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:2410.01601 · Physical Review A

Measurement of ionization delays in atomic resonance-enhanced multiphoton ionization using photoelectron vortices

D. Köhnke, Tim Bayer, M. Wollenhaupt

Published Dec 16, 2024• 4 citations
arXivHTMLPDF

Abstract

We study time delays in atomic multiphoton ionization (MPI) using the phase-sensitive detection of photoelectron vortices. Photoelectron vortices are created by MPI with counterrotating circularly polarized (CRCP) ultrashort double-pulse sequences. The vortices are characterized by a spiral-shaped photoelectron momentum distribution (PMD) resulting from the Ramsey-type interference of the partial photoelectron wave packets created by each pulse. The slope of the spiral arms encodes the time delay between the partial wave packets with interferometric precision. We study the ionization time delay in the $1+2$ resonance-enhanced multiphoton ionization of potassium atoms using femtosecond CRCP white-light supercontinuum pulses. Pairwise interference of the partial wave packets with a reference wave packet gives rise to vortices of different rotational symmetry, which are superimposed to form the total PMD. The PMD is reconstructed tomographically and decomposed into the vortices using three-dimensional Fourier analysis. From the energy-dependent spectral phases of the vortices, we retrieve a resonant ionization delay on the order of 1 fs, much shorter than the pulse duration. Our results demonstrate the power of photoelectron vortices for the accurate determination of photoionization time delays and open up new perspectives for photoelectron chronoscopy including the measurement of ionization delays on the attosecond timescale.

DOI
10.1103/physreva.110.063111

Related papers

Three-dimensional photoelectron holography with trichromatic polarization-tailored laser pulses

D. Köhnke, Kevin Eickhoff, Tim Bayer +1 more

Abstract We present a three-dimensional (3D) photoelectron wave packet holography scheme based on polarization-tailored trichromatic femtosecond laser pulses for the determination of quantum phases in atomic multiphoton ionization (MPI). Experimentally, we combine supercontinuum polarization pulse shaping with photoelectron tomography for the reconstruction of the 3D photoelectron momentum distribution (PMD). To demonstrate the 3D photoelectron holography scheme, we superimpose a sculptured wave packet encoding a relative continuum phase with a reference wave packet. In particular, we create a sculptured angular momentum superposition wave packet by (2 + 1) resonance-enhanced MPI of potassium atoms using a counter-rotating circularly polarized bichromatic pulse sequence. The sculptured wave packet, consisting of states with different orbital angular momentum quantum numbers, interferes with the reference wave packet generated by direct three-photon ionization with a circularly polarized pulse of the third color. Depending on the circularity of the reference pulse, interference of both wave packets gives rise to 3D photoelectron holograms with c 2 or c 4 rotational symmetry in the laser polarization plane, i.e., in the azimuthal direction. In the polar direction, the azimuthal interference pattern undergoes a phase-shift revealing the relative quantum phase between the p- and f-type continuum partial waves in the sculptured wave packet. We determine the relative continuum phase by fitting the parameters of an analytical model of the hologram to the measured 3D PMD and confirm the result by direct extraction of the continuum phase difference from the polar-angle-dependent azimuthal phase-shift of the photoelectron angular distribution.

Journal of Physics B Atomic Molecular and Optical Physics•Jul 26, 2022•8 citations

Determination of atomic multiphoton-ionization phases by trichromatic multichannel wave-packet interferometry

Kevin Eickhoff, D. Köhnke, Lea Feld +2 more

We present the unambiguous determination of quantum phases in the multiphoton ionization (MPI) of potassium atoms by using a multichannel photoelectron interferometry scheme based on trichromatic pulse shaping. The colors of the laser field are chosen to produce three energetically separated photoelectron interferograms in the continuum. While the red pulse is two-photon resonant with the $3d$ state resulting in a $(2+1)$ resonance-enhanced MPI (REMPI), a $(1+2)$ REMPI occurs via the nonresonant intermediate $4p$ state with an initial green or blue pulse. We show that ionization via a nonresonant intermediate state lifts the degeneracy of photoelectron interferograms from pathways consisting of permutations of the colors. The analysis of the interferograms reveals a phase shift of $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$ depending on the sign of the detunings in the $(1+2)$ REMPI pathways. In addition, we demonstrate that the photoionization time delay in the resonant $(2+1)$ REMPI pathway gives rise to a linear spectral phase in the photoelectron spectra. Insights into the underlying MPI processes are gained through an analytic perturbative description and numerical simulations of a trichromatic driven three-level system coupled to the continuum.

