Fast algorithm for simulating nonlinear ultrafast spectroscopies

We present Ultrafast Ultrafast (UF²) spectroscopy, a fast algorithm for calculating perturbative n-wave mixing signals in nonlinear optical spectroscopies including arbitrary optical pulse shapes and overlaps. It was demonstrated for closed systems, and we present here the extension to open systems, including vibronic systems with Lindblad or Redfield evolution. UF² is more computationally efficient than any method of which we are aware when the dimension of the relevant system Hilbert space is sufficiently small, as in energy-transfer systems. The speed of UF² comes from working in the eigenbasis of the time evolution operator, which enables costless time evolution between pulses, and performing the time evolution due to the pulses using the FFT and convolution theorem. We characterize the computational cost for a range of system sizes, showing when UF² gives significant speed improvements over other methods.

UF² automatically generates all Feynman diagrams for a specified phase-matching condition. It is well-suited to calculating higher-order signals (6-wave mixing and above). UF² allows easy and quick prediction of nonlinear optical spectra for a wide range of system parameters and optical pulse shapes.