An efficient spectral method for numerical time-dependent perturbation theory

Area of Science:

• Quantum mechanics
• Computational physics
• Laser physics

Background:

• Perturbative expansions are crucial for understanding quantum systems.
• Simulating multiphoton pulsed laser experiments presents computational challenges.
• Existing methods struggle with complex pulse shapes and scaling.

Purpose of the Study:

• To develop a novel, numerically exact method for computing density matrix perturbative expansions.
• To create a "black box" tool applicable to complex quantum systems.
• To enhance the simulation of multiphoton pulsed laser experiments.

Main Methods:

• The Fourier-Laplace Inversion of the Perturbation Theory (FLIPT) is introduced.
• Tensor products are used for numerical evaluation of frequency integrals.
• Rigorous convergence conditions are established for the method.

Main Results:

• FLIPT is shown to be well-suited for complex multiphoton pulsed laser experiments.
• The method achieves O(N^2) computational complexity for N-point integrals.
• This represents a significant improvement over the O(N^n) scaling of standard quadrature methods.

Conclusions:

• FLIPT offers a computationally efficient and accurate approach for density matrix calculations.
• The method provides a powerful new tool for simulating advanced laser-matter interactions.
• FLIPT overcomes limitations of traditional perturbative expansion techniques.