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

Exact analytic characterization of the Autler-Townes doublet via the extended semiclassical Rabi model

András Csehi

Published Feb 18, 2026• 2 citations
Publisher

Abstract

We study the resonance-enhanced multiphoton ionization (REMPI) of atoms by intense, short, XUV radiation fields. To characterize Rabi oscillations and the resulting Autler-Townes doublet in the photoelectron spectrum, a minimal-state effective description is utilized, incorporating energy-level shifts, multiphoton couplings, and irreversible losses. Extending the semiclassical Rabi model with such higher-order terms, the complex population amplitudes of the Rabi cycling atom are found in simple analytic forms. This allows for the exact analytic evaluation of the photoelectron spectrum under various simultaneous physical effects. The origins of the spectral characteristics, such as the splitting, shifting, asymmetry, and multipeak pattern, are identified through the found spectrum formula. Furthermore, the dependence of these features on the field intensity, frequency detuning, and interaction time are analyzed in detail. Finally, as the simplicity of the spectrum formula is preserved when further higher-order light-matter interaction terms are added, the presented general framework is suitable for studying arbitrary ( n + m ) photon REMPI phenomena.

DOI
10.1103/3gz9-s6hv

Related papers

Exactly solvable two-level model with time-dependent coupling, detuning, and loss: Application to strong-field resonance ionization

Ayoub Ait Elarabi, András Csehi

We present an exactly solvable two-level model with smoothly varying coupling, detuning, and loss functions. Whenever the common temporal profile of these parameter functions is analytically integrable, the complex population amplitudes are found for all times in simple analytic forms. This makes the model suitable for studying the population and phase dynamics of resonance-enhanced ionization processes. Incorporating two-photon Rabi frequency, dynamical Stark shifts, and one-photon ionization rate into this model, the 2 + 1 photon ionization of atomic lithium is studied as a showcase example. Finally, when the intensity profile of the laser pulse has the sine-squared shape, we find the exact analytic expression of the photoelectron spectrum, allowing additional insight into the structure of the Autler-Townes doublet.

Physical Review A•Jun 2, 2025•7 citations

Photoelectron signature of dressed-atom stabilization in an intense XUV field

Edvin Olofsson, Jan Marcus Dahlström

Nonperturbative resonant multiphoton ionization $(1+1)$ is studied using the resolvent operator technique. Scaling parameters for effective two-level Hamiltonians are computed for hydrogen and helium atoms to provide a quantitative description of Rabi oscillations at XUV wavelengths, which were recently observed using a seeded free-electron laser [S. Nandi et al., Nature (London) 608, 488 (2022)]. The resulting photoelectron spectra exhibit a range of Autler-Townes doublets, which are studied for different intensities, detunings, and interaction times. We identify a photoelectron signature that originates from stabilization against ionization of helium atoms interacting with intense circularly polarized XUV light. Thus, our study shows how it is possible to test the prediction of dressed-atom stabilization by Beers and Armstrong [B. L. Beers and L. Armstrong, Phys. Rev. A 12, 2447 (1975)], without the demanding requirement of atomic saturation in the time domain.

Physical Review Research•Oct 5, 2023•24 citations

Enhancing Autler-Townes splittings by ultrafast XUV pulses

Wei‐Chao Jiang, Hao Liang, Shun Wang +2 more

We study the photoelectron spectra of hydrogen and helium ionized by intense ultrafast two-color XUV laser pulses by numerically solving the time-dependent Schrödinger equation.The photon energy of the pump pulse is tuned to the 1s-2p excitation energy, inducing Rabi oscillations between these bound states and forming an Autler-Townes (AT) doublet of dressed states.When ionized by a time-delayed ultrafast XUV pulse with duration shorter than the Rabi oscillation period, we find novel and drastically enhanced AT splittings in the photoionization spectrum.We identify their origin in terms of the temporal interference of two attosecond wave packets whose spectral distribution is controlled by the interplay between Rabi frequency and bandwidth of the probe pulse.These time-dependent features in the spectra can be much larger than the standard AT spacing induced by the pump pulse alone and can be controlled by the time delay and the duration of the probe pulse.

