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arXiv:2412.00808 · Physical Review A

Nonperturbative effects in attosecond four-wave-mixing spectra

Sergio Yanez-Pagans, Nathan Harkema, Arvinder S. Sandhu, Coleman Cariker, Luca Argenti

Published Jun 13, 2025• 5 citations
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Abstract

We study the nonlinear optical response of argon to a four-wave-mixing pulse sequence consisting of an extreme ultraviolet pulse, an overlapping collinear IR and an non-collinear delayed IR pulses. Absorption of an extreme ultraviolet and an IR photon from the collinear beams excites, sequentially, the $3s^{-1}4p$ bright state and the {$3s^{-1}3d/5s$} dark states. The subsequent absorption of an IR photon from the non-collinear beam results in an angled extreme ultraviolet emission whose variation with delay encodes coupling between autoionizing-states, dark-state lifetimes, and non-perturbative effects. Both our measurements and \emph{ab initio} simulations of the angled four-wave-mixing signal show a double-peak structure in delay dependence, in excellent agreement with each other. We attribute the minimum at the center of the signal to the rapid Rabi cycling, driven by the IR pulse, between dark states and the $3s^{-1}4p$ resonance, which results in the destructive interference in the final transition amplitude.

DOI
10.1103/jtcp-yt14

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An extreme ultraviolet (EUV) single attosecond pulse passing through a laser-dressed dense gas is studied theoretically. The weak EUV pulse pumps the helium gas from the ground state to the 2s2p(1P)2s2p({}^{1}P)2s2p(1P) autoionizing state, which is coupled to the 2s2(1S)2{s}^{2}{(}^{1}S)2s2(1S) autoionizing state by a femtosecond infrared laser with the intensity in the order of 1012{}^{12}12 W/cm2{}^{2}2. The simulation shows how the transient absorption and emission of the EUV are modified by the coupling laser. A simple analytical expression for the atomic response derived for $\ensuremath{\delta}$-function pulses reveals the strong modification of the Fano lineshape in the spectra, where these features are quite universal and remain valid for realistic pulse conditions. We further account for the propagation of pulses in the medium and show that the EUV signal at the atomic resonance can be enhanced in the gaseous medium by more than 50% for specifically adjusted laser parameters, and that this enhancement persists as the EUV propagates in the gaseous medium. Our result demonstrates the high-level control of nonlinear optical effects that are achievable with attosecond pulses.
The generation of tunable, nanosecond-pulsed extreme-ultraviolet (EUV) light (84.92nm(84.92\mathrm{nm}(84.92nm to 84.97nm84.97\mathrm{nm}84.97nm $\ensuremath{\sim}14.6\mathrm{eV})$ using four-wave mixing in optically deep krypton gas was investigated experimentally and theoretically. The sum-frequency mixing scheme generated light from two overlapping autoionizing resonances, ${17s}^{\ensuremath{'}}$ and ${15d}^{\ensuremath{'}}$. We investigated whether the laser-induced atomic coherence effect of electromagnetically induced transparency (EIT) could enhance the intensity of the EUV light generated. The maximum EUV output was seen from the region where the ${15d}^{\ensuremath{'}}$ autoionizing resonance has a transparency window due to Fano-type quantum interference. An analytical model using appropriate atomic parameters explains how background absorption can prevent EIT enhancement of EUV generation; and shows how a background Raman-like coupling term in the nonlinear susceptibility can well describe the measured EUV generation spectrum.
We report here a detailed study of the four-wave mixing process in the extreme ultraviolet region around 30 nm by using two collinear incommensurate frequency laser pulses. The experimental results reveal evidence of the coherent accumulation of the wave-mixing fields and low-order (third-order and fifth-order) nonlinear response of an argon medium. The dependence of the intensities of the mixing fields on the intensity of a weak control field, on the argon pressure, and on the interaction length is analyzed to show that the four-wave mixing fields in this spectral range are generated under the phase-matched condition.
We theoretically study the infrared (IR)-dressed photoionization of atoms excited by extreme ultraviolet attosecond pulse trains above ionization threshold. The initial state of atoms is treated perturbatively by the IR field, and the continuum states are considered as Coulomb–Volkov (CV) waves. CV waves can much reduce the gauge difference calculated with Volkov waves, and, in general, the contribution of ground-state perturbation to the photoelectron spectrum is negligible. Our calculations show qualitative agreement with the experimental results [Phys. Rev. Lett. 95, 013001 (2005)]. An evident dependence of the photoelectron spectrum on the delay phase between the IR field and the attosecond pulse train is exhibited in both helium and argon. The angular distribution of photoelectrons with various IR polarizations and the corresponding photoelectron spectra are presented. The linearly polarized IR fields are shown to have a higher controlling capability of the spectrum via IR delay phases than the circularly polarized fields. On the other hand, the circularly polarized IR fields have a fruitful angular dependence of photoelectrons with various IR delay phases.
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In the present paper, we investigate the time-resolved transient absorption spectroscopy of doubly excited states of helium atoms by solving the time-dependent two-electron Schr\"odinger equation numerically based on a one-dimensional model. The helium atoms are subjected to an extreme ultraviolet (XUV) attosecond pulse and a time-delayed infrared (IR) few-cycle laser pulse. A superposition of doubly excited states populated by the XUV pulse is identified, which interferes with the direct ionization pathway leading to Fano resonance profiles in the photoabsorption spectrum. In the presence of an IR laser, however, the Fano line profiles are strongly modified: A shifting, splitting, and broadening of the original absorption lines is observed when the XUV attosecond pulse and infrared few-cycle laser pulse overlap in time, which is in good agreement with recent experimental results. At certain time delays, we observe symmetric Lorentz, inverted Fano profiles, and even negative absorption cross sections indicating that the XUV light can be amplified during the interaction with atoms. We further prove that the above pictures are general for different doubly excited states by suitably varying the frequency of the IR field to coherently couple the corresponding states.