  The coupled electronic-vibrational dynamics of nitrogen ions induced by
strong-field ionization is investigated theoretically to corroborate the recent
transient X-ray K-edge absorption experiment [PRL 129, 123002 (2022)], where
the population distribution of three electronic states in air lasing of N2+ was
determined for the first time. By extending the ionization-coupling model to
include the transient absorption, we successfully reproduce the time-resolved
X-ray absorption spectra of nitrogen ions observed in the experiment. By
identifying the contributions from different electronic states, the study
provides different interpretation revealing the significant role of excited
state A arising from the strong coupling between vibrational states in strong
laser fields. It indicates that the electronic population inversion occurs at
least for certain alignment of nitrogen molecules. The theory helps uncovering
new features of absorption from forbidden transitions during ionization and
confirming that the vibration coherence at each electronic channel induces the
modulation of absorbance after strong field ionization. A new scheme is
proposed to determine the population transfer at different probing geometry to
avoid the spectral overlap. This work offers valuable insights into the
intricate interplay between electronic and vibrational dynamics and helps to
resolve the debate on nitrogen air lasing.
