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arXiv:2606.21526 · Physical Review Research

Quantitative analysis of resonant ionization by smooth laser pulses: Connection between effective Hamiltonian theory and strong-field dressed continua

Jakob Nicolai Bruhnke, Jan Marcus Dahlström

Published Aug 20, 2026• 0 citations
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Abstract

Resonant photoionization in the intense high-frequency regime can exhibit extremely asymmetric Autler-Townes doublets whose origin remains debated. It has been attributed either to interference between perturbative ionization pathways or to a nonperturbative dressing of the continuum. Here, we show that these interpretations arise from a common effective Hamiltonian framework, in which dressed-state stabilization is governed by the coherent interplay of resonant and nonresonant pathways. We demonstrate that further simplification, using the strong-field approximation, obscures this mechanism. In contrast, our time-dependent essential-state model, where electrons are rigorously coupled to the continuum, achieves excellent agreement with simulations of the time-dependent Schrödinger equation for helium.

DOI
10.1103/lnbk-npp9

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arXiv:physics/9901017•Physical Review A•Apr 1, 1999•49 citations
Resonant photoionization in the intense high-frequency regime can exhibit extremely asymmetric Autler-Townes doublets whose origin remains debated. It has been attributed either to interference between perturbative ionization pathways or to a nonperturbative dressing of the continuum. Here, we show that these interpretations arise from a common effective Hamiltonian framework, in which dressed-state stabilization is governed by the coherent interplay of resonant and nonresonant pathways. We demonstrate that further simplification, using the strong-field approximation, obscures this mechanism. In contrast, our time-dependent essential-state model, where electrons are rigorously coupled to the continuum, achieves excellent agreement with simulations of the time-dependent Schrödinger equation for helium.
Nonperturbative resonant multiphoton ionization (1+1)(1+1)(1+1) is studied using the resolvent operator technique. Scaling parameters for effective two-level Hamiltonians are computed for hydrogen and helium atoms to provide a quantitative description of Rabi oscillations at XUV wavelengths, which were recently observed using a seeded free-electron laser [S. Nandi et al., Nature (London) 608, 488 (2022)]. The resulting photoelectron spectra exhibit a range of Autler-Townes doublets, which are studied for different intensities, detunings, and interaction times. We identify a photoelectron signature that originates from stabilization against ionization of helium atoms interacting with intense circularly polarized XUV light. Thus, our study shows how it is possible to test the prediction of dressed-atom stabilization by Beers and Armstrong [B. L. Beers and L. Armstrong, Phys. Rev. A 12, 2447 (1975)], without the demanding requirement of atomic saturation in the time domain.
Non-perturbative resonant multiphoton ionization (1+1)(1+1)(1+1) is studied using the resolvent operator technique. Scaling parameters for effective two-level Hamiltonians are computed for hydrogen and helium atoms to provide a quantitative description of Rabi oscillations at XUV wavelengths, which were recently observed using a seeded Free-Electron Laser [S. Nandi et al., Nature 608, 488-493 (2022)]. The resulting photoelectron spectra exhibit a range of Autler-Townes doublets, which are studied for different intensities, detunings and interaction times. We identify a photoelectron signature that originates from stabilization against ionization of helium atoms interacting with intense circularly polarized XUV light. Thus, our work shows how it is possible to test the prediction of dressed-atom stabilization by Beers and Armstrong [B. L. Beers and L. Armstrong, Phys. Rev. A 12, 2447 (1975)], without the demanding requirement of atomic saturation in the time domain.
We study the photoelectron spectra of hydrogen and helium ionized by intense ultrafast two-color XUV laser pulses by numerically solving the time-dependent Schrödinger equation.The photon energy of the pump pulse is tuned to the 1s-2p excitation energy, inducing Rabi oscillations between these bound states and forming an Autler-Townes (AT) doublet of dressed states.When ionized by a time-delayed ultrafast XUV pulse with duration shorter than the Rabi oscillation period, we find novel and drastically enhanced AT splittings in the photoionization spectrum.We identify their origin in terms of the temporal interference of two attosecond wave packets whose spectral distribution is controlled by the interplay between Rabi frequency and bandwidth of the probe pulse.These time-dependent features in the spectra can be much larger than the standard AT spacing induced by the pump pulse alone and can be controlled by the time delay and the duration of the probe pulse.
