Algorithms for Efficient Calculation of Nonlinear Optical Spectra: Ultrafast Spectroscopy Suite and its Applications

Abstract

This thesis presents analytic and computational advances in the prediction of perturbative nonlinear optical spectroscopies. The contributions of this thesis are packaged together in an open source, freely available piece of software called ultrafast spectroscopy suite (UFSS). It is designed to automatically simulate nonlinear optical spectroscopies for any phase-matching or phase-cycling condition, including finite pulse effects. UFSS includes an algorithm called the diagram generator (DG) that automates the process of writing out all of the Feynman diagrams that contribute to a desired phase-matching or phase-cycling condition, and includes all pulse overlap diagrams when relevant, paving the way toward automation of perturbative calculations. Further, many diagrams can be automatically combined into composite diagrams, giving an exponential decrease in computation time of high-order calculations. Composite diagrams even allow for the efficient study of Rabi oscillations as a function of pulse amplitude, by summing many orders of perturbation theory. The perturbative calculations are done using a novel algorithm presented in this thesis called Ultrafast Ultrafast spectroscopy (UF2). UF2 is an efficient method for determining diagrammatic contributions to spectra including arbitrary (whether analytical or experimentally measured) pulse shapes. It uses the speed of the fast Fourier transform to be as much as 500 times faster than direct propagation techniques for small model Hamiltonians (for Hamiltonian dimension of 100 or less). UF2 outperforms direct propagation techniques for a wide range of model systems, with the speed boost diminishing as the dimension of the model Hamiltonian increases. UF2 can predict spectra for any model system whose relevant Hilbert space that can be described using a finite basis and that can be diagonalized numerically, and users are free to specify their own model. UFSS includes a model generator that generates Hamiltonians and Liouvillians of vibronic systems, allowing users to easily simulate NLOSs for a wide range of model system parameters. UFSS is a fully functional piece of software for simulating any NLOS, to any desired order in perturbation theory.