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

Unveiling Rabi dynamics through angle-resolved photoelectron momentum distributions using an ω−2ω pulse pair

Yi-Jia Mao, Hongbin Yao, Mingrui He, Zhaohan Zhang, Yang Li, Feng He

Published Nov 22, 2023• 16 citations
Publisher

Abstract

We present an interferometric method for studying the Rabi dynamics in atoms by employing an $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ extreme ultraviolet pulse pair generated from the seeded free-electron laser. By solving the time-dependent Schr\"odinger equation (TDSE) for hydrogen atoms, we study the photoelectron spectrum that emerges when the $\ensuremath{\omega}$ pulse triggers Rabi oscillations between the ground state and the first excited state. The interference between the one-photon and two-photon ionization pathways in the photoelectron signal gives access to the phase difference between the one- and two-photon transition amplitudes. Compared to the cases without Rabi oscillations, an additional $\ensuremath{\pi}$ phase jump is observed in the energy domain. Based on perturbation theory, we demonstrate that this phase jump directly reflects the ultrafast buildup of Rabi oscillations in the time domain. The present $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ scheme can be generalized and applied to other more complex atoms or molecules provided that the populations of bound states can be efficiently and coherently modulated using the free-electron laser.

DOI
10.1103/physreva.108.053117

Related papers

Observation of Rabi dynamics with a short-wavelength free-electron laser

Saikat Nandi, Edvin Olofsson, Mattias Bertolino +26 more

Abstract Rabi oscillations are periodic modulations of populations in two-level systems interacting with a time-varying field1. They are ubiquitous in physics with applications in different areas such as photonics2, nano-electronics3, electron microscopy4 and quantum information5. While the theory developed by Rabi was intended for fermions in gyrating magnetic fields, Autler and Townes realized that it could also be used to describe coherent light–matter interactions within the rotating-wave approximation6. Although intense nanometre-wavelength light sources have been available for more than a decade7–9, Rabi dynamics at such short wavelengths has not been directly observed. Here we show that femtosecond extreme-ultraviolet pulses from a seeded free-electron laser10 can drive Rabi dynamics between the ground state and an excited state in helium atoms. The measured photoelectron signal reveals an Autler–Townes doublet and an avoided crossing, phenomena that are both fundamental to coherent atom–field interactions11. Using an analytical model derived from perturbation theory on top of the Rabi model, we find that the ultrafast build-up of the doublet structure carries the signature of a quantum interference effect between resonant and non-resonant photoionization pathways. Given the recent availability of intense attosecond12 and few-femtosecond13 extreme-ultraviolet pulses, our results unfold opportunities to carry out ultrafast manipulation of coherent processes at short wavelengths using free-electron lasers.

Nature•Aug 17, 2022•106 citations

Studying ultrafast Rabi dynamics with a short-wavelength seeded free-electron laser

Saikat Nandi, Edvin Olofsson, Mattias Bertolino +26 more

Rabi oscillations are periodic modulations of populations in two-level systems interacting with a time-varying field. They are ubiquitous in physics with applications in different areas such as photonics, nano-electronics, electron microscopy, and quantum information. While the theory developed by Rabi was intended for fermions in gyrating magnetic fields, Autler and Townes realized that it could also be used to describe coherent light-matter interaction within the rotating wave approximation\cite. Although intense nanometer-wavelength light-sources have been available for more than a decade, Rabi dynamics at such short wavelengths have not been observed directly. Here we show that femtosecond extreme-ultraviolet pulses from a seeded free-electron laser can drive Rabi oscillations between the ground state and an excited state in helium atoms. The measured photoemission signal revealed an Autler-Townes doublet as well as an avoided crossing, phenomena that are both trademarks of quantum optics. Using theoretical analyses that go beyond the strong-field approximation, we found that the ultrafast build-up of the doublet structure follows from a quantum interference effect between resonant and non-resonant photoionization pathways. Given the recent availability of intense attosecond and few-femtosecond extreme-ultraviolet pulses, our results offer opportunities to carry out ultrafast manipulation of coherent processes at short wavelengths using free-electron lasers.

arXiv:2201.10950•Jan 26, 2022•0 citations

Photoelectron Signatures of Nonperturbative Dynamics in Resonant Two-Photon Ionization of Helium

Edvin Olofsson, Jan Marcus Dahlström

When an atom is driven by a laser field with a photon energy that is nearly resonant with an atomic transition, it can undergo periodic population transfers between the ground and excited state, known as Rabi oscillations [1], [2]. The aim of this work is to study photoionization from atoms for parameters accessible to a free-electron laser (FEL) [3]. Using time dependent perturbation theory to model photoionization from a Rabi oscillating atom, we have shown that in addition to the expected pathway of ionization from the excited state, non-resonant two-photon ionization will have a comparable amplitude at intensities on the order of 1013W/cm2[3].

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 26, 2023•0 citations

Quantum control of Rabi dynamics using chirped extreme ultraviolet pulses

Dongyang He, Boren Shen, Yi-Jia Mao +4 more

Abstract We present a theoretical study on the quantum control of ultrafast Rabi dynamics in atoms driven by chirped extreme ultraviolet (XUV) pulses. Motivated by recent experimental advances using free-electron lasers, we derive an analytical solution of the Rabi oscillation under the rotating wave approximation, incorporating the spectral chirp of the XUV field. Within the essential-states model, we demonstrate how the chirp modulates the phase of the excited-state amplitude, inducing an observable asymmetry in the Autler–Townes (AT) doublets of the photoelectrons. Our theoretical predictions, benchmarked against time-dependent Schrödinger equation simulations, reveal that chirp-dependent phase modulation governs the spectral asymmetry, offering a time-domain perspective for interpreting strong-field photoionization at short wavelengths. This work provides a compact analytical framework for chirp-mediated coherent control in the XUV regime and sheds light on recent experimental observations of asymmetric AT structures in helium.

