Testing the Role of Recollision in N_{2}^{+} Air Lasing.

It has been known for many years that during filamentation of femtosecond light pulses in air, gain is observed on the B to X transition in N_{2}^{+}. While the gain mechanism remains unclear, it has been proposed that recollision, a process that is fundamental to much of strong field science, is critical for establishing gain. We probe this hypothesis by directly comparing the influence of the ellipticity of the pump light on gain in air filaments. Then, we decouple filamentation from gain by measuring the gain in a thin gas jet that we also use for high harmonic generation. The latter allows us to compare the dependence of the gain on the ellipticity of the pump with the dependence of the high harmonic signal on the ellipticity of the fundamental. We find that gain and harmonic generation have very different behavior in both filaments and in the jet. In fact, in a jet we even measure gain with circular polarization. Thus, we establish that recollision does not play a significant role in creating the inversion.