An efficient spectral method for numerical time-dependent perturbation theory

We develop the Fourier-Laplace Inversion of the Perturbation Theory (FLIPT), a novel numerically exact "black box" method to compute perturbative expansions of the density matrix with rigorous convergence conditions. Specifically, the FLIPT method is extremely well-suited to simulate multiphoton pulsed laser experiments with complex pulse shapes. The n-dimensional frequency integrals of the nth order perturbative expansion are evaluated numerically using tensor products. The N-point discretized integrals are computed in O(N²) operations, a significant improvement over the O(Nⁿ) scaling of standard quadrature methods.