arXiv:2203.00323•Physical Review A•May 16, 2022•9 citations

Molecular Free Electron Vortices in Photoionization by Polarization-Tailored Ultrashort Laser Pulses

Tim Bayer, M. Wollenhaupt

Atomic and molecular free electron vortices (FEVs), characterized by their spiral-shaped momentum distribution, have recently attracted a great deal of attention due to their varied shapes and their unusual topological properties. Shortly after their theoretical prediction by the single-photon ionization (SPI) of He atoms using pairs of counterrotating circularly polarized attosecond pulses, FEVs have been demonstrated experimentally by the multiphoton ionization (MPI) of alkali atoms using single-color and bichromatic circularly polarized femtosecond pulse sequences. Recently, we reported on the analysis of the experimental results employing a numerical model based on the ab initio solution of the time-dependent Schrödinger equation (TDSE) for a two-dimensional (2D) atom interacting with a polarization-shaped ultrashort laser field. Here, we apply the 2D TDSE model to study molecular FEVs created by SPI and MPI of a diatomic molecule using polarization-tailored single-color and bichromatic femtosecond pulse sequences. We investigate the influence of the coupled electron-nuclear dynamics on the vortex formation dynamics and discuss the effect of CEP- and rotational averaging on the photoelectron momentum distribution. By analyzing how the molecular structure and dynamics is imprinted in the photoelectron spirals, we explore the potential of molecular FEVs for ultrafast spectroscopy.

Frontiers in Chemistry•Jun 2, 2022•10 citations

Signatures beyond the rotating-wave approximation in retrieving the photoionization time delay from an ω−2ω interferometric method

Mingqing Liu, Xinqiang Wang, Lijuan Jia +2 more

We propose a protocol to retrieve the photoionization time delay that employs a pair of oppositely circularly polarized attosecond extreme ultraviolet pulses with frequencies $\ensuremath{\omega}$ and $2\ensuremath{\omega}$. By numerically solving the three-dimensional time-dependent Schr\"odinger equation, we observe an oscillation in the energy-resolved photoionization time delay encoded in the relative optical phase between $\ensuremath{\omega}$ and $2\ensuremath{\omega}$ pulses when the emission asymmetry of the photoelectron is maximal. Our results show that this oscillation arises from the interference between two one-photon ionization pathways from the ground state due to the broad bandwidth effect of an ultrashort pulse: the absorption of one left-handed circularly polarized photon and the emission of one right-handed circularly polarized photon. The latter is regarded as a consequence of the breakdown of the rotating-wave approximation (RWA). We compare the perturbation theory with and without RWA and demonstrate that photon emission plays a crucial role in retrieving photoionization time delay. Our study enriches the underlying physics of attosecond spectroscopy and provides a framework for accurately measuring photoionization time delays in atoms and molecules.

Physical Review A•Jul 7, 2023•8 citations

Coherent control of electron-ion entanglement in multiphoton ionization

Yi-Jia Mao, Zhaohan Zhang, Yang Li +3 more

Quantitative control and measurement of quantum entanglement are essential for advancing quantum technologies. Photoionization induced by ultrashort laser pulses provides a unique platform for studying entanglement between photoelectrons and residual ions, representing one of the most intriguing quantum phenomena in attosecond physics. Although extensive studies have focused on the coherence properties within either the emitted electrons or the ions individually, the electron-ion entanglement has remained largely unexplored. In this work, we bridge this gap by investigating the resonance-enhanced multiphoton ionization of argon atoms driven by two time-delayed ultrashort ultraviolet pulses. Employing state-of-the-art first-principles multi-electron simulations, we demonstrate the ability to reconstruct and precisely manipulate the purity of electron quantum states through detailed analysis of the photoelectron angular distributions. Our results reveal distinct scattering-phase differences among various electron configurations within the same partial wave channel, providing unequivocal evidence of electron-ion correlation and entanglement. With the fast development of free-electron lasers, this study establishes an experimentally feasible framework for directly controlling quantum entanglement in ultrafast ionization processes, offering new insights and powerful methodologies for exploring complex electron dynamics in many-electron systems.

