Quantum and quasi-classical effects in the strong field ionization and subsequent excitation of nitrogen molecules

Abstract

The processes leading to the N2+ lasing are rather complex and even the population distribution after the pump laser excitation is unknown. In this paper, we study the population distribution at electronic and vibrational levels in N2+ driven by ultra-short laser pulse at the wavelengths of 800 nm and 400 nm by using the quantum-mechanical time-domain incoherent superposition model based on the time-dependent Schrödinger equation and the quasi-classical model assuming instantaneous ionization injection described by density matrix. It is shown that while both models provide qualitatively similar results, the quasi-classical instantaneous ionization injection model underestimates the population inversions corresponding to the optical transitions at 391 nm, 423 nm and 428 nm due to the assumption of quantum mixed states at the ionization time. A fast and accurate correction to this error is proposed. This work solidifies the theoretical models for population at vibrational states in N2+ and paves the way to uncover the mechanism of the N2+ lasing.

Laser emission at 428 nm in N2+: Competition between two- and three-level amplification

“…Such a nearly equal population between B0 and X0 is supported by a recent measurement by x-ray absorption spectroscopy 16 . On the other hand, the same calculations show a robust population inversion between B0 and X1 levels at the same wavelengths 15 . Therefore, even if the case of 391 nm emission is still unsettled, it is natural to expect a conventional two levels amplification scheme to be operative for the 428 nm emission.…”

“…1(b) and (c) for a schematic representation of the first two processes. Recent calculations show that population inversion between B0 and X0 is very sensitive to the particular pump pulse conditions 14,15 . B0/X0 inversion occurs if the pump central wavelength from a Ti:Sapphire laser exceeds 780 nm and if the pump intensity exceeds 1.5 × 10 14 W/cm 2 , but it disappears if one of these two values is decreased by less than 5%.…”