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

Chinese Physics Letters

The Two-Photon Nondipole Transition Phases Across the Cooper Minima and Resonant States

Baichao Liu, Yongkun Chen, Chunyang Zhai, Qiming Zhao, J. S. Li, Pu Wang, Jingkun Xu, Qingbin Tang, Yingbin Li, Benhai Yu, Yufang Liu

Published Mar 9, 2026• 0 citations
Publisher

Abstract

Abstract Beyond the widely adopted dipole approximation, nondipole effects play an important role in completely understanding the electronic dynamics in light–matter interaction. We present a two-photon interferometric scheme to theoretically study the under-threshold nondipole transition phase over a broad energy range. It is found a significant difference between the nondipole and dipole two-photon transition phases near the Cooper minimum, which originates from the multichannel interference in the nondipole transition. Through the angular dependence of transition phase, we uncover the competition among partial waves in nondipole ionization. This work advances the fundamental understanding of nondipole dynamics in two-photon ionization, and opens a route toward the complete reconstruction of nondipole photoelectron wave packets.

DOI
10.1088/0256-307x/43/4/040301

Related papers

Time-dependent perturbation theory beyond the dipole approximation for two-photon ionization of atoms

M. Wang, H Liang, X Xiao +2 more

Synopsis We develop a time-dependent perturbation theory beyond the dipole approximation to analyze the two-photon ionization dynamics of atoms exposed to short laser pulses with an arbitrary polarization. Subse-quent applications of the PT method in the nonresonant regime allow us to analyze one of the most important nondipole effects, i.e., the linear-momentum-transfer law in the two-photon ionization process and to unveil the important role of the interferences between the dipole and nondipole transition pathways to the photoelectron momentum shift along the laser-propagation direction.

Journal of Physics Conference Series•Jan 1, 2020•0 citations

Time-dependent perturbation theory beyond the dipole approximation for two-photon ionization of atoms

Mu-Xue Wang, Hao Liang, Xiang-Ru Xiao +2 more

We develop a time-dependent perturbation theory (PT) beyond the dipole approximation to analyze the two-photon ionization dynamics of atoms exposed to short laser pulses with an arbitrary polarization. In a wide range of laser parameters, the good performance of the PT method is validated by comparing the results of a number of physical quantities with those calculated by numerically solving the time-dependent Schr\"odinger equation beyond the dipole approximation. Subsequent applications of the PT method in the nonresonant regime allow us to unveil the important role of the interferences between the dipole and nondipole transition pathways to the photoelectron momentum shift along the laser-propagation direction. In particular, we find that the ratio of the probability of each dipole transition channel to the total ionization probability oscillates with the increase of the photon energy. The interferences among different pathways and the oscillatory behavior of the ratios jointly lead to a series of minima in the linear momentum transfer for the case of the linear polarization.

Physical Review A•Feb 5, 2019•8 citations

Nondipole effects in the angular distribution of photoelectrons in two-photon two-color above-threshold atomic ionization

Alexei N. Grum-Grzhimailo, Грызлова Елена Владимировна

Expressions for the angular distribution of photoelectrons produced in two-photon two-color atomic ionization are obtained within the statistical tensor formalism, taking into account a full multipole expansion of the radiation in electric and magnetic moments. The general expressions are reduced to a simpler form for a particular geometry used in experiments with XUV + optical radiation beams and analyzed within the first-order nondipole corrections for different polarization states of the photons. As a numerical example, the Ne $1s$ above-threshold ionization by two-color radiation is considered within the second-order perturbation theory. A large forward-backward asymmetry in the photoelectron angular distribution is predicted.

Physical Review A•Apr 23, 2014•22 citations

Characterization of the two-photon transition phase in the buildup process of Rabi oscillations

Xu Zhang, Yijie Liao, Yongkun Chen +4 more

We achieve the complete characterization of the transition phase in the resonant two-photon ionization (TPI) of hydrogen at the high laser intensity where Rabi oscillation occurs. Different from previous studies which focused on the transition phase of resonant TPI in the perturbation region, in our work, we reveal the effect of Rabi oscillations on the transition phase in the high-intensity region. With bichromatic extreme-ultraviolet light, the transition phases of the $S$ and $D$ partial waves are decoded. By solving the time-dependent Schrodinger equation, we show that the transition phase depends on not only the pulse duration but also the laser intensity. This dependence is traced back to the modification of the atomic state structure, rather than the competition between resonant and nonresonant ionization paths at the lower laser intensity. Our work provides a way to manipulate the two-photon transition phase through laser intensity.

Physical Review A•Mar 1, 2024•10 citations

Transition dynamics in two-photon ionisation

Morgane Vacher, Romain Gaillac, A. Maquet +2 more

Abstract We review various aspects of photoemission dynamics in the case of two-photon ionisation. We first recall the definition of a transition phase specific to two-photon transitions. Numerical experiments on model atoms are used to show how the group delay associated with the transition phase is actually representative of the early dynamics of the detected photoelectron wave packets. Then we address the question of measuring these transition delays using a standard interferometric technique of experimental attosecond physics, so-called rabbit . Finally, we outline different reinterpretations of rabbit giving access to the more fundamental scattering dynamics affecting any photoemission processes.