The resonant dynamic Stark effect, observed in the Autler-Townes (AT) splitting, plays a central role in ultrafast strong-field physics. Recent experiments have demonstrated the phase control of the AT doublet in atomic resonance-enhanced multiphoton ionization using intense resonant shaped femtosecond laser pulses [Bayer et al., Adv. Chem. Phys. 159, 235 (2016)]. Based on a two-state model, we showed that the underlying control mechanism is the selective population of dressed states (SPODS). In this work, we use a numerical model to calculate the photoelectron momentum distribution (PMD) based on the ab initio solution of the two-dimensional (2D) time-dependent Schr\"odinger equation (TDSE) to obtain a more complete physical picture of the nonperturbative control of the AT doublet. The 2D-TDSE model reproduces the ultrafast switching among the AT components while also revealing deviations from the signatures predicted by the two-state model. These deviations are attributed to the influence of additional intermediate states. To rationalize our observations, we propose a refined five-state model that includes all significantly populated bound states from the full calculation and accurately reproduces the 2D PMD. Based on the validated five-state model, we conduct a dressed-state analysis which provides a clear physical picture of the SPODS mechanism in a multistate system and sheds light on the role of the intermediate states in strong-field control.
The energy levels of atoms and molecules exposed to intense, short, high-frequency laser pulses undergo time-dependent distortion known as dynamic Stark shift (DSS). These level shifts are induced by the coupling with nonresonant (nonessential) states and follow the temporal intensity profile of the laser pulse. Owing to the different DSSs of the individual atomic levels, transient resonance suppressions and enhancements significantly modify the multiphoton ionization pathway, leaving clear fingerprints (asymmetry, splitting, and shifting) in the energy spectrum of emitted photoelectrons. Here we investigate this phenomenon by solving the time-dependent Schr\"odinger equation of the valence electron of Na and Li in increasing levels of complexity: (i) developing minimal models for two-photon transition and (2+12+12+1)-photon ionization, (ii) applying a spectral method without continuum-continuum couplings, and (iii) propagating the electron wave packet on a large spatial grid accounting for all possible couplings. We show that appropriately detuned transform limited pulses provide a high level of control in strong-field excitation, when the atomic levels are dynamically shifted. Furthermore, we demonstrate the role of DSSs in the multipeak structure of the Autler-Townes doublet, found when several Rabi oscillations are induced during the strong-field resonant ionization.
We present experimental and theoretical results of a detailed study of laser-induced continuum structures (LICS's) in the photoionization continuum of helium out of the metastable state 2s1S0.2s{}^{1}{S}_{0}.2s1S0​. The continuum dressing, with a 1064-nm laser, couples the same region of the continuum to the 4s1S04s{}^{1}{S}_{0}4s1S0​ state. The experimental data, presented for a range of intensities, show pronounced ionization suppression (by as much as 70% with respect to the far-from-resonance value) as well as enhancement, in a Beutler-Fano resonance profile. This ionization suppression is a clear indication of population trapping mediated by coupling to a continuum. We present experimental results demonstrating the effect of pulse delay upon the LICS's, and for the behavior of LICS's for both weak and strong probe pulses. Simulations based upon numerical solution of the Schr\"odinger equation model the experimental results. The atomic parameters (Rabi frequencies and Stark shifts) are calculated using a simple model-potential method for the computation of the needed wave functions. The simulations of the LICS profiles are in excellent agreement with experiment. We also present an analytic formulation of pulsed LICS's. We show that in the case of a probe pulse shorter than the dressing one, the LICS profile is the convolution of the power spectra of the probe pulse with the usual Fano profile of stationary LICS's. We discuss some consequences of deviation from steady-state theory.