Numerical Method for Nonlinear Optical Spectroscopies: Ultrafast Ultrafast Spectroscopy

Abstract

We outline a novel numerical method, called Ultrafast Ultrafast (UF${}^2$), for calculating the $n^{\text{th}}$-order wavepackets required for calculating n-wave mixing signals. The method is simple to implement, and we demonstrate that it is computationally more efficient than other methods in a wide range of use cases. Resulting spectra are identical to those calculated using the standard response function formalism but with increased efficiency. The computational speed-ups of UF${}^2$ come from (a) non-perturbative and costless propagation of the system time-evolution (b) numerical propagation only at times when perturbative optical pulses are non-zero and (c) use of the fast Fourier transform convolution algorithm for efficient numerical propagation. The simplicity of this formalism allows us to write a simple software package that is as easy to use and understand as the Feynman diagrams that organize the understanding of $n$-wave mixing processes.

arXiv comment16 pages, 7 figures; major revisions; forthcoming in J Chem Phys

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