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

Physical Review A

Excitation and ionization dynamics in short-pulse multiphoton ionization

George N. Gibson, Richard R. Freeman, Thomas J. Mcilrath, Harm Geert Muller

Published May 1, 1994• 49 citations
Publisher

Abstract

We present results from a time-dependent two-level-plus-continuum model of multiphoton ionization in order to better understand the short-pulse photoelectron spectrum resulting from multiphoton ionization and the role of intermediate states. Both resonant and nonresonant population transfer to the upper state are found to play an important role in the multiphonon ionization process. The dynamic modeling reveals the potential for broadening and shifting peaks in the photoelectron spectrum. However, we conclude that despite the complex dynamics of the excitation, short-pulse photoelectron spectra can be used to measure ac Stark shifts of both ponderomotively and nonponderomotively shifted states in strong laser fields.

DOI
10.1103/physreva.49.3870

Related papers

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

Dynamics of Short-Pulse Multiphoton Ionization

George N. Gibson, Richard R. Freeman, Thomas J. Mcilrath

We investigate the relative importance of resonant enhancement and real population transfer in short-pulse multiphoton ionization. Total ionization and excited state population after the laser pulse are calculated numerically by integrating the time dependent Schödinger for a two level atom in a short-pulse high-intensity laser field.

Shortwavelength: Physics with Intense Laser Pulses•Jan 1, 1993•0 citations

The many faces of resonances in multiphoton ionization

X. Tang, A. Lyras, P. Lambropoulos

We present a theoretical analysis of multiphoton ionization through resonant intermediate states shifted through resonance during a short, intense pulse. The resonant structure in the photoelectron spectra is compared with what it would be if the peak intensity or the frequency of the laser were scanned, and the various differences are discussed in detail. The dynamical behavior is described in terms of a density matrix evolving under a realistic temporal and spatial pulse shape. Our results, on atoms with realistic parameters, show structure similar to that observed in recent experiments. Results for circularly polarized light are also presented. The limitations and advantages of the model are discussed.

Journal of the Optical Society of America B•Apr 1, 1990•13 citations

A time-dependent theory of resonant multiphoton ionization of atoms by short pulses. II. Strong field results for the two-photon ionization of caesium

Avi J. Adler, A. Rachman, Edward J. Robinson

For pt.I see ibid., vol.28, p.5057-75 (1995). In the previous paper, a non-perturbative time-dependent theory of resonant multiphoton ionization by both smooth and rectangular pulses was derived, and as a first step, applied to the two-photon ionization of caesium in weak fields. In the present paper, we continue the analysis of the same system, extending the weak-field results and considering the case of stronger fields. At higher intensities the spectra exhibit energy modulations of a different character from those predicted for low power. Here, for stronger fields, the structure arises from Rabi oscillations, which, for the smooth pulses assumed here, are triggered by time-dependent Stark shifts. In order to obtain a better understanding of the energy oscillations, we also look at the photoelectron energy spectrum produced by a rectangular pulse, a problem which is solved exactly. We show that there are other sources of strong-field structure.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 14, 1995•5 citations

Probing strong-field two-photon transitions through dynamic interference

Attila Tóth, András Csehi

Abstract We demonstrate how strong-field multiphoton transitions between dynamically shifted atomic levels can be traced in the energy spectra of emitted photoelectrons. Applying an ultrafast and intense laser pulse, two-photon Rabi oscillations are induced between two bound states of an atom. A third photon from the same pulse directly ionizes the atom, thus the emitted photoelectrons coherently probe the underlying dynamics. As the instantaneous energy of photoelectrons follows the pulse intensity envelope, modulated by the ac Stark shifts, electrons emitted with the same energy but at different times—at the rising and falling edge of the pulse—will interfere leading to pronounced dynamic interference pattern in the spectra. We investigate this phenomenon both numerically and analytically by developing a minimal three-state model that incorporates two-photon coupling and dynamically shifted atomic levels. On the example of atomic lithium (2 s → → 4 s → continuum) we show how the individual ac Stark shifts and the two-photon Rabi frequency are reflected through the asymmetry, shifting and splitting of the interference structure of the computed photopeaks.

