Role of rotational coherence in femtosecond-pulse-driven nitrogen ion lasing

We experimentally investigated the rotationally resolved polarization characteristics of N$_2^+$ lasing at 391 and 428 nm using a pump-seed scheme. By varying the relative angle between the linear polarizations of the pump and seed, it is found that the polarizations of the P and R branches of 391-nm lasing are counter-rotated. By contrast, both branches of 428-nm lasing remain polarized along the pump. The origin of the puzzled abnormal polarization characteristics is found based on a complete physical model that simultaneously includes the transient photoionization and the subsequent coupling among the electronic, vibrational and rotational quantum states of ions.It suggests that the cascaded resonant Raman processes following ionization create negative coherence between the rotational states of $J$ and $J$+2 in the ionic ground state X$^2\Sigma_g^+(
u=0)$, which leads to mirror-symmetrical polarization for the P and R branches of 391-nm lasing. Both the experiment and theory indicate that the demonstrated rotational coherence plays an extremely pivotal role in clarifying the gain mechanism of N$_2^+$ lasing and opens up the route toward quantum optics under ultrafast strong fields.