Electronic State Population Dynamics upon Ultrafast Strong Field Ionization and Fragmentation of Molecular Nitrogen

Air lasing from single ionized ${\mathrm{N}}_2^{+}$ molecules induced by laser filamentation in air has been intensively investigated and the mechanisms responsible for lasing are currently highly debated. We use ultrafast nitrogen $K$-edge spectroscopy to follow the strong field ionization and fragmentation dynamics of ${\mathrm{N}}_2$ upon interaction with an ultrashort 800 nm laser pulse. Using probe pulses generated by extreme high-order harmonic generation, we observe transitions indicative of the formation of the electronic ground $X{}^2{\mathrm{\Sigma }}_g^{+}$, first excited $A{{}^2\mathrm{\Pi }}_u$, and second excited $B{}^2{\mathrm{\Sigma }}_u^{+}$ states of ${\mathrm{N}}_2^{+}$ on femtosecond timescales, from which we can quantitatively determine the time-dependent electronic state population distribution dynamics of ${\mathrm{N}}_2^{+}$. Our results show a remarkably low population of the $A{}^2{\mathrm{\Pi }}_u$ state, and nearly equal populations of the $X{}^2{\mathrm{\Sigma }}_g^{+}$ and $B{}^2{\mathrm{\Sigma }}_u^{+}$ states. In addition, we observe fragmentation of ${\mathrm{N}}_2^{+}$ into N and ${\mathrm{N}}^{+}$ on a timescale of several tens of picoseconds that we assign to significant collisional dynamics in the plasma, resulting in dissociative excitation of ${\mathrm{N}}_2^{+}$.

Figure 1

In the top panel, the steady-state XAS of ${\mathrm{N}}_2$, measured with our high harmonic source (blue line) and at a synchrotron by [32] (black line), is shown, together with the steady-state absorption spectrum of ${\mathrm{N}}_2^{+}(X{}^2{\mathrm{\Sigma }}_g^{+})$ taken from [33] (red line). In the bottom-left panel, a visualization of the level scheme of ${\mathrm{N}}_2$ is provided, showing the molecular orbitals with orbital symmetry annotation and the associated ionization potentials $I_P$. Core excitations to the highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO) are displayed as well.

Figure 2

(a) Measured XAS integrated over time delays between 160 and 300 fs (black curve) and XAS of ${\mathrm{N}}_2(X{}^1{\mathrm{\Sigma }}_g)$ (grey area), ${\mathrm{N}}_2^{+}(X{}^2{\mathrm{\Sigma }}_g)$ (red area), and ${\mathrm{N}}^{+}$ (blue area) reproduced from Refs. [32, 33], and [35], respectively. (b) Transient XAS of strong field ionized ${\mathrm{N}}_2$. The central energy positions resulting from a Gaussian fit of the lowest ionic state transitions are displayed as dotted color lines [see text and Fig. 3]. The spectral regions indicated by dashed lines were used to extract the temporal evolution of the absorbance at the ${\mathrm{N}}_2$ $1{\sigma }_u\to 1{\pi }_g$, ${\mathrm{N}}_2^{+}$ ($X{}^2{\mathrm{\Sigma }}_g$) $1{\sigma }_u\to 3{\sigma }_g$, and ${\mathrm{N}}_2^{+}$ ($X{}^2{\mathrm{\Sigma }}_g$) $1{\sigma }_u\to 1{\pi }_g$ transitions shown in Fig. 3.

Figure 3

(a) Temporal evolution of the absorbance at the ${\mathrm{N}}_2$ $1{\sigma }_u\to 1{\pi }_g$ (blue), ${\mathrm{N}}_2^{+}$ ($X{}^2{\mathrm{\Sigma }}_g^{+}$) $1{\sigma }_u\to 3{\sigma }_g$ (black) and ${\mathrm{N}}_2^{+}$ ($X{}^2{\mathrm{\Sigma }}_g^{+}$) $1{\sigma }_u\to 1{\pi }_g$ (red) transitions, spectrally integrated over the spectral regions indicated in Fig. 2 by dashed lines. Simulations of the transient signals accounting for ionization only (solid lines) and ionization and alignment (dashed lines) are also shown in panel (a). (b) Ultrafast population dynamics of the $X{}^2{\mathrm{\Sigma }}_g^{+}$, $A{}^2{\mathrm{\Pi }}_u$, and $B{}^2{\mathrm{\Sigma }}_u^{+}$ states of ${\mathrm{N}}_2^{+}$ retrieved using Eq. (1).

Figure 4

(a) Transient soft x-ray spectra, integrated for short (0.2–1.0 ps) and long (45–80 ps) delays, revealing the disappearance of the ${\mathrm{N}}_2^{+}$ contributions and the appearance of N and ${\mathrm{N}}^{+}$ contributions. Reference spectra (colored area) have been taken from an $R$-matrix calculation reported in Ref. [35] and are energy shifted to match the experimental values reported in [52, 53]. (b) Transient XAS in the time window between $-0.6\mathrm{ps}$ and 80 ps. (c) Temporal evolution of N and ${\mathrm{N}}^{+}$ absorption signals (dots) spectrally integrated over the spectral regions indicated by the dashed lines in panel (a) corresponding to $1s\to 2p$ transitions in the ${}^4{S}^0$, ${}^2{D}^0$, and ${}^{3}P$ states of N and ${\mathrm{N}}^{+}$. The kinetic fits (solid lines) have been derived by singular value decomposition using a single time constant (see SM and [47]). (d) ${\mathrm{N}}_2^{+}$ dissociation time as a function of the ${\mathrm{N}}_2$ backing pressure (dots) and corresponding fit (dashed line) using an inverse function $1/p$.