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Real-time Entanglement of Auger and XPS-electrons: a preliminary investigation

Philip Johansson

Published Jan 1, 2019• 0 citations
OpenAlex

Abstract

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.

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Einstein-Podolsky-Rosen-Bohm correlation in photoelectron–Auger-electron coincidence spectroscopy of atoms

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We present a theoretical analysis of spin-entanglement between a photoelectron and an Auger electron sequentially ejected from an atom (say, $A$) following the absorption of a single photon. Entanglement, both without and with spin-orbit interaction has been analyzed. In the former case, entanglement in a photo-Auger electron pair is generated only by the electrostatic Coulomb forces inside an atom and completely characterized merely by the multiplicities of the electronic states of $A$, ${A}^{{+}^{*}}$, ${A}^{2+}$ participating in the process, without using any protocols already suggested in the literature for this purpose. The presence of both the Coulomb and spin-orbit interactions, on the other hand, couples the entanglement of this bipartite state with the dynamics and kinematics of the whole process, as well as with the properties of the absorbed photon. In such cases, therefore, it is not possible to predict, a priori, the photo-Auger electron entanglement. These discussions have quantitatively been illustrated by several examples.

Physical Review A•Nov 20, 2006•16 citations

Theoretical perspectives on ultrafast and non-linear spectroscopy

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In this thesis we discuss a theoretical description of ultrafast and non-linear spectroscopy. Due to the high intensities and ultrashort pulse durations involved in such experiments, it is necessary to use an explicitly time-dependent formalism. In addition, many of the systems we have considered exhibit strong interactions between the constituent particles, such as electron-electron, electron-nuclear and electron-photon interactions. To properly account for such interactions we have made extensive use of effective models, designed to capture the qualitative aspects of the systems.The thesis is based on six papers, that can be broadly categorized as follows: In Papers III and VI we study the non-linear interaction of light and matter. In Paper III we look at the multi-photon photo-emission from InAs nanowires, and in particular at the polarization dependence of the photo-emission signal on the crystal structure. In Paper VI we discuss second harmonic generation in a two-level system, and compare the fluorescence spectra from a quantum and semi-classical treatment of radiation.The remaining four papers are concerned with ultrafast dynamical processes: In Papers I and II we study atomic desorption from a surface, resulting from strong electron-nuclear interactions. To account for these interactions we consider a finite system that can be solved using exact diagonalization. We show that the desorption yield can be controlled by using a protocol with two ultrashort pulses and varying their delay. To assess finite size effects we compare the exact solution of the finite system to an approximate solution of a semi-infinite system based on non-equilibrium Green's functions and Ehrenfest dynamics. In Paper V we study Auger decay in a real-time description, and propose a protocol to induce the quantum Zeno effect by driving the system during decay. The Zeno effect leads to an increase in the Auger lifetime, that is experimentally measurable and can be controlled by varying the intensity of the driving field. In Paper IV we discuss the role of electron-electron interactions for charge-separation in donor-acceptor systems. We identify a regime where the charge-separation is driven solely by electronic correlations, that are captured by treating interactions to first order beyond a mean-field description.

•May 7, 2018•0 citations

Coherent Control of Absorption and Entanglement via Ultrafast Strong Coupling

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This thesis investigates quantum dynamics induced in atoms by ultrashort pulses of light. The work is motivated by recent developments in free-electron lasers, which generate ultrashort pulses of intense, coherent light and enable coherent control of quantum dynamics. We develop theoretical models to study the processes of absorption and emission in laser-atom interactions. Additionally, we study photoionisation, which creates an ion and an electron, and the entanglement that can be generated between these particles. Finally, we have investigated how the spontaneous decay of the ion induces entanglement transfer from the ion-electron pair to the electron-photon pair.This thesis compiles seven papers. Paper I investigates the absorption of light from an attosecond pulse by an atom in a prepared coherent superposition of states. We show how the evolution of the phase of the superposition wave packet influences the attosecond transient absorption spectra. Paper II predicts the existence of Mollow-like triplets in the absorption spectra of strongly coupled atoms. We establish the conditions for the pulse envelope under which this triplet pattern can be supported.Paper III studies two-photon Rabi oscillations, establishing which systems can sustain such dynamics. We find that a two-photon Rabi oscillating system can induce giant counter-rotating oscillations in the population dynamics, enabling investigations of physical effects beyond the rotating-wave approximation.Paper IV studies ionisation from an atom strongly coupled by a dichromatic field, where interference between the two frequency components shapes the temporal symmetry of the atomic dynamics, allowing for coherent control of the photoelectron distribution.Paper V considers an experiment performed at a Free-Electron Laser facility where a helium atom is ionised and the resulting ion is subsequently strongly coupled. The photoelectron spectra are theoretically reproduced and the entanglement between the ion and photoelectron is studied. Paper VI investigates how the entanglement in the ion--electron pair, generated via photoionisation followed by strong coupling, can be coherently controlled by harnessing the time symmetry of the pulse. We find that the observable manifestation of the entanglement can be altered in such a way that the electron energy becomes associated with the ionic state, allowing the entanglement to be detected via coincidence measurements. Paper VII investigates how quantum correlations between the ion and the electron can be coherently controlled by sequential strong coupling of the ion. We find that both the build-up of entanglement and its manifestation can be controlled, and we establish a quantitative measure of the amplitude entanglement that explains the dynamics in an intuitive way. Paper VIII studies the process of entanglement transfer induced by the spontaneous decay of the ion. We find that the ion--electron entanglement generated during the ultrashort interaction with the laser field is transferred to the electron--photon system over the much longer timescale of fluorescence.

