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Physical Review A

Spectral phase control of an ultrashort pulse for exploring the Autler-Townes effect in hydrogen atomic ionization through a resonant state

An Yang, Wen-Quan Jing, Bingshuang Zhang, Li‐Bao Fan, Lijuan Jia, Chuan‐Cun Shu

Published Nov 24, 2025• 7 citations
Publisher

Abstract

We present a bound-continuum ionization model combined with numerical simulations to investigate the asymmetric features of Autler-Townes (AT) splitting in the ionization spectra of hydrogen atoms, induced by a spectrally phase-modulated ultrashort pulse. This model incorporates a resonance-enhanced two-photon ionization process, enabling transitions from the ground electronic state to the continuum state via the first excited electronic state through the absorption of two photons. By comparing our model predictions with exact numerical simulations based on time-dependent electronic wave-packet calculations, we demonstrate that the characteristics of the AT doublets, shaped by the spectral phase, emerge from the competing effects of selective population of dressed states and the transition amplitude to the continuum. In addition, through a perturbative analysis of the photoelectronic spectrum and the application of the Magnus expansion, we reveal a correlation between the number of AT fringes, resonant states, and pulse area, while drawing insights from bound states. This work enhances our understanding of how the spectral phase can be utilized to explore bound-state effects in ultrafast ionization dynamics.

DOI
10.1103/7fw3-pvpx

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We present a bound-continuum ionization model combined with numerical simulations to investigate the asymmetric features of Autler-Townes (AT) splitting in the ionization spectra of hydrogen atoms, induced by a spectrally phase-modulated ultrashort pulse. This model incorporates a resonance-enhanced two-photon ionization process, enabling transitions from the ground electronic state to the continuum state via the first excited electronic state through the absorption of two photons. By comparing our model predictions with exact numerical simulations based on time-dependent electronic wave-packet calculations, we demonstrate that the characteristics of the AT doublets, shaped by the spectral phase, emerge from the competing effects of selective population of dressed states and the transition amplitude to the continuum. In addition, through a perturbative analysis of the photoelectronic spectrum and the application of the Magnus expansion, we reveal a correlation between the number of AT fringes, resonant states, and pulse area, while drawing insights from bound states. This work enhances our understanding of how the spectral phase can be utilized to explore bound-state effects in ultrafast ionization dynamics.
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.
We theoretically investigate the resonant two-photon ionization of a hydrogen atom in the counter-rotating circularly polarized double-pulse sequences, by solving the time-dependent Schr\"odinger equation. Due to the induced Rabi oscillations between the ground and excited states, the well-known Autler-Townes doublet is observed in the photoelectron spectra. More interestingly, our numerical results reveal an additional peak located between the Autler-Townes doublets, which originates from single-photon ionization from the excited state by the second pulse. By adjusting the laser intensity of the two pulses, the photoelectron yields of the three peaks can be sensitively modulated, under the control of completed Rabi cycles within the first pulse. In addition, our results show a potential of manipulating the photoemission anisotropy by both the laser intensity and the two-pulse time delay, through adjusting the competition of different partial waves generated by the two pulses.
We propose a scheme to control the shape of the Autler-Townes (AT) doublet in the photoelectron spectrum from atomic resonance-enhanced multiphoton ionization (REMPI). The scheme is based on the interference of two AT doublets created by ionization of the strongly driven atom from the ground and the resonantly excited state using tailored bichromatic femtosecond laser pulses. In this scheme, the quantum phase of the photoelectrons is crucial for the manipulation of the AT doublet. The laser polarization state and the relative optical phase between the two colors are used to manipulate the interference pattern. We develop an analytical model to describe the bichromatic REMPI process and provide a physical picture of the control mechanism. To validate the model, the results are compared to an ab initio calculation based on the solution of the two-dimensional time-dependent Schr\"odinger equation for the nonperturbative interaction of an atom with intense polarization-shaped bichromatic femtosecond-laser pulses. Our results indicate that the control mechanism is robust with respect to the laser intensity, facilitating its experimental observation.
Abstract Based on numerical solutions of the time-dependent Schrödinger equation, we theoretically investigate the photoelectron spectrum of hydrogen atoms ionized by a pair of ultrashort, intense, and orthogonally polarized laser pulses with a relative time delay in a pump–probe configuration. The pump pulse resonantly excites electrons from the 1s and 2p levels, inducing Rabi oscillations. The resulting dynamically enhanced Autler–Townes (AT) splitting is observed in the photoelectron energy spectrum upon interaction with the second probe pulse. In contrast to the previous parallel-polarization scheme, the proposed orthogonal-polarization configuration enables the resolution of dynamically enhanced AT splitting over a considerably wider range of probe photon energies.
A two-photon resonance in the sodium atom $3s\text{\ensuremath{-}}4s$ transition is investigated in the strong coupling regime with photoelectron momentum imaging techniques. The kinetic energies of the ionized electron map out the eigenenergies of the dressed states and emerge as the Autler-Townes (AT) splitting, which is proportional to the laser intensity due to the two-photon nature. The partial wave analysis of the angular distribution of the photoelectrons reveals the relative phase shift from dressed states which is related to the attosecond ionization time delays. The phase shift between the two electron wave packets produced from AT splitting are attributed to the combination of the Coulomb phase and the quantum defect phase.