XUV lasing during strong-field-assisted transient absorption in molecules

Using ab initio non-Born-Oppenheimer simulations, we demonstrate the amplification of XUV radiation in a high-harmonic-generation-type process using the example of the hydrogen molecular ion. A small fraction of the molecules is pumped to a dissociative excited state from which IR-assisted XUV amplification is observed. We show that starting at sufficiently high IR driving field intensities, the ground-state molecules become quasitransparent for XUV radiation, while due to stabilization, gain from excited states is maintained. While the basic physics should also be observable in atomic media, the main advantage of the investigated molecular laser is, first, efficient lasing from field-free excited states with a high mean angular momentum and, second, the possibility to tune the amplified XUV frequency windows via control of the internuclear distance.

Figure 1

Schematics of IR-assisted amplification of XUV light in the molecular ion ${\mathrm{H}}_2{}^{+}$. (a) In a HHG-type process, a strong IR pulse drives an electronic excited state. Recombination is stimulated by the weak XUV seed present in the medium. (b) Combination of VUV pump pulse (blue), IR driving field (black), and XUV-probe pulse (red) used in the simulations. (c) A fraction of the molecules is pumped via a two-photon transition to a dissociative electronic excited state. Timing of the IR driving field allows the control of XUV amplification. (d) In the absence of the IR pulse, XUV absorption (red arrow) is possible both by the unexcited (left, internuclear distance $R=2.6$ a.u.) and the excited molecules (right, sketched for internuclear distance $R=4$ a.u.). The intense IR pulse can strongly attenuate XUV absorption while assisting XUV recombination, reminiscent of “lasing without inversion.”

Figure 2

(a) XUV transient absorption spectra $S_{\mathrm{XUV}}\left(\mathrm{\Omega }\right)$ from excited-state molecules (left) and ground-state molecules (right) for variable IR intensities $I_{\mathrm{IR}}$ with ${\mathrm{\Delta }}_{\mathrm{IR}}=3$ fs, ${\mathrm{\Delta }}_{\mathrm{XUV}}=2.4$ fs [cf. Fig. 1], and central XUV frequency ${\mathrm{\Omega }}_{\mathrm{XUV}}=20.4$ eV. Here, we assume complete population transfer to the excited state ${\sigma }_{\mathrm{g}}2p$ at time zero. (b) Corresponding integrated signals $\int S_{\mathrm{XUV}}\left(\mathrm{\Omega }\right)d\mathrm{\Omega }$ as a function of the intensity of the IR driving field for excited-state (red) and ground-state (blue) molecules identifying three amplification regimes. Values without the IR pulse are indicated by the horizontal arrows. (c) Dependence of integrated signals from excited-state molecules on XUV-probe delay time for $I_{\mathrm{IR}}=5\times {10}^{15}\text{W}/{\mathrm{cm}}^2$.

Figure 3

Influence of the XUV-probe pulse duration $T$ on the XUV transient absorption spectrum $S_{\mathrm{XUV}}\left(\mathrm{\Omega }\right)$ from excited ${\sigma }_{\mathrm{g}}2p$ molecules, for $I_{\mathrm{IR}}=5\times {10}^{15}\text{W}/{\mathrm{cm}}^2,{\mathrm{\Delta }}_{\mathrm{IR}}=3$ fs, ${\mathrm{\Delta }}_{\mathrm{XUV}}=1.9$ fs, and ${\mathrm{\Omega }}_{\mathrm{XUV}}=20$ eV [cf. Fig. 1]. (a) From top to bottom: Electric field of the IR and XUV-probe pulses with durations $T=2.75$ fs (blue, corresponding to the durations used in Figs. 2 and 4), $T=5.5$ fs (green), $T=8.25$ fs (red), and $T=11$ fs (cyan). (b) XUV transient absorption spectra $S_{\mathrm{XUV}}\left(\mathrm{\Omega }\right)$ for the XUV pulses from (a), shown in corresponding colors.

Figure 4

Full pump-probe simulations: (a) Integrated XUV transient absorption spectrum $\int S_{\mathrm{XUV}}\left(\mathrm{\Omega }\right)d\mathrm{\Omega }$ as a function of the central frequency of the XUV seed ${\mathrm{\Omega }}_{\mathrm{XUV}}$ and the time delay of the IR driving field ${\mathrm{\Delta }}_{\mathrm{IR}}$. The pump intensity is set to $I_{\mathrm{pump}}=3\times {10}^{13}\text{W}/{\mathrm{cm}}^2$, exciting 16% of the molecules to the dissociative excited state ${\sigma }_{\mathrm{g}}2p$. In all simulations, the intensity of the IR driving field is set to $I_{\mathrm{IR}}=3\times {10}^{15}\text{W}/{\mathrm{cm}}^2$ and the delay of the XUV seed is ${\mathrm{\Delta }}_{\mathrm{XUV}}=2.4$ fs. (b) Integrated signals as a function of pump intensity $I_{\mathrm{pump}}$ for central XUV frequency ${\mathrm{\Omega }}_{\mathrm{XUV}}=15.7$ eV for large internuclear distances $({\mathrm{\Delta }}_{\mathrm{IR}}=14.9$ fs) (black) and for ${\mathrm{\Omega }}_{\mathrm{XUV}}=18.8$ eV for short internuclear distances $({\mathrm{\Delta }}_{\mathrm{IR}}=3.9$ fs) (red). The vertical arrows indicate the pump intensities for which the overall gain is equal to the absorption from the unperturbed molecules, i.e., in the absence of the VUV pump and the IR pulse.