Short- and long-term gain dynamics in N2+ air lasing

Air lasing in the nitrogen molecular ion is not well understood because the complex physics responsible for gain is interwoven with pulse propagation in an extreme environment. Here we use a short gas jet to limit the interaction length, thereby removing the propagation effects. We report on several mechanisms that contribute to the decay of gain in different conditions, and experimentally isolate two decay timescales: the decay of long-term gain due to collisional state mixing, and short-term gain that cannot be explained by population inversion. To test the former, we control the inelastic electron scattering rate by varying the gas concentration while keeping the propagation length fixed, and predict the change of the decay using a model of collisional state mixing. We show that the same mechanism causes the decay of rotational wave packets in the states of the ion. Finally, we simulate the complex modulations of gain due to rotational wave packets and the propagation of the probe pulse through the evolving rotationally excited and inverted medium.