Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0707.3111 · Journal of Physics B Atomic Molecular and Optical Physics

Nonperturbative resonant strong field ionization of atomic hydrogen

M G Girju, K. Hristov, Oleg Kidun, D. Bauer

Published Oct 17, 2007• 31 citations
arXivHTMLPDF

Abstract

We investigate resonant strong field ionization of atomic hydrogen with respect to the 1s–2p transition. By 'strong' we understand that Rabi periods are executed on a femtosecond time scale. Ionization and AC Stark shifts modify the bound state dynamics severely, leading to nonperturbative signatures in the photoelectron spectra. We introduce an analytical model, capable of predicting qualitative features in the photoelectron spectra such as the positions of the Autler–Townes peaks for modest field strengths. Ab initio solutions of the time-dependent Schrödinger equation show a pronounced shift and broadening of the left Autler–Townes peak as the field strength is increased. The right peak remains rather narrow and shifts less. This result is analysed and explained with the help of exact AC Stark shifts and ionization rates obtained from Floquet theory. Finally, it is demonstrated that in the case of finite pulses as short as 20 fs the Autler–Townes duplet can still be resolved. The fourth generation light sources under construction worldwide will provide bright, coherent radiation with photon energies ranging from a tenth of an meV up to tens of keV, hence covering the regime studied in the paper so that measurements of nonperturbative, relative AC Stark shifts should become feasible with these new light sources.

DOI
10.1088/0953-4075/40/21/004

Related papers

Effect of nonresonant states in near-resonant two-photon ionization of hydrogen

Xu Zhang, Yueming Zhou, Yijie Liao +6 more

By numerically solving the three-dimensional time-dependent Schr\"odinger equation, two-photon ionization of hydrogen is investigated at the near-resonant frequencies of the $1s\text{\ensuremath{-}}2p$ transition. Due to the Rabi oscillations between the $1s$ and $2p$ states, the photoelectron energy spectra exhibit the Autler-Townes (AT) doublets and we focus on the energy spacing and the asymmetry of the doublets. Our results show that the laser frequency for the minimum energy spacing of AT doublets locates at the resonant frequency of the ac-stark-shifted states, while the symmetry of the AT doublets is affected both by the ac-stark shift and the nonresonant ionization pathway. Developing the minimal three-state model including all of the nonresonant (nonessential) states, the effects of the ac-stark shift and the nonresonant ionization pathway on the AT doublets due to the nonresonant states are identified. Furthermore, due to the nonresonant ionization pathway, the photoelectron angular distributions are distinctly different for the lower- and higher-energy peaks in the AT doublets and these angular distributions sensitively depend on the laser intensity and pulse duration. These results are well reproduced by our minimal three-state model.

Physical Review A•Dec 30, 2022•32 citations

Role of dynamic Stark shifts in strong-field excitation and subsequent ionization

Attila Tóth, S. Borbély, Yueming Zhou +1 more

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 ($2+1$)-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.

Physical Review A•May 1, 2023•24 citations

Benchmark of few-level quantum theory vs ab initio numerical solutions for the strong-field Autler–Townes effect in photoionization of hydrogen

Daniel Younis, Joseph H. Eberly

Abstract The temporal and spectral consequences of an intermediate resonance en route to photoionization are investigated theoretically in two ways: by solving few-level model equations and by ab initio numerical solution of the time-dependent Schrödinger equation, in both cases for hydrogen in three dimensions. The model consists of atomic states resonantly field-dressed in a three-level reduction of the hydrogen atom that consists of the 2p–3d (Balmer) transition and one energetically-distant continuum state. The model’s level occupation probabilities are derived from three Schrödinger amplitude equations and are benchmarked against an ab initio numerical solution for the hydrogen electron’s wavefunction under the same field. We examine contrasts between the results of the two approaches with a particular focus on Autler–Townes doublets that appear in the photoelectron spectrum.

Journal of Physics B Atomic Molecular and Optical Physics•Jun 30, 2022•7 citations

Unveiling nonperturbative factors in the resonant photoionization time delay

Xiao‐Yun Zhao, Ming-Qing Liu

Abstract Atomic photoionization time delay is a vital component of attosecond metrology for investigating the ultrafast electron dynamics in atomic systems on their natural time scale. Here, we probe the factor which leads to the nonperturbative characteristics of resonant photoionization time delay (RPTD) of atomic hydrogen by numerically solving the time-dependent Schrödinger equation (TDSE) and the strong-field nonperturbation theory (SFNPT) with considering the population depletion and ac-Stark energy shift of ground state. RPTD can be retrieved from the energy-resolved optical phase of a bicircular two-color field corresponding to the maximal asymmetry of photoelectron angular distribution even in the nonperturbative regime. Our results reveal that as laser intensity increases the RPTD shows a remarkable difference of energy-dependent behaviors. At lower intensity, the absolute value of RPTD displays a smooth drop with increasing electron energy, however, at higher intensity its absolute value exhibits an obvious enhancement. Given the agreement between TDSE and SFNPT, we clearly elucidate the physical origin of nonperturbative characteristics, i.e., the population depletion of ground state plays a crucial role rather than ac-Stark energy shift. More specifically, the population depletion severely affects the Fourier transformation of the laser envelope, which is an important phase component of transition amplitude. Our work clarifies the physical mechanism of atomic photoionization time delay in nonperturbative environments, advancing the comprehensive understanding of time in attosecond science.

