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arXiv:1909.09812 · Physical Review A

Photoelectron spectra after multiphoton ionization of Li atoms in the one-photon Rabi-flopping regime

D. A. Tumakov, Dmitry A. Telnov, G. Plunien, В. М. Шабаев

Published Aug 9, 2019• 23 citations
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Abstract

We calculate two-dimensional photoelectron momentum distributions and energy spectra after multiphoton ionization of Li atoms subject to intense laser fields in the one-photon Rabi-flopping regime. The time-dependent Schr\"odinger equation is solved within the single-active-electron approximation using a model potential which reproduces accurately the binding energies and dipole matrix elements of the Li atom. Interaction with the external electromagnetic field is treated within the dipole approximation. We show that the Rabi oscillations of the population between the ground $2s$ state and the excited $2p$ state in the one-photon resonance regime are reflected in the energy spectra of emitted photoelectrons, which manifest interference structures with minima. Transformations of the interference structures in the photoelectron energy spectra caused by the variation of the laser peak intensity and pulse duration are analyzed.

DOI
10.1103/physreva.100.023407

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We calculate two-dimensional photoelectron momentum distributions and energy spectra after multiphoton ionization of Li atoms subject to intense laser fields in the one-photon Rabi-flopping regime. The time-dependent Schr"odinger equation is solved within the single-active-electron approximation using a model potential which reproduces accurately the binding energies and dipole matrix elements of the Li atom. Interaction with the external electromagnetic field is treated within the dipole approximation. We show that the Rabi oscillations of the population between the ground 2s2s2s state and the excited 2p2p2p state in the one-photon resonance regime are reflected in the energy spectra of emitted photoelectrons, which manifest interference structures with minima. Transformations of the interference structures in the photoelectron energy spectra caused by the variation of the laser peak intensity and pulse duration are analyzed.
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 present a comprehensive theoretical and computational study on harmonic generation (HG) of Li atoms in one- and two-photon Rabi-flopping regimes where the population transfer from the ground 2s2s2s state to the excited 2p2p2p, 3s3s3s, and 3d3d3d states is substantial. Our all-electron approach is based on the time-dependent density-functional theory and takes into account the polarization of the core and the dynamic response of the electrons to the laser field. We show that the population oscillations in the time domain with the Rabi frequency $\mathrm{\ensuremath{\Omega}}$ are reflected in the fine structure of the HG spectra in the frequency domain on the scale of $2\mathrm{\ensuremath{\Omega}}$. Our results also manifest that even finer structures of the harmonic peaks on the smaller frequency scale originate from the pulse-shape-related interference effects. These features are clearly seen in one-photon Rabi-flopping regime between the 2s2s2s and 2p2p2p states. The pattern in the HG spectra becomes more complex in the two-photon Rabi-flopping regime involving 3s3s3s and 3d3d3d states. Our findings can be used for developing coherent control methods for HG in the Rabi-flopping regime.
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.
We theoretically study the photoelectron momentum distributions from multiphoton ionization of a model lithium atom over a range of laser wavelengths from 500 nm to 700 nm by numerically solving the time-dependent Schrödinger equation. The photoelectron momentum distributions display many ring-like patterns for the three-photon ionization, which vary dramatically with the change of the laser wavelength. We show that the wavelength-dependent photoelectron energy spectrum can be used to effectively identify the resonant and nonresonant ionization pathways. We also find an abnormal ellipticity dependence of the electron yield for the (2+1) resonance-enhanced ionization via the 4d intermediate state, which is relevant to the two-photon excitation probability from the ground state to the 4d state.
We study nondipole effects in multiphoton ionization of a two-dimensional hydrogen-like atom by a flat-top laser pulse of varied intensity. For this purpose, we solve numerically a two-dimensional Schrödinger equation treating a propagating laser pulse exactly. The resulting distributions are then compared to those calculated in the dipole approximation. A directional dependence of the energy-angular photoelectron distributions is demonstrated numerically in the case of a propagating laser pulse of a moderate and a high intensity. It is analytically interpreted based on the leading order relativistic expansion of the electron Volkov state, showing a significant contribution of the electron recoil to that behavior. In contrast, the retardation correction originating from the space- and time-dependence of the laser field leads to a tiny redshift of the photoelectron energy spectra. Other features of ionization distributions are also analyzed, including the sidelobes and the double-hump structures of multiphoton peaks, or their disappearance for intense propagating laser pulses.
Abstract We study the three-photon ionization of atomic lithium by intense, short light pulses, via numerically solving the time-dependent Schrödinger equation. Two-photon Rabi oscillations are induced between the 2s and 4s states, which are damped due to single-photon ionization to the p continuum. Developing a minimal three-level model, we analyze the spectral features of the Autler–Townes (AT) doublet that is formed upon the resonant coupling with the laser pulse. Furthermore, we show that this 2 s →→ 4 s → p c o n t i n u u m pathway is the dominant process, if the duration of the laser pulse exceeds a certain value. For shorter pulses, ionization through the 2p state ( 2 s → 2 p → 4 d → f c o n t i n u u m ) gradually becomes the dominant process, provided that the pulse is strong enough to induce several Rabi floppings. Here, we trace the competition of these ionization pathways by observing the structural changes in the shape of the AT doublet.