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arXiv:2511.21373

Excited core-level dependence of entanglement between a photoelectron and an emitted X-ray photon in X-ray inner-shell excitation

Ryo B. Tanaka, Goro Oohata, Takayuki Uozumi

quant-phSubmitted Nov 26, 2025• Announced Nov 27, 2025
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Abstract

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\ $2$p$ and 3$d\rightarrow\ $3$p$ SPR-XEPECS (spin- and polarization-resolved XEPECS) processes for $\rm Ti_{2}O_{3}$-type system, and the 4$f\rightarrow\ $4$d$ SPR-XEPECS process for $\rm CeF_{3}$-type system. In the calculation for $\rm Ti_{2}O_{3}$-type system, we used $\rm TiO_{6}$ cluster model with the full-multiplet structure of the Ti ion and the charge-transfer effect between Ti 3$d$ and ligand O 2$p$ orbitals. For $\rm CeF_{3}$-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\ $2$p$ and 4$f\rightarrow\ $4$d$ cases. The first is generated by the spin-orbit interaction of the 2$p$ core electron, whereas the second is generated by the spin-orbit interaction of the 4$f$ valence electron and strong exchange interaction between the 4$f$ and 4$d$ electrons. However, in the 3$d\rightarrow\ $3$p$ case with the strong 3$d-$3$p$ 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.

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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 3d→ d\rightarrow\ d→ 2ppp and 3d→ d\rightarrow\ d→ 3ppp SPR-XEPECS (spin- and polarization-resolved XEPECS) processes for Ti2O3\rm Ti_{2}O_{3}Ti2​O3​-type system, and the 4f→ f\rightarrow\ f→ 4ddd 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 3d→ d\rightarrow\ d→ 2ppp and 4f→ f\rightarrow\ f→ 4ddd 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 3d→ d\rightarrow\ d→ 3ppp case with the strong 3d−d-d−3ppp 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.
We have theoretically investigated the character of entanglement between photoelectrons and emitted X-ray photons in XEPECS process which is a coincidence spectroscopy of photoelectrons and emitted X-ray photons. In the calculations, we used a three-electron sp-model consisting of an inner-shell 1s orbital and an outer-shell 2p orbital. We found that entanglement occurs between spin of photoelectrons and linear polarization of emitted X-ray photons, using the wavefunction of the whole system including the photon as well as the electron system. Furthermore, we calculated the degree of entanglement and found that it shows maximum at a particular angle of emitted X-ray photon.
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.
X-Ray photoemission (XPS) spectra, which have been used for analyzing the chemical and nano structural characteristics of thin film- gate dielectric of nano devices and optoelectronic devices, need to be studied with considering the Quantum entanglement between photoelectron (pe) and emitted X-ray photon (ph) as an indication of the quantum technology. In the present work, as an innovation in the quantum technology, a three-electron S-P model consisting of a 1s orbital in the inner shell and a XPS 2p3/2, 2p1/2) orbital in the outer shell by writing the wave function and second quantization - based on creation and annihilation operators. Regarding the pe-ph entanglement (PPE) via an optical selection rule, we found that the linear polarization of emitted X-ray photons; ph, to pe (or pe-ph) entanglement transfer, reveled in reduced density matrix in von Neumann approach can be useful equation for exploring PPE transfers and for applications to nano chip devices.
In this work, we employ a semi-classical approach to light matter interaction to describe and char- acterize spin configurations resulting from quantum correlations between electrons created by a photoemission event and by the following Auger decay. The system studied consists of three atomic levels and two continua. Initially, an external classical light field, in the form of a narrow Gaussian packet, perturbs the system, and transfers the density of charge, corresponding to one electron (the photoelectron), from the core level to the continuum. The Auger decay then occurs, whereby an electron from either of the valence levels decay to the core while, at the same time, another electron (the Auger electron) is emitted to the continuum. The description of the system is performed in the time domain, by time-evolving the many-particle wave function. Tracking the density of charge in the atomic levels and the continuum levels allows for a description of the dynamics of photoe- mission and Auger decay. Calculating the concurrence, as measure of entanglement, between the photoelectron and the Auger electron, gives insight about the correlation between their spins. We consider two scenarios; altering the relative strengths of the matrix elements responsible for anti-parallel and parallel spin configuration while keeping the interaction between the photoelectron and the Auger electron fixed, and secondly varying the interaction while keeping all the matrix elements fixed. The effect of increasing the strength of the parallel-spin configuration can be seen in the concurrence decreasing, diminishing the correlation between the spin of the photo- and the Auger electron. Furthermore, we find that the interactions between the electrons in the continuum strongly affect the modality of entanglement. While giving a rather simplistic description of a realistic atomic system, our results support the scope of the model to give valuable conceptual insight, into novel qualitative aspects of the temporal dynamics of the Auger decay.
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.
The 3s-3p excitation of spin-polarized Na atoms by Ne+{\mathrm{Ne}}^{+}Ne+ ions has been studied for impact energies Elab=200{E}_{\mathrm{lab}=200}Elab=200​ eV to 6 keV, i.e., in the adiabatic regime. The total excitation cross section and the three Stokes polarization parameters of the fluorescence light have been measured. The linear polarization of the light shows a preferential excitation of the \ensuremath{\Vert}ml{m}_{l}ml​\ensuremath{\Vert}=1 magnetic substates. The circular polarization probes the spin orientation of the excited 3p state. At the highest impact energies investigated the experimental data are compatible with conservation of spin orientation during the collision. With decreasing impact energy, the spin polarization of the final 3p state becomes smaller than the spin polarization of the initial 3s state. This apparent spin depolarization is attributed to the exchange interaction between the Na valence electron and the unfilled Ne+{\mathrm{Ne}}^{+}Ne+ 2p5{p}^{5}p5 core in the quasimolecule formed during the collision.