Trigonometric pulse envelopes for laser-induced quantum dynamics

We relate powers of trigonometric functions to Gaussians by proving that properly truncated cos n functions converge to a Gaussian as n tends to infinity. For an application, we analyse the laser-induced population transfer | X 1 Σ + ⟩ → | A 1 Π x ⟩ in a two-level model system of aluminium monochloride (AlCl) with fixed nuclei. We apply linearly x -polarized ultraviolet laser pulses with a trigonometric envelope function, whose square has full width at half-maximum of 2.5 fs and 5.0 fs. Studying population dynamics and optimized laser parameters, we find that the optimal field amplitude for trigonometric pulses with n = 20 and n = 1000 has a relative difference of 1%, which is below experimental resolution.