Rotational, Vibrational, and Electronic Modulations in N_{2}^{+} Lasing at 391 nm: Evidence of Coherent B^{2}Σ_{u}^{+}-X^{2}Σ_{g}^{+}-A^{2}Π_{u} Coupling.

We investigate lasing of a N_{2} gas induced by intense few-cycle near-IR laser pulses. By the pump-probe measurements, we reveal that the intensity of the B^{2}Σ_{u}^{+}-X^{2}Σ_{g}^{+} lasing emission of N_{2}^{+} oscillates at high (0.3-0.5 PHz), medium (50-75 THz), and low (∼3  THz) frequencies, corresponding to the energy separations between the rovibrational levels of the A^{2}Π_{u} and X^{2}Σ_{g}^{+} states. By solving the time-dependent Schrödinger equation, we reproduce the oscillations in the three different frequency ranges and show that the coherent population transfer among the three electronic states of N_{2}^{+} creates the population inversion between the B^{2}Σ_{u}^{+} and X^{2}Σ_{g}^{+} states, resulting in the lasing at 391 nm.