets the third-order nonlinear response function as a convolution of a homogeneous system's response with a two-dimensional oscillator distribution, we simulate 2D spectra for arbitrary inhomogeneity. Additionally, a weighted correlation coefficient of the spectral maps directly estimates frequency-frequency correlation functions without assuming specific forms for the inhomogeneity. This method enables more accurate analysis of experimental 2D spectra, providing insights into dynamics and spectral diffusion in systems exhibiting discrete inhomogeneity.

[1] M. E. Siemens, G. Moody, H. Li, A. D. Bristow, and S. T. Cundiff, “Resonance lineshapes in two-dimensional fourier transform spectroscopy,” Opt. Express 18, 17699 (2010).

[2] S. T. Roberts, J. J. Loparo, and A. Tokmakoff, “Characterization of spectral diffusion from two-dimensional line shapes,” J. Chem. Phys. 125 (2006).