Chinese Physics B•Aug 25, 2026•0 citations

Dynamically enhanced Autler–Townes splitting by orthogonal XUV fields

Li-Long Wu, Wei‐Chao Jiang, Liang-You Peng

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.

Chinese Physics B•Apr 12, 2024•6 citations

Photoelectron signature of dressed-atom stabilization in an intense XUV field

Edvin Olofsson, Jan Marcus Dahlström

Nonperturbative resonant multiphoton ionization $(1+1)$ 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.

Physical Review Research•Oct 5, 2023•24 citations
We investigate resonant strong field ionization of atomic hydrogen with respect to the 1s–2p transition. By 'strong' we understand that Rabi periods are executed on a femtosecond time scale. Ionization and AC Stark shifts modify the bound state dynamics severely, leading to nonperturbative signatures in the photoelectron spectra. We introduce an analytical model, capable of predicting qualitative features in the photoelectron spectra such as the positions of the Autler–Townes peaks for modest field strengths. Ab initio solutions of the time-dependent Schrödinger equation show a pronounced shift and broadening of the left Autler–Townes peak as the field strength is increased. The right peak remains rather narrow and shifts less. This result is analysed and explained with the help of exact AC Stark shifts and ionization rates obtained from Floquet theory. Finally, it is demonstrated that in the case of finite pulses as short as 20 fs the Autler–Townes duplet can still be resolved. The fourth generation light sources under construction worldwide will provide bright, coherent radiation with photon energies ranging from a tenth of an meV up to tens of keV, hence covering the regime studied in the paper so that measurements of nonperturbative, relative AC Stark shifts should become feasible with these new light sources.
By numerically solving the three-dimensional time-dependent Schr\"odinger equation, two-photon ionization of hydrogen is investigated at the near-resonant frequencies of the $1s\text{\ensuremath{-}}2p$ transition. Due to the Rabi oscillations between the 1s1s1s and 2p2p2p states, the photoelectron energy spectra exhibit the Autler-Townes (AT) doublets and we focus on the energy spacing and the asymmetry of the doublets. Our results show that the laser frequency for the minimum energy spacing of AT doublets locates at the resonant frequency of the ac-stark-shifted states, while the symmetry of the AT doublets is affected both by the ac-stark shift and the nonresonant ionization pathway. Developing the minimal three-state model including all of the nonresonant (nonessential) states, the effects of the ac-stark shift and the nonresonant ionization pathway on the AT doublets due to the nonresonant states are identified. Furthermore, due to the nonresonant ionization pathway, the photoelectron angular distributions are distinctly different for the lower- and higher-energy peaks in the AT doublets and these angular distributions sensitively depend on the laser intensity and pulse duration. These results are well reproduced by our minimal three-state model.
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.
Abstract The temporal and spectral consequences of an intermediate resonance en route to photoionization are investigated theoretically in two ways: by solving few-level model equations and by ab initio numerical solution of the time-dependent Schrödinger equation, in both cases for hydrogen in three dimensions. The model consists of atomic states resonantly field-dressed in a three-level reduction of the hydrogen atom that consists of the 2p–3d (Balmer) transition and one energetically-distant continuum state. The model’s level occupation probabilities are derived from three Schrödinger amplitude equations and are benchmarked against an ab initio numerical solution for the hydrogen electron’s wavefunction under the same field. We examine contrasts between the results of the two approaches with a particular focus on Autler–Townes doublets that appear in the photoelectron spectrum.
Abstract Atomic photoionization time delay is a vital component of attosecond metrology for investigating the ultrafast electron dynamics in atomic systems on their natural time scale. Here, we probe the factor which leads to the nonperturbative characteristics of resonant photoionization time delay (RPTD) of atomic hydrogen by numerically solving the time-dependent Schrödinger equation (TDSE) and the strong-field nonperturbation theory (SFNPT) with considering the population depletion and ac-Stark energy shift of ground state. RPTD can be retrieved from the energy-resolved optical phase of a bicircular two-color field corresponding to the maximal asymmetry of photoelectron angular distribution even in the nonperturbative regime. Our results reveal that as laser intensity increases the RPTD shows a remarkable difference of energy-dependent behaviors. At lower intensity, the absolute value of RPTD displays a smooth drop with increasing electron energy, however, at higher intensity its absolute value exhibits an obvious enhancement. Given the agreement between TDSE and SFNPT, we clearly elucidate the physical origin of nonperturbative characteristics, i.e., the population depletion of ground state plays a crucial role rather than ac-Stark energy shift. More specifically, the population depletion severely affects the Fourier transformation of the laser envelope, which is an important phase component of transition amplitude. Our work clarifies the physical mechanism of atomic photoionization time delay in nonperturbative environments, advancing the comprehensive understanding of time in attosecond science.
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.
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.