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

Photoionization by pulses with a modulated frequency

Piotr Bała, Jacek Matulewski, Andrzej Raczyński, Jarosław Zaremba

Published Jun 1, 1998• 6 citations
Publisher

Abstract

The dynamics of the bound-state populations and the photoelectron spectra are calculated for model atomic systems irradiated by a pulse with a harmonically modulated frequency. For a system including a single bound state a model is adopted, which takes into account the threshold behavior typical of negative ions and admits continuum-continuum transitions. For a model one-dimensional atom the results are obtained through a numerical integration of the Schr\"odinger equation. The case of a resonant ionization is also considered. The modulation of the frequency results in changing the instantaneous rate of decay of the initial state, in inducing additional population oscillations for multilevel systems, and in additional peaks in the photoelectron spectra.

DOI
10.1103/physreva.57.4561

Related papers

Near-threshold photoionization by pulses with modulated frequency

Andrzej Raczyński, Jarosław Zaremba

Model photoionization by a pulse with a modulated frequency is discussed. An approximation generalizing that of Weisskopf-Wigner is proposed, with a pole moving in the rhythm of the modulation. A model taking into account the ionization threshold is adopted, and relatively simple formulas for the nondecay probability and the photoelectron spectrum are obtained. A nonexponential character of the decay curves is demonstrated together with a raising and narrowing of the peaks in the photoelectron spectra.

Physical Review A•Mar 1, 1998•1 citation

Threshold effects and photoelectron spectra in model-system descriptions of photodetachment

Stanley L. Haan, P. A. Polstra, W. H. Schotanus +1 more

Near-threshold single-photon photodetachment processes are considered for simple model systems representing negative ions exposed to monochromatic radiation. The model systems considered feature an initial discrete state, the photoelectron continuum, and in some cases an excited or autodetaching discrete state. Population trapping through the formation of a bound dressed state and the photoelectron spectra are examined. Two photoelectron spectra are defined : a primary spectrum which results from decay while the laser interaction is on and a secondary spectrum which results from the destabilization of the bound dressed state if the interaction is turned off again. Careful attention is given to the passage of the poles of the Green's operator through the low-energy boundary of a continuum, and it is concluded that such poles move nonmonotonically through the boundary of an s-wave continuum, but monotonically through the boundary of a p-wave or higher-l-wave continuum. Two example systems, one featuring a single discrete state and an s-wave continuum and one featuring two discrete states and a p-wave continuum, are considered in detail.

Physical Review A•Nov 1, 1992•2 citations

Two-frequency above threshold ionization with pulses

L. Wang, J. W. Haus, K. Rzazewski

We solve a model with one bound state and two continua.1 Two lasers are used to study the above threshold ionization process. The first laser couples the electron in a bound state to a continuum state. The photons are assumed to be energetic enough to promote the electron directly into the continuum far from the threshold; this avoids complications due to the Rydberg levels and the ponderomotive shifts of the threshold. The second laser mixes the electron wavefunction between two continuum states (C—C transitions); since we avoid the rotating wave approximation, multiple transitions between these continua are allowed. We find that the ionization rate is unaffected by the C—C transitions. Our model of hydrogenic atoms allows redistribution among the continua only during the ionization process and the photoelectron spectra exhibits peak suppression; i.e., the population is not the strongest at the energy of the ionization laser.

Annual Meeting Optical Society of America•Jan 1, 1989•0 citations

Two-frequency above-threshold ionization with smooth pulses

Kazimierz Rza̧ewski, Li Wang, Joseph W. Haus

A model of atomic ionization by smooth pulses is solved with bound-continuum and energy-dependent continuum-continuum (C-C) dipole coupling. The rotating-wave approximation for the C-C transitions is avoided. In contrast with the flat continuum result, our ionization rate is independent of the C-C coupling. We also derive the photoelectron energy spectra and show that counterrotating terms make important contributions. Relation to above-threshold ionization experiments with two frequencies is discussed.

Physical Review A•Sep 1, 1989•26 citations

Above-threshold ionization of atoms irradiated by sinusoidally phase-modulated pulses

Haiying Yuan, Yujun Yang, Fu-Ming Guo +3 more

By solving the time-dependent Schr\"odinger equation in momentum space, the photoelectron emission from atoms under the irradiation of 400 nm sinusoidal phase-modulated shaped pulses was investigated. It was found that by controlling the phase and amplitude of the pulses in the frequency domain, in addition to the photoelectron peaks generated by the interference of multiple-cycle ionization, additional resonant peak structures and interference phenomena can be observed in the photoelectron emission spectrum. Through the analysis of photoelectrons from different subpulses within the shaped pulse, it was discovered that these structures arise from the modulation of ionization and excitation processes by multiple subpulses within the shaped pulse. This study demonstrates the significant importance of utilizing shaped pulses for the control of photoelectron emission.

