Rotational population transfer through the $A{}^2{\mathrm{\Pi }}_u-X{}^2{\mathrm{\Sigma }}_g{}^{+}-B{}^2{\mathrm{\Sigma }}_u{}^{+}$ coupling in ${\mathrm{N}}_2{}^{+}$ lasing

The lasing of ${\mathrm{N}}_2{}^{+}$ at 391 nm, originating from the population inversion between $X{}^2{\mathrm{\Sigma }}_g{}^{+}(v=0)$ and $B{}^2{\mathrm{\Sigma }}_u{}^{+}(v=0)$ achieved by the irradiation of a pair of few-cycle intense near-IR laser pulses in a pump-probe scheme, is investigated both experimentally and theoretically. The characteristic periodic intensity modulations recorded experimentally in both $P$- and $R$-branch emission lines are reproduced well by the theoretical simulation, in which the population transfer processes among the rovibrational levels of the three lowest electronic states, $X{}^2{\mathrm{\Sigma }}_g{}^{+}, A{}^2{\mathrm{\Pi }}_u$, and $B{}^2{\mathrm{\Sigma }}_u{}^{+}$, of ${\mathrm{N}}_2{}^{+}$ induced by pump and probe few-cycle intense laser pulses are calculated. Based on the results of the theoretical simulation, the periodic intensity modulations are ascribed to the difference between the rotational selection rules in the $A{}^2{\mathrm{\Pi }}_u-X{}^2{\mathrm{\Sigma }}_g{}^{+}$ coupling, which suppresses the rotational excitation in the $X{}^2{\mathrm{\Sigma }}_g{}^{+}\left(0\right)\text{state}$, and those in the $B{}^2{\mathrm{\Sigma }}_u{}^{+}-X{}^2{\mathrm{\Sigma }}_g{}^{+}$ coupling, which enhances the rotational excitation in the $B{}^2{\mathrm{\Sigma }}_u{}^{+}$(0) state.

Figure 1

Potential energy curves of the three electronic states $X{}^2{\mathrm{\Sigma }}_g{}^{+}, A{}^2{\mathrm{\Pi }}_u$, and $B{}^2{\mathrm{\Sigma }}_u{}^{+}$ of ${\mathrm{N}}_2{}^{+}$ [20]. The $A{}^2{\mathrm{\Pi }}_u-X{}^2{\mathrm{\Sigma }}_g{}^{+}$ and $B{}^2{\mathrm{\Sigma }}_u{}^{+}-X{}^2{\mathrm{\Sigma }}_g{}^{+}$ transitions are dipole allowed and the $B{}^2{\mathrm{\Sigma }}_u{}^{+}-A{}^2{\mathrm{\Pi }}_u$ transition is dipole forbidden.

Figure 2

(a) Experimental and (b) theoretical emission spectra of ${\mathrm{N}}_2{}^{+}$ plotted as a function of the pump-probe delay time. The intensity of the emission is shown in a logarithmic color scale. The spectral resolution in (b) is set to $t=0.2$ nm, which is 7.5 times better than that in (a) (FWHM equal to 1.5 nm), so that the time evolution of the spectral structure can be seen clearly.

Figure 3

Rotational population distributions in the (a) $X{}^2{\mathrm{\Sigma }}_g{}^{+}(v=0)$, (b) $A{}^2{\mathrm{\Pi }}_u(v=0)$, and (c) $B{}^2{\mathrm{\Sigma }}_u{}^{+}(v=0)$ states of ${\mathrm{N}}_2{}^{+}$ as a function of the pump-probe delay time

Figure 4

Rotational population distributions in the (a) $X{}^2{\mathrm{\Sigma }}_g{}^{+}(v=0)$, (b) $A{}^2{\mathrm{\Pi }}_u(v=0)$, and (c) $B{}^2{\mathrm{\Sigma }}_u{}^{+}(v=0)$ states of ${\mathrm{N}}_2{}^{+}$ just after the ionization [only for (a) with the vertical axis on the right side], just after the pump pulse, and after the probe pulse at a delay time of 350 fs. Because it is assumed that ${\mathrm{N}}_2{}^{+}$ is prepared exclusively in the $X{}^2{\mathrm{\Sigma }}_g{}^{+}$ state after ionization, no “after ionization” line is shown in (b) or (c).

Figure 5

Rotational transition probabilities in the (a) $X{}^2{\mathrm{\Sigma }}_g{}^{+}\left(0\right)$, (b) $A{}^2{\mathrm{\Pi }}_u\left(0\right)$, and (c) $X{}^2{\mathrm{\Sigma }}_g{}^{+}\left(0\right)\text{states}$ of ${\mathrm{N}}_2{}^{+}$ by the probe pulse through the Raman-type transitions. The red dotted zigzag lines represent the probabilities for the population to remain in the same rotational level and the blue zigzag lines show the probabilities for the population to be transferred to the other rotational levels.