Journal of Physics B Atomic Molecular and Optical Physics•Jan 14, 2021•32 citations

Revival of Stark-Induced Resonances in Multiphoton Ionization of Krypton with Femtosecond Intense Pulses

E. Mével, Rusty P. Trainham, P. Breger +5 more

As it is well known now1, electron energy spectra from multiphoton ionization (MPI) and Above-Threshold Ionization (ATI) of atoms by subpicosecond pulses reveal Stark-induced resonances and provide an elegant and unique method to investigate AC-Stark shifts of strongly perturbed excited states. In this work we have systematically studied such spectra and their interpretation in the case of MPI of Rare gases with 100 fs, 617 nm pulses. The intensity ranges from 1013 (for xenon) to 1015 W.cm−2 (for helium). The corresponding shifts range from .3 eV to 30 eV and may be, in principle, larger than the atomic ionization potential. Besides the measurement of AC-Stark shifts, the photoelectron spectra provide valuable information about the ionization process itself in a highly non-perturbative regime.

International Conference on Ultrafast Phenomena•Jan 1, 1992•0 citations
We present results from a time-dependent two-level-plus-continuum model of multiphoton ionization in order to better understand the short-pulse photoelectron spectrum resulting from multiphoton ionization and the role of intermediate states. Both resonant and nonresonant population transfer to the upper state are found to play an important role in the multiphonon ionization process. The dynamic modeling reveals the potential for broadening and shifting peaks in the photoelectron spectrum. However, we conclude that despite the complex dynamics of the excitation, short-pulse photoelectron spectra can be used to measure ac Stark shifts of both ponderomotively and nonponderomotively shifted states in strong laser fields.
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 a theoretical analysis of multiphoton ionization through resonant intermediate states shifted through resonance during a short, intense pulse. The resonant structure in the photoelectron spectra is compared with what it would be if the peak intensity or the frequency of the laser were scanned, and the various differences are discussed in detail. The dynamical behavior is described in terms of a density matrix evolving under a realistic temporal and spatial pulse shape. Our results, on atoms with realistic parameters, show structure similar to that observed in recent experiments. Results for circularly polarized light are also presented. The limitations and advantages of the model are discussed.
For pt.I see ibid., vol.28, p.5057-75 (1995). In the previous paper, a non-perturbative time-dependent theory of resonant multiphoton ionization by both smooth and rectangular pulses was derived, and as a first step, applied to the two-photon ionization of caesium in weak fields. In the present paper, we continue the analysis of the same system, extending the weak-field results and considering the case of stronger fields. At higher intensities the spectra exhibit energy modulations of a different character from those predicted for low power. Here, for stronger fields, the structure arises from Rabi oscillations, which, for the smooth pulses assumed here, are triggered by time-dependent Stark shifts. In order to obtain a better understanding of the energy oscillations, we also look at the photoelectron energy spectrum produced by a rectangular pulse, a problem which is solved exactly. We show that there are other sources of strong-field structure.
Abstract We demonstrate how strong-field multiphoton transitions between dynamically shifted atomic levels can be traced in the energy spectra of emitted photoelectrons. Applying an ultrafast and intense laser pulse, two-photon Rabi oscillations are induced between two bound states of an atom. A third photon from the same pulse directly ionizes the atom, thus the emitted photoelectrons coherently probe the underlying dynamics. As the instantaneous energy of photoelectrons follows the pulse intensity envelope, modulated by the ac Stark shifts, electrons emitted with the same energy but at different times—at the rising and falling edge of the pulse—will interfere leading to pronounced dynamic interference pattern in the spectra. We investigate this phenomenon both numerically and analytically by developing a minimal three-state model that incorporates two-photon coupling and dynamically shifted atomic levels. On the example of atomic lithium (2 s → → 4 s → continuum) we show how the individual ac Stark shifts and the two-photon Rabi frequency are reflected through the asymmetry, shifting and splitting of the interference structure of the computed photopeaks.
As it is well known now1, electron energy spectra from multiphoton ionization (MPI) and Above-Threshold Ionization (ATI) of atoms by subpicosecond pulses reveal Stark-induced resonances and provide an elegant and unique method to investigate AC-Stark shifts of strongly perturbed excited states. In this work we have systematically studied such spectra and their interpretation in the case of MPI of Rare gases with 100 fs, 617 nm pulses. The intensity ranges from 1013 (for xenon) to 1015 W.cm−2 (for helium). The corresponding shifts range from .3 eV to 30 eV and may be, in principle, larger than the atomic ionization potential. Besides the measurement of AC-Stark shifts, the photoelectron spectra provide valuable information about the ionization process itself in a highly non-perturbative regime.