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

Resonance enhancement of above-threshold peaks in multiphoton ionization

Martin Dörr, Robin Shakeshaft

Published Jul 1, 1988• 26 citations
Publisher

Abstract

We have solved the time-dependent Schr\"odinger equation for a one-dimensional model atom exposed to a spatially homogeneous laser field that is turned on smoothly. We have studied the ionization of this "atom" at a laser frequency close to a three-photon resonance and have found a spike on top of each of the above-threshold peaks of the ionization signal, in accordance with the findings of a recent experimental investigation.

DOI
10.1103/physreva.38.543

Related papers

Resonant multiphoton ionization of atomic hydrogen

Yves Gontier, N. K. Rahman, M. Trahin

The resonantly enhanced multiphoton ionization of atomic hydrogen is studied for the case of four-photon ionization (three-photon resonant). The time-dependent probabilities, the shape of the resonance profile at different intensities, and the nonlinear index are computed for coherent light at frequencies around the resonance (365 nm). The systematic dependence of the cross section as a function of the principal quantum number of the resonant state (as this tends towards the Rydberg states) is investigated at zero detuning. The probabilities of absorption of one photon more than necessary for the four-photon ionization process (resonantly enhanced above-threshold ionization) is computed and the relevant branching ratios are examined. Then it is shown that the effect of the spatio-temporal structures of the laser pulse is to red shift the maximum of the resonance profile, whereas that of an ideal chaotic light is to blue shift and broaden the resonance peak. The shape, shift, and width of the profile resulting from both these effects are in very fair agreement with the experimental ones.

Physical Review A•Jun 1, 1988•15 citations

Resonance-enhanced multiphoton ionization of atomic hydrogen

L. R. Brewer, Fritz Buchinger, Martin Ligare +1 more

We have measured the resonance-enhanced four-photon ionization of atomic hydrogen. The degenerate four-photon process occurs via a three-photon resonance between the 1s and the 2p levels, with subsequent one-photon ionization near threshold. We have studied the highly asymmetric resonance-enhanced profile, i.e., the photoion yield as a function of laser detuning from three-photon resonance between the 1s and 2p levels. In particular, we have determined the width, shift, peak, and asymmetry of the profile as a function of laser intensity. The experimental results are compared to theoretical models. These models involve both the properties of the atom in an intense near-resonant radiative field, and a detailed model for the multimode laser field, particularly the field fluctuations due to mode beating. The asymmetric resonance-enhanced photoionization profile is well reproduced by both a random-phase and a chaotic-light model.

Physical Review A•Apr 1, 1989•21 citations

Multiphoton resonant ionization of hydrogen atom exposed to two-colour laser pulses

Peijie Wang, Fang Yan

This paper studies the multiphoton resonant ionization by two-colour laser pulses in the hydrogen atom by solving the time-dependent Schrodinger equation. By fixing the parameters of fundamental laser field and scanning the frequency of second laser field, it finds that the ionization probability shows several resonance peaks and is also much larger than the linear superposition of probabilities by applying two lasers separately. The enhancement of the ionization happens when the system is resonantly pumped to the excited states by absorbing two or more colour photons non-sequentially.

Chinese Physics B•Oct 1, 2008•4 citations

Theory of the effect of third-harmonic generation on three-photon resonantly enhanced multiphoton ionization in focused beams