Physical Review Research•Aug 25, 2021•31 citations

Bichromatic phase control of interfering Autler-Townes spectra

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

We propose a scheme to control the shape of the Autler-Townes (AT) doublet in the photoelectron spectrum from atomic resonance-enhanced multiphoton ionization (REMPI). The scheme is based on the interference of two AT doublets created by ionization of the strongly driven atom from the ground and the resonantly excited state using tailored bichromatic femtosecond laser pulses. In this scheme, the quantum phase of the photoelectrons is crucial for the manipulation of the AT doublet. The laser polarization state and the relative optical phase between the two colors are used to manipulate the interference pattern. We develop an analytical model to describe the bichromatic REMPI process and provide a physical picture of the control mechanism. To validate the model, the results are compared to an ab initio calculation based on the solution of the two-dimensional time-dependent Schr\"odinger equation for the nonperturbative interaction of an atom with intense polarization-shaped bichromatic femtosecond-laser pulses. Our results indicate that the control mechanism is robust with respect to the laser intensity, facilitating its experimental observation.

arXiv:2311.08248•Physical Review A•Mar 15, 2024•5 citations

Photoelectron signature of dressed-atom stabilization in intense XUV field

Edvin Olofsson, Jan Marcus Dahlström

Non-perturbative resonant multiphoton ionization $(1+1)$ is studied using the resolvent operator technique. Scaling parameters for effective two-level Hamiltonians are computed for hydrogen and helium atoms to provide a quantitative description of Rabi oscillations at XUV wavelengths, which were recently observed using a seeded Free-Electron Laser [S. Nandi et al., Nature 608, 488-493 (2022)]. The resulting photoelectron spectra exhibit a range of Autler-Townes doublets, which are studied for different intensities, detunings and interaction times. We identify a photoelectron signature that originates from stabilization against ionization of helium atoms interacting with intense circularly polarized XUV light. Thus, our work shows how it is possible to test the prediction of dressed-atom stabilization by Beers and Armstrong [B. L. Beers and L. Armstrong, Phys. Rev. A 12, 2447 (1975)], without the demanding requirement of atomic saturation in the time domain.

arXiv:2305.07363•May 12, 2023•0 citations

Transition from Rabi oscillations to dynamic interference: The multipeak pattern of the Autler-Townes doublet revisited

Ayoub Ait Elarabi, András Csehi

Recent studies have shown that both Rabi oscillations (ROs) and dynamic interference (DI) lead to pronounced multipeak patterns in the spectrum of ionized photoelectrons. These two prominent dynamical effects---characteristic of intense, short, and (near-)resonant laser pulses interacting with matter---usually coexist, and are thus hard to distinguish. Here, we revisit the multipeak pattern of the Autler-Townes doublet to uncover its physical origin, by calculating the photoelectron spectrum accurately. Our joint analytical and numerical analysis reveals that selectively populating the two emerging dynamically dressed states is key to an efficient balancing between ROs and DI. We demonstrate physical situations where either ROs or DI dictate the spectrum shape, and explore the transition between these regimes. The present work provides further insight into our results reported in a previous work [Phys. Rev. A 108, L061101 (2023)].

