An efficient spectral method for numerical time-dependent perturbation theory

Abstract

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 n-th order perturbative expansion are evaluated numerically using tensor products. The N points discretized integrals are computed in O(N 2 ) operations, a significant improvement over the O(N n ) scaling of standard quadrature methods. arXiv:1907.07734v1 [physics.chem-ph]

Considerations regarding one-photon phase control

“…is required. 47 As such, the results of this article apply generally to open and closed systems. Finally, the dipolar approximation is taken, which assumes that the molecule of interest is much smaller than the wavelength of the exciting pulse, and that the important transitions are dipole allowed.…”

“…26 The semiclassical, perturbative approach forms the basis of the usual description of coherent control and ultrafast spectroscopy. 47 As such, no further analysis of the above assumptions will be made. An experimental demonstration of one-photon phase control, in the regime of validity of all the further assumptions and approximations described below, would require a significant and interesting change in the way coherent control and nonlinear spectroscopy are generally understood, but one that is beyond the scope of this paper.…”

Ultrashort pulse two-photon coherent control of a macroscopic phenomena: light-induced current from channelrhodopsin-2 in live brain cells

“…These features also appear in this model study and are explained as the result of nonzero phase-independent one-photon excitations. 28,[58][59][60] The one-photon contribution can be directly measured by increasing the laser intensity while reducing the repetition rate, i.e.…”