M. G. Payne, W. R. Garrett

Multiphoton ionization in the region near a three-photon resonance is treated for focused, plane-polarized Gaussian beams with diffraction-limited beam divergence. In this situation, a third-harmonic field is generated within the laser beam. At, and very near, three-photon resonance the driving rate for the upper-state probability amplitude due to one-photon absorption of third-harmonic light becomes nearly equal to the corresponding three-photon rate due to the laser field, but these effects are 180\ifmmode^\circ\else\textdegree\fi{} out of phase. As a consequence of this cancellation between two pumping terms, the three-photon resonance line essentially disappears at moderate concentrations and the observed ionization has a line shape that is close to the phase-matching curve for third-harmonic generation. The ionization signal, near but not on the resonance, is due almost entirely to absorption of third-harmonic photons plus other laser photons; three-photon resonantly enhanced multiphoton ionization by the laser is much weaker. This is particularly true on the blue side of the three-photon resonance at detunings where phase matching occurs. The problem is treated quite generally with predictions of the full line shape for $n$-photon ionization and third-harmonic light generation near three-photon resonance, including the rather strong influences of positively dispersive buffer gases. We also show that the cancellation between the one-photon and the three-photon process is partially spoiled in the presence of a counterpropagating beam at the same frequency.

Physical Review A•Dec 1, 1983•72 citations

Coherence in multistate resonance-enhanced four-photon ionization of lithium atoms

Michael Schuricke, Klaus Bartschat, Alexei N. Grum-Grzhimailo +5 more

A joint experimental and theoretical study of four-photon ionization of Li is performed using a pump-probe setup with the laser frequency tuned in between the excitation energies of the $2s$--$4p$ and $2s$--$4f$ three-photon transitions. The three-dimensional photoelectron momentum pattern is recorded as a function of the delay time between two otherwise identical laser pulses. The process is modeled by numerically solving the time-dependent Schr\"odinger equation. While complicated interference patterns arise in the electron spectrum when the two pulses partially overlap in time, the expected quantum-beat phenomenon between Li atoms in either the $4p$ or the $4f$ state are seen when the fast oscillations involving the $2s$ initial state are averaged over. The qualitative agreement between the predicted and observed beating patterns is very good.

Physical Review A•Aug 30, 2013•15 citations

Resonance excitation and ionization in short-pulse laser-atom interaction

Mark Edwards

It has been widely believed that short-pulse multiphoton ionization is dominated by a resonance process: excited states of the atom are shifted by the radiation field into multiphoton resonance with the ground state, are populated, and then rapidly ionized. A recent experiment, shows significant population remaining in excited states at the end of the laser pulse, and this result has been interpreted as indicating that ionization proceeds slowly out of these states. We investigate this issue in the framework of Floquet theory, supplemented by direct numerical solution of the time-dependent Schrodinger equation. In this framework, the standard picture is portrayed as an adiabatic transition between Floquet eigenstates, which occurs as the amplitude of the laser field is ramped through the resonance value (i.e. through an avoided crossing of Floquet quasienergies). Thus it follows that the same type of transition must occur as the field is turned off. This mechanism can yield significant populations of excited states that do not suffer appreciable ionization. We exhibit this effect by numerical studies of a model atom with two bound states and two continua.