Light Science & Applications•Mar 6, 2026•1 citation

Amplitude and Phase Reconstruction of Electron Wave Packets for Probing Ultrafast Photoionization Dynamics

Kyung Taec Kim, Dong Hyuk Ko, Juyun Park +5 more

Ultrafast atomic processes, such as excitation and ionization occurring on the femtosecond or shorter time scale, were explored by employing attosecond high-harmonic pulses. With the absorption of a suitable high-harmonic photon a He atom was ionized, or resonantly excited with further ionization by absorbing a number of infrared photons. The electron wave packets liberated by the two processes generated an interference containing the information on ultrafast atomic dynamics. The attosecond electron wave packet, including the phase, from the ground state was reconstructed first and, subsequently, that from the 1s3p state was retrieved by applying the holographic technique to the photoelectron spectra comprising the interference between the two ionization paths. The reconstructed electron wave packet revealed details of the ultrafast photoionization dynamics, such as the instantaneous two-photon ionization rate.

Physical Review Letters•Feb 29, 2012•22 citations
We study time delays in atomic multiphoton ionization (MPI) using the phase-sensitive detection of photoelectron vortices. Photoelectron vortices are created by MPI with counterrotating circularly polarized (CRCP) ultrashort double-pulse sequences. The vortices are characterized by a spiral-shaped photoelectron momentum distribution (PMD) resulting from the Ramsey-type interference of the partial photoelectron wave packets created by each pulse. The slope of the spiral arms encodes the time delay between the partial wave packets with interferometric precision. We study the ionization time delay in the 1+21+21+2 resonance-enhanced multiphoton ionization of potassium atoms using femtosecond CRCP white-light supercontinuum pulses. Pairwise interference of the partial wave packets with a reference wave packet gives rise to vortices of different rotational symmetry, which are superimposed to form the total PMD. The PMD is reconstructed tomographically and decomposed into the vortices using three-dimensional Fourier analysis. From the energy-dependent spectral phases of the vortices, we retrieve a resonant ionization delay on the order of 1 fs, much shorter than the pulse duration. Our results demonstrate the power of photoelectron vortices for the accurate determination of photoionization time delays and open up new perspectives for photoelectron chronoscopy including the measurement of ionization delays on the attosecond timescale.
Abstract We present a three-dimensional (3D) photoelectron wave packet holography scheme based on polarization-tailored trichromatic femtosecond laser pulses for the determination of quantum phases in atomic multiphoton ionization (MPI). Experimentally, we combine supercontinuum polarization pulse shaping with photoelectron tomography for the reconstruction of the 3D photoelectron momentum distribution (PMD). To demonstrate the 3D photoelectron holography scheme, we superimpose a sculptured wave packet encoding a relative continuum phase with a reference wave packet. In particular, we create a sculptured angular momentum superposition wave packet by (2 + 1) resonance-enhanced MPI of potassium atoms using a counter-rotating circularly polarized bichromatic pulse sequence. The sculptured wave packet, consisting of states with different orbital angular momentum quantum numbers, interferes with the reference wave packet generated by direct three-photon ionization with a circularly polarized pulse of the third color. Depending on the circularity of the reference pulse, interference of both wave packets gives rise to 3D photoelectron holograms with c 2 or c 4 rotational symmetry in the laser polarization plane, i.e., in the azimuthal direction. In the polar direction, the azimuthal interference pattern undergoes a phase-shift revealing the relative quantum phase between the p- and f-type continuum partial waves in the sculptured wave packet. We determine the relative continuum phase by fitting the parameters of an analytical model of the hologram to the measured 3D PMD and confirm the result by direct extraction of the continuum phase difference from the polar-angle-dependent azimuthal phase-shift of the photoelectron angular distribution.
We present the unambiguous determination of quantum phases in the multiphoton ionization (MPI) of potassium atoms by using a multichannel photoelectron interferometry scheme based on trichromatic pulse shaping. The colors of the laser field are chosen to produce three energetically separated photoelectron interferograms in the continuum. While the red pulse is two-photon resonant with the 3d3d3d state resulting in a (2+1)(2+1)(2+1) resonance-enhanced MPI (REMPI), a (1+2)(1+2)(1+2) REMPI occurs via the nonresonant intermediate 4p4p4p state with an initial green or blue pulse. We show that ionization via a nonresonant intermediate state lifts the degeneracy of photoelectron interferograms from pathways consisting of permutations of the colors. The analysis of the interferograms reveals a phase shift of $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$ depending on the sign of the detunings in the (1+2)(1+2)(1+2) REMPI pathways. In addition, we demonstrate that the photoionization time delay in the resonant (2+1)(2+1)(2+1) REMPI pathway gives rise to a linear spectral phase in the photoelectron spectra. Insights into the underlying MPI processes are gained through an analytic perturbative description and numerical simulations of a trichromatic driven three-level system coupled to the continuum.
