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Physical Review A

Effect of nonresonant states in near-resonant two-photon ionization of hydrogen

Xu Zhang, Yueming Zhou, Yijie Liao, Yongkun Chen, Jintai Liang, Qinghua Ke, Min Li, András Csehi, Peixiang Lu

Published Dec 30, 2022• 32 citations
Publisher

Abstract

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 $1s$ and $2p$ 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.

DOI
10.1103/physreva.106.063114

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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\ensuremath-2p1s\text{\ensuremath{-}}2p1s\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.
We investigate resonant strong field ionization of atomic hydrogen with respect to the 1s–2p transition. By 'strong' we understand that Rabi periods are executed on a femtosecond time scale. Ionization and AC Stark shifts modify the bound state dynamics severely, leading to nonperturbative signatures in the photoelectron spectra. We introduce an analytical model, capable of predicting qualitative features in the photoelectron spectra such as the positions of the Autler–Townes peaks for modest field strengths. Ab initio solutions of the time-dependent Schrödinger equation show a pronounced shift and broadening of the left Autler–Townes peak as the field strength is increased. The right peak remains rather narrow and shifts less. This result is analysed and explained with the help of exact AC Stark shifts and ionization rates obtained from Floquet theory. Finally, it is demonstrated that in the case of finite pulses as short as 20 fs the Autler–Townes duplet can still be resolved. The fourth generation light sources under construction worldwide will provide bright, coherent radiation with photon energies ranging from a tenth of an meV up to tens of keV, hence covering the regime studied in the paper so that measurements of nonperturbative, relative AC Stark shifts should become feasible with these new light sources.
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.
The energy levels of atoms and molecules exposed to intense, short, high-frequency laser pulses undergo time-dependent distortion known as dynamic Stark shift (DSS). These level shifts are induced by the coupling with nonresonant (nonessential) states and follow the temporal intensity profile of the laser pulse. Owing to the different DSSs of the individual atomic levels, transient resonance suppressions and enhancements significantly modify the multiphoton ionization pathway, leaving clear fingerprints (asymmetry, splitting, and shifting) in the energy spectrum of emitted photoelectrons. Here we investigate this phenomenon by solving the time-dependent Schr\"odinger equation of the valence electron of Na and Li in increasing levels of complexity: (i) developing minimal models for two-photon transition and (2+12+12+1)-photon ionization, (ii) applying a spectral method without continuum-continuum couplings, and (iii) propagating the electron wave packet on a large spatial grid accounting for all possible couplings. We show that appropriately detuned transform limited pulses provide a high level of control in strong-field excitation, when the atomic levels are dynamically shifted. Furthermore, we demonstrate the role of DSSs in the multipeak structure of the Autler-Townes doublet, found when several Rabi oscillations are induced during the strong-field resonant ionization.
We present a bound-continuum ionization model combined with numerical simulations to investigate the asymmetric features of Autler-Townes (AT) splitting in the ionization spectra of hydrogen atoms, induced by a spectrally phase-modulated ultrashort pulse. This model incorporates a resonance-enhanced two-photon ionization process, enabling transitions from the ground electronic state to the continuum state via the first excited electronic state through the absorption of two photons. By comparing our model predictions with exact numerical simulations based on time-dependent electronic wave-packet calculations, we demonstrate that the characteristics of the AT doublets, shaped by the spectral phase, emerge from the competing effects of selective population of dressed states and the transition amplitude to the continuum. In addition, through a perturbative analysis of the photoelectronic spectrum and the application of the Magnus expansion, we reveal a correlation between the number of AT fringes, resonant states, and pulse area, while drawing insights from bound states. This work enhances our understanding of how the spectral phase can be utilized to explore bound-state effects in ultrafast ionization dynamics.
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 present ionization probability and lineshape calculations for the two-step three-photon ionization process, , of the ground state of hydrogenic atoms in a non-monochromatic laser field with a time-dependent amplitude. Within the framework of a three-level model, the AC Stark shifts and non-zero ionization rates of all states involved were taken into account, together with spatial and temporal inhomogeneities of the laser signal. In contrast with the usual perturbative technique, the time evolution of the atomic states was simulated by directly solving the system of coupled time-dependent inhomogeneous differential equations numerically, the equations being equivalent to the appropriate non-stationary Schrödinger equation. Particular numerical results were obtained for typical parameters of the pulsed laser field that are employed in a new experiment to measure the 1S-2S energy separation with muonium at the Rutherford Appleton Laboratory. The shifts and asymmetries of the photoionization lineshapes revealed may be of relevance for ultra-high-precision experiments in hydrogen in CW laser fields.