Ramsey interferometry through coherent A²Πu−X²Σg+−B²Σu+ coupling and population transfer in N₂+ air laser

Motivated by the hot debate on the mechanism of the laser like emission at 391nm from N₂ gas irradiated by a strong 800nm pump laser and a weak 400nm seed laser, we theoretically study the temporal profile, optical gain and periodic modulation of the 391nm signal from N₂+ . Our calculation sheds light on the long standing controversy on whether population inversion is indispensable for the optical gain, and demonstrate the Ramsey fringes of the emission intensity at 391nm formed by additionally injecting another 800nm pump or 400nm seed, which provides strong evidence for the coherence driven modulation of transition dipole moment and population transfer between the A²Πu(ν = 2)-X²Σg+ states and the B²Σu+ (ν = 0) - X²Σg+ states. Our results show that the 391nm optical gain is susceptible to the degree of population inversion within N₂+ states manipulated by the Ramsey technique, and thus clearly reveal their symbiosis. This study provides with not only the physical picture of producing population inversion in N₂+ but also versatile methods for coherent control of N₂+ air laser.