Giant Enhancement of Air Lasing by Complete Population Inversion in ${\mathrm{N}}_2^{+}$

A fine manipulation of population transfer among molecular quantum levels is a key technology for control of molecular processes. When a light field intensity is increased to the TW-PW ${\mathrm{cm}}^{-2}$ level, it becomes possible to transfer a population to specific excited levels through nonlinear light-molecule interaction, but it has been a challenge to control the extent of the population transfer. We deplete the population in the ${\mathrm{X}}^2{\mathrm{\Sigma }}_g^{+}(v=0)$ state of ${\mathrm{N}}_2^{+}$ almost completely by focusing a dual-color (800 nm and $1.6\mu \mathrm{m}$) intense femtosecond laser pulse in a nitrogen gas, and make the intensity of ${\mathrm{N}}_2^{+}$ lasing at 391 nm enhanced by 5–6 orders of magnitude. By solving a time-dependent Schrödinger equation describing the population transfer among the three lowest electronic states of ${\mathrm{N}}_2^{+}$, we reveal that the ${\mathrm{X}}^2{\mathrm{\Sigma }}_g^{+}(v=0)$ population is depleted by the vibrational Raman excitation followed by the electronic excitation ${\mathrm{A}}^2{\mathrm{\Pi }}_u(v=2,3,4)\leftarrow {\mathrm{X}}^2{\mathrm{\Sigma }}_g^{+}(v=1)\leftarrow {\mathrm{X}}^2{\mathrm{\Sigma }}_g^{+}(v=0)$, resulting in the excessive population inversion between the ${\mathrm{B}}^2{\mathrm{\Sigma }}_u^{+}(v=0)$ and ${\mathrm{X}}^2{\mathrm{\Sigma }}_g^{+}(v=0)$ states. Our results offer a promising route to efficient population transfer among vibrational and electronic levels of molecules by a precisely designed intense laser field.

Figure 1

Strong-field-induced ${\mathrm{N}}_2^{+}$ air lasing emissions. The spectra of the forwardly propagating lasing emission peaked at 391.4 nm obtained by the LP (dark red solid line), PG (orange dotted line), and $\mathrm{PG}+\mathrm{IR}$ (cyan dashed line) cases in the linear (a) and log (b) scales. The intensities of the lasing emissions for the PG and $\mathrm{PG}+\mathrm{IR}$ cases are attenuated using neutral density filters by 11 and 21 991 times, respectively.

Figure 2

Lasing intensity versus NIR laser energy. The recorded intensities of lasing at 391 nm generated by the LP (blue circles), PG (green triangles), and $\mathrm{PG}+\mathrm{IR}$ (red squares) laser fields as a function of the energy of the NIR laser pulse. The pressure of the sample ${\mathrm{N}}_2$ gas is set to be 70 mbar.

Figure 3

Lasing intensity versus IR laser wavelength and energy. (a) The recorded intensities of lasing at 391 nm generated by the $\mathrm{PG}+\mathrm{IR}$ field and the incident IR laser energies as a function of the central wavelength of the IR laser. (b) The recorded intensities of lasing at 391 nm generated by the $\mathrm{PG}+\mathrm{IR}$ field as a function of the energy of the incident IR laser pulse. For both (a) and (b), the intensity of the NIR PG pulse is kept at $0.44\mathrm{mJ}/\mathrm{pulse}$ and the pressure of the sample ${\mathrm{N}}_2$ gas is kept at 70 mbar.

Figure 4

Population distributions in the vibrational and electronic states of ${\mathrm{N}}_2^{+}$. The time-dependent populations in the ${\mathrm{X}}^2{\mathrm{\Sigma }}_g^{+}(v=0)$ (blue solid line), ${\mathrm{X}}^2{\mathrm{\Sigma }}_g^{+}(v=1)$ (light blue solid line), ${\mathrm{A}}^2{\mathrm{\Pi }}_u$ ($v=0$, 1) (green solid line), ${\mathrm{A}}^2{\mathrm{\Pi }}_u(v>1)$ (purple solid line), and ${\mathrm{B}}^2{\mathrm{\Sigma }}_u^{+}(v=0)$ (red solid line) levels are shown for the LP (a), PG (b), and $\mathrm{PG}+\mathrm{IR}$ (c) cases, and the final populations in the respective vibrational levels at $t=100\mathrm{fs}$ are shown for the LP (d), PG (e), and $\mathrm{PG}+\mathrm{IR}$ (f) cases. The laser field intensities for the NIR (800 nm) LP and PG pulses are $3.2\times {10}^{14}\mathrm{W}{\mathrm{cm}}^{-2}$ and the laser field intensity of the IR (1580 nm) pulse is $1.07\times {10}^{14}\mathrm{W}{\mathrm{cm}}^{-2}$.