PHYSICAL REVIEW A 99, 063425 (2019) Extreme-ultraviolet coherent pulse amplification in argon C. Serrat * Department of Physics, Polytechnic University of Catalonia, Colom 11, E-08222 Terrassa (Barcelona), Spain J. Seres and E. Seres Institute of Atomic and Subatomic Physics, Vienna University of Technology, Stadionalle 2, A-1020 Vienna, Austria S. Namba Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8527, Japan (Received 21 March 2019; published 25 June 2019) The amplification of ultrashort extreme-ultraviolet (XUV) pulses in argon in high-order harmonic generation processes is studied by using the time-dependent Schrödinger equation in the spin-free one-active-electron and single-atom approximation. We consider a neutral argon atom initially in the valence 3p state and a sufficiently intense two-cycle driving infrared (IR) pulse for the atom to be mainly ionized after the first laser cycle. The correlated dynamics and transitions from the valence 3p to a virtual subvalence 3s state and in the ionized regions are examined by synchronizing a 1.5-fs XUV pulse to the IR pulse. The calculated single-atom gain spectrum (26–45 eV) agrees with recent experimental measurements. We discuss different channels that can be present in the gain process as a function of pulse parameters and through an analysis of the dynamics of the populations in terms of field-free eigenstates. When the XUV pulse is considered at the end of the driving IR field the amplification is due to contributions of stimulated recombination from excited Rydberg and low energy continuum states to the 3s and 3p states of argon. In regions where the IR field is intense, high energy and angular momentum states are populated and the medium can interact with the pulses through bound and continuum states involving parametric transitions, which is further confirmed by studying classical electron trajectories. We discuss how these parametric interactions might be suitable for amplification of photon energies far from the ionization threshold as observed in the experiments. DOI: 10.1103/PhysRevA.99.063425 I. INTRODUCTION The amplification of extreme-ultraviolet (XUV) and x-ray radiation in high-order harmonic generation (HHG) processes has been largely studied in previous years because of the importance of enhancing the associated HHG low conversion efficiency and for understanding the generation process more accurately. This improvement is key for the use of table-top coherent XUV and x-ray sources in many applications [1,2]. In particular, simultaneous excitation of atoms with an intense infrared (IR) driving pulse and a weak XUV pulse or train of pulses conveniently synchronized has been extensively investigated both theoretically and experimentally as a method to amplify the signal from the single-atom level interaction and also considering the effects of propagation [3–21]. Ultrashort XUV pulses of central frequencies far from the ionization threshold were successfully amplified in ex- periments using helium gas [8,9,12,13,15]. The fundamental physics behind the involved scattering mechanisms, however, lack a detailed explanation which is certainly very necessary for the possibility of amplifying XUV and x-ray coherent pulses at any desired photon energies. Different theoretical * carles.serrat-jurado@upc.edu approaches [9,10,12,14,15,17] have described the amplifica- tion in terms of extended electron trajectories in the HHG pro- cess together with parametric interactions, such as x-ray para- metric amplification (XPA) and intra-XUV-pulse parametric amplification (IXPA), although only qualitative agreement with the measurements has been reported so far [8,9,12,13]. Some of these studies have been performed in the frame of the solution of the time-dependent Schrödinger equation (TDSE) both in the strong-field (SFA) and in the single-active- electron (SAE) approximations. Other faithful theories also based on ab initio simulations have considered the need of population inversion to overcome the possible loss channels in the medium [19], leading to some weak amplification at the lower photon energies only close to the ionization threshold. Previously in Refs. [15,17] enhancement of high photon en- ergies far from the ionization threshold in accordance with the measurements was achieved on the basis of parametric and intra-XUV-pulse parametric processes, but this was not accounted for at all in Ref. [19] and amplification any distant from the ionization threshold as observed in the experiments is there missing. A single-electron theoretical study has also been reported in the basis of angular momentum dependent potentials for the Li + ion and a comparison between one- dimensional (1D) and three-dimensional (3D) simulations has been performed [20], although no intent to compare to the experimental results is realized. 2469-9926/2019/99(6)/063425(11) 063425-1 ©2019 American Physical Society