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Journal of Physics B Atomic Molecular and Optical Physics

Spin-dependent effects in high-order above-threshold ionization: spin–orbit interaction and exchange effects

Dejan B. Milošević

Published Jul 6, 2017• 15 citations
Publisher

Abstract

Abstract Spin-dependent effects in atomic processes can be caused by the spin–orbit interaction or/and by the requirement that the wave function of identical electrons is antisymmetric. Such effects are usually neglected in strong-field physics. We show two examples, supported by theoretical results and numerical calculations, in which these effects are important. The first one is based on strong-field ionization of Xe atoms by a bicircular field. The corresponding momentum distribution of spin-polarized electrons emitted in the above-threshold ionization process exhibits wavelength-dependent fast oscillations. For longer wavelengths and small electron emission angle there is a wide photoelectron kinetic energy region in which the spin asymmetry parameter changes continuously from large positive to large negative values. In addition, the emission time of such electrons in high-order above-threshold ionization is determined on the attosecond time scale. The second process considered is high-order above-threshold ionization of excited Li + ions. We have found that in this case, even in the absence of spin–orbit coupling, the photoelectron momentum distribution strongly depends on the initial spin state. In the singlet state we have characteristic minima, which are caused by the destructive interference of the direct and exchange rescattering amplitudes. Such minima are absent in the triplet state.

DOI
10.1088/1361-6455/aa7e02

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Abstract Spin-dependent effects in atomic processes can be caused by the spin–orbit interaction or/and by the requirement that the wave function of identical electrons is antisymmetric. Such effects are usually neglected in strong-field physics. We show two examples, supported by theoretical results and numerical calculations, in which these effects are important. The first one is based on strong-field ionization of Xe atoms by a bicircular field. The corresponding momentum distribution of spin-polarized electrons emitted in the above-threshold ionization process exhibits wavelength-dependent fast oscillations. For longer wavelengths and small electron emission angle there is a wide photoelectron kinetic energy region in which the spin asymmetry parameter changes continuously from large positive to large negative values. In addition, the emission time of such electrons in high-order above-threshold ionization is determined on the attosecond time scale. The second process considered is high-order above-threshold ionization of excited Li + ions. We have found that in this case, even in the absence of spin–orbit coupling, the photoelectron momentum distribution strongly depends on the initial spin state. In the singlet state we have characteristic minima, which are caused by the destructive interference of the direct and exchange rescattering amplitudes. Such minima are absent in the triplet state.
The strong-field-approximation theory of high-order above-threshold ionization of atoms is generalized to include the electron spin. The obtained rescattering amplitude consists of a direct and exchange part. On the examples of excited He atoms as well as Li+{\mathrm{Li}}^{+}Li+ and Be++{\mathrm{Be}}^{++}Be++ ions, it is shown that the interference of these two amplitudes leads to an observable difference between the photoelectron momentum distributions corresponding to different initial spin states: Pronounced minima appear for singlet states, which are absent for triplet states.
Abstract We investigate the influence of singlet and triplet spin states on rescattered photoelectrons in strong-field ionization of excited helium. Choosing either a symmetric or antisymmetric spatial wave function as the initial state results in different scattering cross sections for the 1 s 2 s 1 S and 3 S states. These cross sections are used in the semi-classical model of strong-field ionization. Our investigations show that the photoelectron momentum distributions of rescattered electrons exhibit a significant dependence on the relative spin state of the projectile and the bound electron which should be observable in experiments. The proposed experimental approach can be understood as a testbed for probing the spin dynamics of electrons during strong-field ionization and the presented results as a baseline for their identification.
The ionization of the prealigned nitric oxide molecule by strong circularly polarized laser fields is studied via theoretical simulations of the spin-resolved photoelectron momentum distributions by solving numerically the three-dimensional time-dependent Schr\"odinger equation. Due to the spin-orbit entanglement in the ground state of nitric oxide and the sensitivity of the tunnel ionization of its doubly degenerate valence $2{\ensuremath{\pi}}_{\ifmmode\pm\else\textpm\fi{}}$ orbitals carrying opposite electron ring currents to the sense of the laser-field rotation, the momentum-resolved spin-polarized photoelectrons are produced. We show that the spin polarization exhibits strong dependence on the kinetic energy as well as the emitting angle of the photoelectron. In addition to the laser control, the momentum gate in strong-field experiments would enable full control of the spin polarization.
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We theoretically investigated how the quantum entanglement between the spin of the photoelectron and the polarization of the emitted X-ray photon depends on the excited core-level, using the 3$d\rightarrow\ 222p$ and 3$d\rightarrow\ 333p$ SPR-XEPECS (spin- and polarization-resolved XEPECS) processes for Ti2O3\rm Ti_{2}O_{3}Ti2​O3​-type system, and the 4$f\rightarrow\ 444d$ SPR-XEPECS process for CeF3\rm CeF_{3}CeF3​-type system. In the calculation for Ti2O3\rm Ti_{2}O_{3}Ti2​O3​-type system, we used TiO6\rm TiO_{6}TiO6​ cluster model with the full-multiplet structure of the Ti ion and the charge-transfer effect between Ti 3ddd and ligand O 2ppp orbitals. For CeF3\rm CeF_{3}CeF3​-type system, we used ionic model with the full-multiplet structure of the Ce ion. We found two distinct mechanisms for entanglement generation in the 3$d\rightarrow\ 222p$ and 4$f\rightarrow\ 444d$ cases. The first is generated by the spin-orbit interaction of the 2ppp core electron, whereas the second is generated by the spin-orbit interaction of the 4fff valence electron and strong exchange interaction between the 4fff and 4ddd electrons. However, in the 3$d\rightarrow\ 333p$ case with the strong 3$d-333p$ exchange interaction, we found that the entanglement is not generated due to the crystal field effect. These results reveal the existence of two distinct mechanisms for entanglement generation in X-ray inner-shell excitation processes.
Using field ionization combined with the direct detection of excited neutral atoms we measured the distribution of principal quantum number n of excited He Rydberg states after strong-field excitation at laser intensities well in the tunneling regime. Our results confirm theoretical predictions from semiclassical and quantum mechanical calculations and simultaneously underpin the validity of the semiclassical frustrated tunneling ionization model. Moreover, since our experimental detection scheme is spin sensitive in the case of He atoms, we show that strong-field excitation leads to strong population of triplet states. The origin of it lies in the fact that high angular momentum states are accessible in strong-field excitation. Thus, singlet-triplet transitions become possible due to the increased importance of spin-orbit interaction rather than due to direct laser induced spin-flip processes.