Using ab-initio non-Born-Oppenheimer simulations, we demonstrateamplification of XUV radiation in a high-harmonic generation type process usingthe example of the hydrogen molecular ion. A small fraction of the molecules ispumped to a dissociative Rydberg state from which IR-assisted XUV amplificationis observed. We show that starting at sufficiently high IR driving fieldintensities the ground state molecules become quasi-transparent for XUVradiation, while due to stabilization gain from Rydberg states is maintained,thus leading to lasing from strongly driven Rydberg states. Further increase ofthe IR intensity even leads to gain by initially unexcited molecules, which arequickly excited by the driving IR pulse.
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