Atomic and molecular free electron vortices (FEVs), characterized by their spiral-shaped momentum distribution, have recently attracted a great deal of attention due to their varied shapes and their unusual topological properties. Shortly after their theoretical prediction by the single-photon ionization (SPI) of He atoms using pairs of counterrotating circularly polarized attosecond pulses, FEVs have been demonstrated experimentally by the multiphoton ionization (MPI) of alkali atoms using single-color and bichromatic circularly polarized femtosecond pulse sequences. Recently, we reported on the analysis of the experimental results employing a numerical model based on the ab initio solution of the time-dependent Schrödinger equation (TDSE) for a two-dimensional (2D) atom interacting with a polarization-shaped ultrashort laser field. Here, we apply the 2D TDSE model to study molecular FEVs created by SPI and MPI of a diatomic molecule using polarization-tailored single-color and bichromatic femtosecond pulse sequences. We investigate the influence of the coupled electron-nuclear dynamics on the vortex formation dynamics and discuss the effect of CEP- and rotational averaging on the photoelectron momentum distribution. By analyzing how the molecular structure and dynamics is imprinted in the photoelectron spirals, we explore the potential of molecular FEVs for ultrafast spectroscopy.
We propose a protocol to retrieve the photoionization time delay that employs a pair of oppositely circularly polarized attosecond extreme ultraviolet pulses with frequencies $\ensuremath{\omega}$ and $2\ensuremath{\omega}$. By numerically solving the three-dimensional time-dependent Schr\"odinger equation, we observe an oscillation in the energy-resolved photoionization time delay encoded in the relative optical phase between $\ensuremath{\omega}$ and $2\ensuremath{\omega}$ pulses when the emission asymmetry of the photoelectron is maximal. Our results show that this oscillation arises from the interference between two one-photon ionization pathways from the ground state due to the broad bandwidth effect of an ultrashort pulse: the absorption of one left-handed circularly polarized photon and the emission of one right-handed circularly polarized photon. The latter is regarded as a consequence of the breakdown of the rotating-wave approximation (RWA). We compare the perturbation theory with and without RWA and demonstrate that photon emission plays a crucial role in retrieving photoionization time delay. Our study enriches the underlying physics of attosecond spectroscopy and provides a framework for accurately measuring photoionization time delays in atoms and molecules.
Quantitative control and measurement of quantum entanglement are essential for advancing quantum technologies. Photoionization induced by ultrashort laser pulses provides a unique platform for studying entanglement between photoelectrons and residual ions, representing one of the most intriguing quantum phenomena in attosecond physics. Although extensive studies have focused on the coherence properties within either the emitted electrons or the ions individually, the electron-ion entanglement has remained largely unexplored. In this work, we bridge this gap by investigating the resonance-enhanced multiphoton ionization of argon atoms driven by two time-delayed ultrashort ultraviolet pulses. Employing state-of-the-art first-principles multi-electron simulations, we demonstrate the ability to reconstruct and precisely manipulate the purity of electron quantum states through detailed analysis of the photoelectron angular distributions. Our results reveal distinct scattering-phase differences among various electron configurations within the same partial wave channel, providing unequivocal evidence of electron-ion correlation and entanglement. With the fast development of free-electron lasers, this study establishes an experimentally feasible framework for directly controlling quantum entanglement in ultrafast ionization processes, offering new insights and powerful methodologies for exploring complex electron dynamics in many-electron systems.
Ultrafast atomic processes, such as excitation and ionization occurring on the femtosecond or shorter time scale, were explored by employing attosecond high-harmonic pulses. With the absorption of a suitable high-harmonic photon a He atom was ionized, or resonantly excited with further ionization by absorbing a number of infrared photons. The electron wave packets liberated by the two processes generated an interference containing the information on ultrafast atomic dynamics. The attosecond electron wave packet, including the phase, from the ground state was reconstructed first and, subsequently, that from the 1s3p state was retrieved by applying the holographic technique to the photoelectron spectra comprising the interference between the two ionization paths. The reconstructed electron wave packet revealed details of the ultrafast photoionization dynamics, such as the instantaneous two-photon ionization rate.