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Physical Review A

Time- and energy-domain interference in the dynamically dressed Rabi-cycling atom

Yutong Deng, Xu Zhang, Yueming Zhou, Peixiang Lu

Published Apr 11, 2025• 4 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.111.043110

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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.
We study the Rabi flopping of the population between the ground and excited 2p states of the hydrogen atom, induced by intense short laser pulses of different shapes and of carrier frequency ω=0.375 a.u. which resonantly couples the two states, and manifestations of this dynamics in the energy spectra of photoelectrons produced in the subsequent ionization of the atom from the excited state. It is found that, for Gaussian, half-Gaussian and rectangular pulses, characterized by the same pulse area, the final populations take the same values and the spectra consist of similar patterns having the same number of peaks and approximately the same separation between the prominent edge (Autler–Townes) peaks. The additional analysis in terms of dressed states showed that the mechanism of formation of multiple-peak structures during the photoionization process is the same regardless of the pulse shape. These facts disprove the hypothesis proposed in earlier studies with Gaussian pulse, that the multiple-peak pattern appears due to dynamic interference of the photoelectrons emitted with a time delay at the rising and falling sides of the pulse, since the hypothesis is not applicable to either a half-Gaussian pulse that has no rising part or a rectangular pulse whose intensity is constant.
We theoretically investigate the resonant two-photon ionization of a hydrogen atom in the counter-rotating circularly polarized double-pulse sequences, by solving the time-dependent Schr\"odinger equation. Due to the induced Rabi oscillations between the ground and excited states, the well-known Autler-Townes doublet is observed in the photoelectron spectra. More interestingly, our numerical results reveal an additional peak located between the Autler-Townes doublets, which originates from single-photon ionization from the excited state by the second pulse. By adjusting the laser intensity of the two pulses, the photoelectron yields of the three peaks can be sensitively modulated, under the control of completed Rabi cycles within the first pulse. In addition, our results show a potential of manipulating the photoemission anisotropy by both the laser intensity and the two-pulse time delay, through adjusting the competition of different partial waves generated by the two pulses.
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)].
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.
By numerically solving the three-dimensional time-dependent Schr\"odinger equation, two-photon ionization of hydrogen is investigated at the near-resonant frequencies of the $1s\text{\ensuremath{-}}2p$ transition. Due to the Rabi oscillations between the 1s1s1s and 2p2p2p states, the photoelectron energy spectra exhibit the Autler-Townes (AT) doublets and we focus on the energy spacing and the asymmetry of the doublets. Our results show that the laser frequency for the minimum energy spacing of AT doublets locates at the resonant frequency of the ac-stark-shifted states, while the symmetry of the AT doublets is affected both by the ac-stark shift and the nonresonant ionization pathway. Developing the minimal three-state model including all of the nonresonant (nonessential) states, the effects of the ac-stark shift and the nonresonant ionization pathway on the AT doublets due to the nonresonant states are identified. Furthermore, due to the nonresonant ionization pathway, the photoelectron angular distributions are distinctly different for the lower- and higher-energy peaks in the AT doublets and these angular distributions sensitively depend on the laser intensity and pulse duration. These results are well reproduced by our minimal three-state model.
Abstract Based on numerical solutions of the time-dependent Schrödinger equation, we theoretically investigate the photoelectron spectrum of hydrogen atoms ionized by a pair of ultrashort, intense, and orthogonally polarized laser pulses with a relative time delay in a pump–probe configuration. The pump pulse resonantly excites electrons from the 1s and 2p levels, inducing Rabi oscillations. The resulting dynamically enhanced Autler–Townes (AT) splitting is observed in the photoelectron energy spectrum upon interaction with the second probe pulse. In contrast to the previous parallel-polarization scheme, the proposed orthogonal-polarization configuration enables the resolution of dynamically enhanced AT splitting over a considerably wider range of probe photon energies.