Bulletin of the American Physical Society•May 1, 1993•0 citations
We have solved the time-dependent Schr"odinger equation for a one-dimensional model atom exposed to a spatially homogeneous laser field that is turned on smoothly. We have studied the ionization of this "atom" at a laser frequency close to a three-photon resonance and have found a spike on top of each of the above-threshold peaks of the ionization signal, in accordance with the findings of a recent experimental investigation.
The resonantly enhanced multiphoton ionization of atomic hydrogen is studied for the case of four-photon ionization (three-photon resonant). The time-dependent probabilities, the shape of the resonance profile at different intensities, and the nonlinear index are computed for coherent light at frequencies around the resonance (365 nm). The systematic dependence of the cross section as a function of the principal quantum number of the resonant state (as this tends towards the Rydberg states) is investigated at zero detuning. The probabilities of absorption of one photon more than necessary for the four-photon ionization process (resonantly enhanced above-threshold ionization) is computed and the relevant branching ratios are examined. Then it is shown that the effect of the spatio-temporal structures of the laser pulse is to red shift the maximum of the resonance profile, whereas that of an ideal chaotic light is to blue shift and broaden the resonance peak. The shape, shift, and width of the profile resulting from both these effects are in very fair agreement with the experimental ones.
We have measured the resonance-enhanced four-photon ionization of atomic hydrogen. The degenerate four-photon process occurs via a three-photon resonance between the 1s and the 2p levels, with subsequent one-photon ionization near threshold. We have studied the highly asymmetric resonance-enhanced profile, i.e., the photoion yield as a function of laser detuning from three-photon resonance between the 1s and 2p levels. In particular, we have determined the width, shift, peak, and asymmetry of the profile as a function of laser intensity. The experimental results are compared to theoretical models. These models involve both the properties of the atom in an intense near-resonant radiative field, and a detailed model for the multimode laser field, particularly the field fluctuations due to mode beating. The asymmetric resonance-enhanced photoionization profile is well reproduced by both a random-phase and a chaotic-light model.
This paper studies the multiphoton resonant ionization by two-colour laser pulses in the hydrogen atom by solving the time-dependent Schrodinger equation. By fixing the parameters of fundamental laser field and scanning the frequency of second laser field, it finds that the ionization probability shows several resonance peaks and is also much larger than the linear superposition of probabilities by applying two lasers separately. The enhancement of the ionization happens when the system is resonantly pumped to the excited states by absorbing two or more colour photons non-sequentially.
Multiphoton ionization in the region near a three-photon resonance is treated for focused, plane-polarized Gaussian beams with diffraction-limited beam divergence. In this situation, a third-harmonic field is generated within the laser beam. At, and very near, three-photon resonance the driving rate for the upper-state probability amplitude due to one-photon absorption of third-harmonic light becomes nearly equal to the corresponding three-photon rate due to the laser field, but these effects are 180\ifmmode^\circ\else\textdegree\fi{} out of phase. As a consequence of this cancellation between two pumping terms, the three-photon resonance line essentially disappears at moderate concentrations and the observed ionization has a line shape that is close to the phase-matching curve for third-harmonic generation. The ionization signal, near but not on the resonance, is due almost entirely to absorption of third-harmonic photons plus other laser photons; three-photon resonantly enhanced multiphoton ionization by the laser is much weaker. This is particularly true on the blue side of the three-photon resonance at detunings where phase matching occurs. The problem is treated quite generally with predictions of the full line shape for nnn-photon ionization and third-harmonic light generation near three-photon resonance, including the rather strong influences of positively dispersive buffer gases. We also show that the cancellation between the one-photon and the three-photon process is partially spoiled in the presence of a counterpropagating beam at the same frequency.
A joint experimental and theoretical study of four-photon ionization of Li is performed using a pump-probe setup with the laser frequency tuned in between the excitation energies of the 2s2s2s--4p4p4p and 2s2s2s--4f4f4f three-photon transitions. The three-dimensional photoelectron momentum pattern is recorded as a function of the delay time between two otherwise identical laser pulses. The process is modeled by numerically solving the time-dependent Schr\"odinger equation. While complicated interference patterns arise in the electron spectrum when the two pulses partially overlap in time, the expected quantum-beat phenomenon between Li atoms in either the 4p4p4p or the 4f4f4f state are seen when the fast oscillations involving the 2s2s2s initial state are averaged over. The qualitative agreement between the predicted and observed beating patterns is very good.
It has been widely believed that short-pulse multiphoton ionization is dominated by a resonance process: excited states of the atom are shifted by the radiation field into multiphoton resonance with the ground state, are populated, and then rapidly ionized. A recent experiment, shows significant population remaining in excited states at the end of the laser pulse, and this result has been interpreted as indicating that ionization proceeds slowly out of these states. We investigate this issue in the framework of Floquet theory, supplemented by direct numerical solution of the time-dependent Schrodinger equation. In this framework, the standard picture is portrayed as an adiabatic transition between Floquet eigenstates, which occurs as the amplitude of the laser field is ramped through the resonance value (i.e. through an avoided crossing of Floquet quasienergies). Thus it follows that the same type of transition must occur as the field is turned off. This mechanism can yield significant populations of excited states that do not suffer appreciable ionization. We exhibit this effect by numerical studies of a model atom with two bound states and two continua.