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We study the nonlinear optical response of argon to a four-wave-mixing pulse sequence consisting of an extreme-ultraviolet pulse, a collinear IR dressing pulse, and a delayed noncollinear IR probe pulse. Sequential absorption of an extreme ultraviolet photon and an IR photon from the collinear beams excites the 3s−1 4p bright state and the 3s−1 3d/5s dark states. The subsequent absorption of an IR photon from the noncollinear beam then leads to an angled extreme ultraviolet emission, whose variation with delay encodes the coupling between autoionizing states, the lifetimes of dark states, and nonperturbative effects. Both our measurements and ab initio simulations of the angled four-wave-mixing signal reveal a double-peak structure in the delay dependence, in good agreement with each other. We attribute the central minimum between the two peaks to rapid Rabi cycling, driven by the collinear IR dressing pulse, between the dark states and the 3s−1 4p resonance, which leads to destructive interference in the final transition amplitude. 

Abstract Atmospheric escape shapes exoplanet evolution and star–planet interactions, with HeI10830 Å absorption serving as a key tracer of mass loss in hot gas giants. However, transit depths vary significantly across observed systems for reasons that remain poorly understood. HD209458b, the archetypal hot-Jupiter, exhibits relatively weak HeI10830 Å and Hαabsorption, which has been interpreted as evidence for a high H/He ratio (98/2), possibly due to diffusive separation. To investigate this possibility and other processes that control these transit depths, we reassess excitation and de-excitation rates for metastable helium and explore the impact of diffusion processes, stellar activity, and tidal forces on the upper atmosphere and transit depths using a model framework spanning the whole atmosphere. Our model reproduces the observed HeItransit depth and Hαupper limit, showing strong diffusive separation. We match the observations assuming a photoelectron efficiency of 20%–40%, depending on the composition of the atmosphere, corresponding to mass-loss rates of 1.9–3 × 10¹⁰g s⁻¹. We find that the HeI10830 Å transit depth is sensitive to both stellar activity and diffusion processes, while Hαis largely unaffected due to its strong dependence on Lyαexcitation. These differences may help explain the system-to-system scatter seen in population-level studies of the HeIline. While HeIdata alone may not tightly constrain mass-loss rates or temperatures, they do confirm atmospheric escape and help narrow the viable parameter space when interpreted with physically motivated models. Simultaneous observations of HeI, Hα, and stellar activity indicators provide powerful constraints on upper atmosphere dynamics and composition, even in the absence of full transmission spectra. 

Temporal delays extracted from photoionization phases are currently determined with attosecond resolution by using interferometric methods. Such methods require special care when photoionization occurs near Feshbach resonances due to the interference between direct ionization and autoionization. Although theory can accurately handle these interferences in atoms, in molecules, it has to face an additional, so far insurmountable problem: Autoionization is slow, and nuclei move substantially while it happens, i.e., electronic and nuclear motions are coupled. Here, we present a theoretical framework to account for this effect and apply it to evaluate time-resolved and vibrationally resolved photoelectron spectra and photoionization phases of N₂irradiated by a combination of an extreme ultraviolet (XUV) attosecond pulse train and an infrared pulse. We show that Feshbach resonances lead to unusual non–Franck-Condon vibrational progressions and to ionization phases that strongly vary with photoelectron energy irrespective of the vibrational state of the remaining molecular cation. 

Autoionizing states are pervasive features of atomic and molecular ionization processes. We illustrate how the evolution of autoionizing states in polyelectronic atoms can be monitored and controlled with attosecond pump-probe photoelectron and transient- absorption spectroscopy.