New Journal of Physics•Oct 28, 2025•2 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

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
We present an interferometric method for studying the Rabi dynamics in atoms by employing an \ensuremathω\ensuremath-2\ensuremathω\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}\ensuremathω\ensuremath-2\ensuremathω extreme ultraviolet pulse pair generated from the seeded free-electron laser. By solving the time-dependent Schr"odinger equation (TDSE) for hydrogen atoms, we study the photoelectron spectrum that emerges when the \ensuremathω\ensuremath{\omega}\ensuremathω pulse triggers Rabi oscillations between the ground state and the first excited state. The interference between the one-photon and two-photon ionization pathways in the photoelectron signal gives access to the phase difference between the one- and two-photon transition amplitudes. Compared to the cases without Rabi oscillations, an additional \ensuremathπ\ensuremath{\pi}\ensuremathπ phase jump is observed in the energy domain. Based on perturbation theory, we demonstrate that this phase jump directly reflects the ultrafast buildup of Rabi oscillations in the time domain. The present \ensuremathω\ensuremath-2\ensuremathω\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}\ensuremathω\ensuremath-2\ensuremathω scheme can be generalized and applied to other more complex atoms or molecules provided that the populations of bound states can be efficiently and coherently modulated using the free-electron laser.
Abstract Rabi oscillations are periodic modulations of populations in two-level systems interacting with a time-varying field1. They are ubiquitous in physics with applications in different areas such as photonics2, nano-electronics3, electron microscopy4 and quantum information5. While the theory developed by Rabi was intended for fermions in gyrating magnetic fields, Autler and Townes realized that it could also be used to describe coherent light–matter interactions within the rotating-wave approximation6. Although intense nanometre-wavelength light sources have been available for more than a decade7–9, Rabi dynamics at such short wavelengths has not been directly observed. Here we show that femtosecond extreme-ultraviolet pulses from a seeded free-electron laser10 can drive Rabi dynamics between the ground state and an excited state in helium atoms. The measured photoelectron signal reveals an Autler–Townes doublet and an avoided crossing, phenomena that are both fundamental to coherent atom–field interactions11. Using an analytical model derived from perturbation theory on top of the Rabi model, we find that the ultrafast build-up of the doublet structure carries the signature of a quantum interference effect between resonant and non-resonant photoionization pathways. Given the recent availability of intense attosecond12 and few-femtosecond13 extreme-ultraviolet pulses, our results unfold opportunities to carry out ultrafast manipulation of coherent processes at short wavelengths using free-electron lasers.
Rabi oscillations are periodic modulations of populations in two-level systems interacting with a time-varying field. They are ubiquitous in physics with applications in different areas such as photonics, nano-electronics, electron microscopy, and quantum information. While the theory developed by Rabi was intended for fermions in gyrating magnetic fields, Autler and Townes realized that it could also be used to describe coherent light-matter interaction within the rotating wave approximation\cite. Although intense nanometer-wavelength light-sources have been available for more than a decade, Rabi dynamics at such short wavelengths have not been observed directly. Here we show that femtosecond extreme-ultraviolet pulses from a seeded free-electron laser can drive Rabi oscillations between the ground state and an excited state in helium atoms. The measured photoemission signal revealed an Autler-Townes doublet as well as an avoided crossing, phenomena that are both trademarks of quantum optics. Using theoretical analyses that go beyond the strong-field approximation, we found that the ultrafast build-up of the doublet structure follows from a quantum interference effect between resonant and non-resonant photoionization pathways. Given the recent availability of intense attosecond and few-femtosecond extreme-ultraviolet pulses, our results offer opportunities to carry out ultrafast manipulation of coherent processes at short wavelengths using free-electron lasers.
When an atom is driven by a laser field with a photon energy that is nearly resonant with an atomic transition, it can undergo periodic population transfers between the ground and excited state, known as Rabi oscillations [1], [2]. The aim of this work is to study photoionization from atoms for parameters accessible to a free-electron laser (FEL) [3]. Using time dependent perturbation theory to model photoionization from a Rabi oscillating atom, we have shown that in addition to the expected pathway of ionization from the excited state, non-resonant two-photon ionization will have a comparable amplitude at intensities on the order of 1013W/cm2[3].
Abstract We present a theoretical study on the quantum control of ultrafast Rabi dynamics in atoms driven by chirped extreme ultraviolet (XUV) pulses. Motivated by recent experimental advances using free-electron lasers, we derive an analytical solution of the Rabi oscillation under the rotating wave approximation, incorporating the spectral chirp of the XUV field. Within the essential-states model, we demonstrate how the chirp modulates the phase of the excited-state amplitude, inducing an observable asymmetry in the Autler–Townes (AT) doublets of the photoelectrons. Our theoretical predictions, benchmarked against time-dependent Schrödinger equation simulations, reveal that chirp-dependent phase modulation governs the spectral asymmetry, offering a time-domain perspective for interpreting strong-field photoionization at short wavelengths. This work provides a compact analytical framework for chirp-mediated coherent control in the XUV regime and sheds light on recent experimental observations of asymmetric AT structures in helium.
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.
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.