Physical Review A•Mar 10, 2025•10 citations
We study the resonance-enhanced multiphoton ionization (REMPI) of atoms by intense, short, XUV radiation fields. To characterize Rabi oscillations and the resulting Autler-Townes doublet in the photoelectron spectrum, a minimal-state effective description is utilized, incorporating energy-level shifts, multiphoton couplings, and irreversible losses. Extending the semiclassical Rabi model with such higher-order terms, the complex population amplitudes of the Rabi cycling atom are found in simple analytic forms. This allows for the exact analytic evaluation of the photoelectron spectrum under various simultaneous physical effects. The origins of the spectral characteristics, such as the splitting, shifting, asymmetry, and multipeak pattern, are identified through the found spectrum formula. Furthermore, the dependence of these features on the field intensity, frequency detuning, and interaction time are analyzed in detail. Finally, as the simplicity of the spectrum formula is preserved when further higher-order light-matter interaction terms are added, the presented general framework is suitable for studying arbitrary ( n + m ) photon REMPI phenomena.
We present an exactly solvable two-level model with smoothly varying coupling, detuning, and loss functions. Whenever the common temporal profile of these parameter functions is analytically integrable, the complex population amplitudes are found for all times in simple analytic forms. This makes the model suitable for studying the population and phase dynamics of resonance-enhanced ionization processes. Incorporating two-photon Rabi frequency, dynamical Stark shifts, and one-photon ionization rate into this model, the 2 + 1 photon ionization of atomic lithium is studied as a showcase example. Finally, when the intensity profile of the laser pulse has the sine-squared shape, we find the exact analytic expression of the photoelectron spectrum, allowing additional insight into the structure of the Autler-Townes doublet.
Nonperturbative resonant multiphoton ionization (1+1)(1+1)(1+1) is studied using the resolvent operator technique. Scaling parameters for effective two-level Hamiltonians are computed for hydrogen and helium atoms to provide a quantitative description of Rabi oscillations at XUV wavelengths, which were recently observed using a seeded free-electron laser [S. Nandi et al., Nature (London) 608, 488 (2022)]. The resulting photoelectron spectra exhibit a range of Autler-Townes doublets, which are studied for different intensities, detunings, and interaction times. We identify a photoelectron signature that originates from stabilization against ionization of helium atoms interacting with intense circularly polarized XUV light. Thus, our study shows how it is possible to test the prediction of dressed-atom stabilization by Beers and Armstrong [B. L. Beers and L. Armstrong, Phys. Rev. A 12, 2447 (1975)], without the demanding requirement of atomic saturation in the time domain.
We study the photoelectron spectra of hydrogen and helium ionized by intense ultrafast two-color XUV laser pulses by numerically solving the time-dependent Schrödinger equation.The photon energy of the pump pulse is tuned to the 1s-2p excitation energy, inducing Rabi oscillations between these bound states and forming an Autler-Townes (AT) doublet of dressed states.When ionized by a time-delayed ultrafast XUV pulse with duration shorter than the Rabi oscillation period, we find novel and drastically enhanced AT splittings in the photoionization spectrum.We identify their origin in terms of the temporal interference of two attosecond wave packets whose spectral distribution is controlled by the interplay between Rabi frequency and bandwidth of the probe pulse.These time-dependent features in the spectra can be much larger than the standard AT spacing induced by the pump pulse alone and can be controlled by the time delay and the duration of the probe pulse.
We propose a scheme to control the shape of the Autler-Townes (AT) doublet in the photoelectron spectrum from atomic resonance-enhanced multiphoton ionization (REMPI). The scheme is based on the interference of two AT doublets created by ionization of the strongly driven atom from the ground and the resonantly excited state using tailored bichromatic femtosecond laser pulses. In this scheme, the quantum phase of the photoelectrons is crucial for the manipulation of the AT doublet. The laser polarization state and the relative optical phase between the two colors are used to manipulate the interference pattern. We develop an analytical model to describe the bichromatic REMPI process and provide a physical picture of the control mechanism. To validate the model, the results are compared to an ab initio calculation based on the solution of the two-dimensional time-dependent Schr\"odinger equation for the nonperturbative interaction of an atom with intense polarization-shaped bichromatic femtosecond-laser pulses. Our results indicate that the control mechanism is robust with respect to the laser intensity, facilitating its experimental observation.
Non-perturbative resonant multiphoton ionization (1+1)(1+1)(1+1) is studied using the resolvent operator technique. Scaling parameters for effective two-level Hamiltonians are computed for hydrogen and helium atoms to provide a quantitative description of Rabi oscillations at XUV wavelengths, which were recently observed using a seeded Free-Electron Laser [S. Nandi et al., Nature 608, 488-493 (2022)]. The resulting photoelectron spectra exhibit a range of Autler-Townes doublets, which are studied for different intensities, detunings and interaction times. We identify a photoelectron signature that originates from stabilization against ionization of helium atoms interacting with intense circularly polarized XUV light. Thus, our work shows how it is possible to test the prediction of dressed-atom stabilization by Beers and Armstrong [B. L. Beers and L. Armstrong, Phys. Rev. A 12, 2447 (1975)], without the demanding requirement of atomic saturation in the time domain.
Recent studies have shown that both Rabi oscillations (ROs) and dynamic interference (DI) lead to pronounced multipeak patterns in the spectrum of ionized photoelectrons. These two prominent dynamical effects---characteristic of intense, short, and (near-)resonant laser pulses interacting with matter---usually coexist, and are thus hard to distinguish. Here, we revisit the multipeak pattern of the Autler-Townes doublet to uncover its physical origin, by calculating the photoelectron spectrum accurately. Our joint analytical and numerical analysis reveals that selectively populating the two emerging dynamically dressed states is key to an efficient balancing between ROs and DI. We demonstrate physical situations where either ROs or DI dictate the spectrum shape, and explore the transition between these regimes. The present work provides further insight into our results reported in a previous work [Phys. Rev. A 108, L061101 (2023)].