Physical Review A•Feb 5, 2024•5 citations

Ionization dynamics in intense pulsed laser radiation. Effects of frequency chirping

Roberta Marani, E J Robinson

Via a non-perturbative method we study the population dynamics and photoelectron spectra of Cs atoms subject to intense chirped laser pulses, with Gaussian beams. We include above threshold ionization spectral peaks. The frequency of the laser is near resonance with the 6s-7p transition. Dominant couplings are included exactly, weaker ones accounted for perturbatively. We calculate the relevant transition matrix elements, including spin-orbit coupling. The pulse is taken to be a hyperbolic secant in time and the chirping a hyperbolic tangent. This choice allows the equations of motions for the probability amplitudes to be solved analytically as a series expansion in the variable , where is a measure of the pulse length. We find that the chirping changes the ionization dynamics and the photoelectron spectra noticeably, especially for longer pulses of the order of au. The peaks shift and change in height, and interference effects between the 7p levels are enhanced or diminished according to the amount of chirping and its sign. The integrated ionization probability is not strongly affected.

arXiv:physics/9812010•Journal of Physics B Atomic Molecular and Optical Physics•Jan 1, 1999•11 citations
The dynamics of the bound-state populations and the photoelectron spectra are calculated for model atomic systems irradiated by a pulse with a harmonically modulated frequency. For a system including a single bound state a model is adopted, which takes into account the threshold behavior typical of negative ions and admits continuum-continuum transitions. For a model one-dimensional atom the results are obtained through a numerical integration of the Schr"odinger equation. The case of a resonant ionization is also considered. The modulation of the frequency results in changing the instantaneous rate of decay of the initial state, in inducing additional population oscillations for multilevel systems, and in additional peaks in the photoelectron spectra.
Model photoionization by a pulse with a modulated frequency is discussed. An approximation generalizing that of Weisskopf-Wigner is proposed, with a pole moving in the rhythm of the modulation. A model taking into account the ionization threshold is adopted, and relatively simple formulas for the nondecay probability and the photoelectron spectrum are obtained. A nonexponential character of the decay curves is demonstrated together with a raising and narrowing of the peaks in the photoelectron spectra.
Near-threshold single-photon photodetachment processes are considered for simple model systems representing negative ions exposed to monochromatic radiation. The model systems considered feature an initial discrete state, the photoelectron continuum, and in some cases an excited or autodetaching discrete state. Population trapping through the formation of a bound dressed state and the photoelectron spectra are examined. Two photoelectron spectra are defined : a primary spectrum which results from decay while the laser interaction is on and a secondary spectrum which results from the destabilization of the bound dressed state if the interaction is turned off again. Careful attention is given to the passage of the poles of the Green's operator through the low-energy boundary of a continuum, and it is concluded that such poles move nonmonotonically through the boundary of an s-wave continuum, but monotonically through the boundary of a p-wave or higher-l-wave continuum. Two example systems, one featuring a single discrete state and an s-wave continuum and one featuring two discrete states and a p-wave continuum, are considered in detail.
We solve a model with one bound state and two continua.1 Two lasers are used to study the above threshold ionization process. The first laser couples the electron in a bound state to a continuum state. The photons are assumed to be energetic enough to promote the electron directly into the continuum far from the threshold; this avoids complications due to the Rydberg levels and the ponderomotive shifts of the threshold. The second laser mixes the electron wavefunction between two continuum states (C—C transitions); since we avoid the rotating wave approximation, multiple transitions between these continua are allowed. We find that the ionization rate is unaffected by the C—C transitions. Our model of hydrogenic atoms allows redistribution among the continua only during the ionization process and the photoelectron spectra exhibits peak suppression; i.e., the population is not the strongest at the energy of the ionization laser.
A model of atomic ionization by smooth pulses is solved with bound-continuum and energy-dependent continuum-continuum (C-C) dipole coupling. The rotating-wave approximation for the C-C transitions is avoided. In contrast with the flat continuum result, our ionization rate is independent of the C-C coupling. We also derive the photoelectron energy spectra and show that counterrotating terms make important contributions. Relation to above-threshold ionization experiments with two frequencies is discussed.
By solving the time-dependent Schr\"odinger equation in momentum space, the photoelectron emission from atoms under the irradiation of 400 nm sinusoidal phase-modulated shaped pulses was investigated. It was found that by controlling the phase and amplitude of the pulses in the frequency domain, in addition to the photoelectron peaks generated by the interference of multiple-cycle ionization, additional resonant peak structures and interference phenomena can be observed in the photoelectron emission spectrum. Through the analysis of photoelectrons from different subpulses within the shaped pulse, it was discovered that these structures arise from the modulation of ionization and excitation processes by multiple subpulses within the shaped pulse. This study demonstrates the significant importance of utilizing shaped pulses for the control of photoelectron emission.
Via a non-perturbative method we study the population dynamics and photoelectron spectra of Cs atoms subject to intense chirped laser pulses, with Gaussian beams. We include above threshold ionization spectral peaks. The frequency of the laser is near resonance with the 6s-7p transition. Dominant couplings are included exactly, weaker ones accounted for perturbatively. We calculate the relevant transition matrix elements, including spin-orbit coupling. The pulse is taken to be a hyperbolic secant in time and the chirping a hyperbolic tangent. This choice allows the equations of motions for the probability amplitudes to be solved analytically as a series expansion in the variable , where is a measure of the pulse length. We find that the chirping changes the ionization dynamics and the photoelectron spectra noticeably, especially for longer pulses of the order of au. The peaks shift and change in height, and interference effects between the 7p levels are enhanced or diminished according to the amount of chirping and its sign. The integrated ionization probability is not strongly affected.