Journal of Optics•Sep 27, 2017•14 citations

Electronic coherences in argon through interfering one- and two-photon ionization processes in the vicinity of Feshbach resonances

Roger Y. Bello, Vicent J. Borràs, Jesús González‐Vázquez +1 more

The role of Rydberg autoionizing states in interfering one- and two-photon ionization paths is theoretically investigated in atomic Ar. The angularly resolved photoionization cross sections for each individual path is provided. By varying the relative optical phase between the two pulses the phase difference between the two interfering paths is extracted. The retrieved phase difference and the photoelectron angular distributions exhibit a strong dependence on the photon energy in the vicinity of the resonant states. In contrast to previous results obtained in atomic Ne, the phase difference features a smooth dependence with photoelectron emission angle.

Physical Review Research•Oct 14, 2022•11 citations
Abstract Beyond the widely adopted dipole approximation, nondipole effects play an important role in completely understanding the electronic dynamics in light–matter interaction. We present a two-photon interferometric scheme to theoretically study the under-threshold nondipole transition phase over a broad energy range. It is found a significant difference between the nondipole and dipole two-photon transition phases near the Cooper minimum, which originates from the multichannel interference in the nondipole transition. Through the angular dependence of transition phase, we uncover the competition among partial waves in nondipole ionization. This work advances the fundamental understanding of nondipole dynamics in two-photon ionization, and opens a route toward the complete reconstruction of nondipole photoelectron wave packets.
Synopsis We develop a time-dependent perturbation theory beyond the dipole approximation to analyze the two-photon ionization dynamics of atoms exposed to short laser pulses with an arbitrary polarization. Subse-quent applications of the PT method in the nonresonant regime allow us to analyze one of the most important nondipole effects, i.e., the linear-momentum-transfer law in the two-photon ionization process and to unveil the important role of the interferences between the dipole and nondipole transition pathways to the photoelectron momentum shift along the laser-propagation direction.
We develop a time-dependent perturbation theory (PT) beyond the dipole approximation to analyze the two-photon ionization dynamics of atoms exposed to short laser pulses with an arbitrary polarization. In a wide range of laser parameters, the good performance of the PT method is validated by comparing the results of a number of physical quantities with those calculated by numerically solving the time-dependent Schr\"odinger equation beyond the dipole approximation. Subsequent applications of the PT method in the nonresonant regime allow us to unveil the important role of the interferences between the dipole and nondipole transition pathways to the photoelectron momentum shift along the laser-propagation direction. In particular, we find that the ratio of the probability of each dipole transition channel to the total ionization probability oscillates with the increase of the photon energy. The interferences among different pathways and the oscillatory behavior of the ratios jointly lead to a series of minima in the linear momentum transfer for the case of the linear polarization.
Expressions for the angular distribution of photoelectrons produced in two-photon two-color atomic ionization are obtained within the statistical tensor formalism, taking into account a full multipole expansion of the radiation in electric and magnetic moments. The general expressions are reduced to a simpler form for a particular geometry used in experiments with XUV + optical radiation beams and analyzed within the first-order nondipole corrections for different polarization states of the photons. As a numerical example, the Ne 1s1s1s above-threshold ionization by two-color radiation is considered within the second-order perturbation theory. A large forward-backward asymmetry in the photoelectron angular distribution is predicted.
We achieve the complete characterization of the transition phase in the resonant two-photon ionization (TPI) of hydrogen at the high laser intensity where Rabi oscillation occurs. Different from previous studies which focused on the transition phase of resonant TPI in the perturbation region, in our work, we reveal the effect of Rabi oscillations on the transition phase in the high-intensity region. With bichromatic extreme-ultraviolet light, the transition phases of the SSS and DDD partial waves are decoded. By solving the time-dependent Schrodinger equation, we show that the transition phase depends on not only the pulse duration but also the laser intensity. This dependence is traced back to the modification of the atomic state structure, rather than the competition between resonant and nonresonant ionization paths at the lower laser intensity. Our work provides a way to manipulate the two-photon transition phase through laser intensity.
Abstract We review various aspects of photoemission dynamics in the case of two-photon ionisation. We first recall the definition of a transition phase specific to two-photon transitions. Numerical experiments on model atoms are used to show how the group delay associated with the transition phase is actually representative of the early dynamics of the detected photoelectron wave packets. Then we address the question of measuring these transition delays using a standard interferometric technique of experimental attosecond physics, so-called rabbit . Finally, we outline different reinterpretations of rabbit giving access to the more fundamental scattering dynamics affecting any photoemission processes.
The role of Rydberg autoionizing states in interfering one- and two-photon ionization paths is theoretically investigated in atomic Ar. The angularly resolved photoionization cross sections for each individual path is provided. By varying the relative optical phase between the two pulses the phase difference between the two interfering paths is extracted. The retrieved phase difference and the photoelectron angular distributions exhibit a strong dependence on the photon energy in the vicinity of the resonant states. In contrast to previous results obtained in atomic Ne, the phase difference features a smooth dependence with photoelectron emission angle.