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Physical Review A

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

Ayoub Ait Elarabi, András Csehi

Published Mar 10, 2025• 10 citations
Publisher

Abstract

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)].

DOI
10.1103/physreva.111.033107

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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)].
We investigate the multipeak structure observed in resonant two-photon ionization of hydrogen, where Rabi oscillations occur. Our results show that the weak peaks appear both between and outside the Autler-Townes (AT) doublets for a rectangular pulse, in contrast to the sin-squared pulse case, where the peaks only appear between the AT doublets. Utilizing a three-level model, we demonstrate that the multipeak structure for the rectangular pulse is attributed to single-slit diffraction in the time domain, rather than to dynamic interference as in the sin-squared pulse. Furthermore, we show that the photoelectron yield of these peaks oscillates with laser intensity for both pulse shapes, with the yields from resonant and nonresonant paths oscillating in opposite directions. This oscillatory behavior is attributed to interference between split energy levels in the energy domain. Our work completes the understanding of the multipeak structure in Rabi oscillations for different laser pulse shapes and provides a way to manipulate the yield of these peaks through laser intensity.
The existence of subpeak structures between the Autler-Townes (AT) doublet of the photoelectron spectrum during resonant ionization of an atom has been predicted in a large number of theoretical calculations, but a convincing physical explanation is still lacking. In this study we establish a temporal interference picture to elucidate the physical origin of these subpeaks. We derive an analytical estimation for the photoelectron spectra based on a three-level model, which agrees well with the numerical solution of the time-dependent Schr\"odinger equation at moderately strong pulse intensities. Our interpretation suggests that the interference of the photoelectron wave packet emitted during each Rabi cycle results in the subpeak structure between the AT doublet. By analyzing the phase difference between two temporally adjacent photoelectron wave packets, we successfully predict the interference minima in the photoelectron energy spectra.
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.
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.
The resonant dynamic Stark effect, observed in the Autler-Townes (AT) splitting, plays a central role in ultrafast strong-field physics. Recent experiments have demonstrated the phase control of the AT doublet in atomic resonance-enhanced multiphoton ionization using intense resonant shaped femtosecond laser pulses [Bayer et al., Adv. Chem. Phys. 159, 235 (2016)]. Based on a two-state model, we showed that the underlying control mechanism is the selective population of dressed states (SPODS). In this work, we use a numerical model to calculate the photoelectron momentum distribution (PMD) based on the ab initio solution of the two-dimensional (2D) time-dependent Schr\"odinger equation (TDSE) to obtain a more complete physical picture of the nonperturbative control of the AT doublet. The 2D-TDSE model reproduces the ultrafast switching among the AT components while also revealing deviations from the signatures predicted by the two-state model. These deviations are attributed to the influence of additional intermediate states. To rationalize our observations, we propose a refined five-state model that includes all significantly populated bound states from the full calculation and accurately reproduces the 2D PMD. Based on the validated five-state model, we conduct a dressed-state analysis which provides a clear physical picture of the SPODS mechanism in a multistate system and sheds light on the role of the intermediate states in strong-field control.
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.