•Sep 3, 2026•0 citations

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Matter wave optics perspective at molecular photoionization: K-shell photoionization and Auger decay of N2

Markus S Schöffler, T. Jahnke, Jasmin Titze +15 more

In this paper, we shed new light on the molecular photoionization of a diatomic molecule. We will elaborate the differences and analogy between a quantum optical and light–matter interaction approach in a study of K-shell photoionization of N 2 in which the photoelectron and the subsequently emitted Auger electron are both measured in coincidence in the body fixed frame of the molecule. The two electrons form an entangled state inside a double slit. By changing the photon energy we create different types of interference in the photoelectron and the Auger electron wave.

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Time-Stretched Spectroscopy by the Quantum Zeno Effect: The Case of Auger Decay

Emil Viñas Boström, Mathieu Gisselbrecht, Tomas Brage +3 more

A tenet of time-resolved spectroscopy is "faster laser pulses for shorter timescales". Here, we suggest turning this paradigm around, and slowing down the system dynamics via repeated measurements, to do spectroscopy on longer timescales. This is the principle of the quantum Zeno effect. We exemplify our approach with the Auger process, and find that repeated measurements increase the core-hole lifetime, redistribute the kinetic energy of Auger electrons, and alter entanglement formation. We further provide an explicit experimental protocol for atomic Li, to make our proposal concrete.

arXiv:1804.06605•Physical Review Letters•Dec 7, 2018•6 citations
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.
We present a theoretical analysis of spin-entanglement between a photoelectron and an Auger electron sequentially ejected from an atom (say, AAA) following the absorption of a single photon. Entanglement, both without and with spin-orbit interaction has been analyzed. In the former case, entanglement in a photo-Auger electron pair is generated only by the electrostatic Coulomb forces inside an atom and completely characterized merely by the multiplicities of the electronic states of AAA, A+∗{A}^{{+}^{*}}A+∗, A2+{A}^{2+}A2+ participating in the process, without using any protocols already suggested in the literature for this purpose. The presence of both the Coulomb and spin-orbit interactions, on the other hand, couples the entanglement of this bipartite state with the dynamics and kinematics of the whole process, as well as with the properties of the absorbed photon. In such cases, therefore, it is not possible to predict, a priori, the photo-Auger electron entanglement. These discussions have quantitatively been illustrated by several examples.
In this thesis we discuss a theoretical description of ultrafast and non-linear spectroscopy. Due to the high intensities and ultrashort pulse durations involved in such experiments, it is necessary to use an explicitly time-dependent formalism. In addition, many of the systems we have considered exhibit strong interactions between the constituent particles, such as electron-electron, electron-nuclear and electron-photon interactions. To properly account for such interactions we have made extensive use of effective models, designed to capture the qualitative aspects of the systems.The thesis is based on six papers, that can be broadly categorized as follows: In Papers III and VI we study the non-linear interaction of light and matter. In Paper III we look at the multi-photon photo-emission from InAs nanowires, and in particular at the polarization dependence of the photo-emission signal on the crystal structure. In Paper VI we discuss second harmonic generation in a two-level system, and compare the fluorescence spectra from a quantum and semi-classical treatment of radiation.The remaining four papers are concerned with ultrafast dynamical processes: In Papers I and II we study atomic desorption from a surface, resulting from strong electron-nuclear interactions. To account for these interactions we consider a finite system that can be solved using exact diagonalization. We show that the desorption yield can be controlled by using a protocol with two ultrashort pulses and varying their delay. To assess finite size effects we compare the exact solution of the finite system to an approximate solution of a semi-infinite system based on non-equilibrium Green's functions and Ehrenfest dynamics. In Paper V we study Auger decay in a real-time description, and propose a protocol to induce the quantum Zeno effect by driving the system during decay. The Zeno effect leads to an increase in the Auger lifetime, that is experimentally measurable and can be controlled by varying the intensity of the driving field. In Paper IV we discuss the role of electron-electron interactions for charge-separation in donor-acceptor systems. We identify a regime where the charge-separation is driven solely by electronic correlations, that are captured by treating interactions to first order beyond a mean-field description.
This thesis investigates quantum dynamics induced in atoms by ultrashort pulses of light. The work is motivated by recent developments in free-electron lasers, which generate ultrashort pulses of intense, coherent light and enable coherent control of quantum dynamics. We develop theoretical models to study the processes of absorption and emission in laser-atom interactions. Additionally, we study photoionisation, which creates an ion and an electron, and the entanglement that can be generated between these particles. Finally, we have investigated how the spontaneous decay of the ion induces entanglement transfer from the ion-electron pair to the electron-photon pair.This thesis compiles seven papers. Paper I investigates the absorption of light from an attosecond pulse by an atom in a prepared coherent superposition of states. We show how the evolution of the phase of the superposition wave packet influences the attosecond transient absorption spectra. Paper II predicts the existence of Mollow-like triplets in the absorption spectra of strongly coupled atoms. We establish the conditions for the pulse envelope under which this triplet pattern can be supported.Paper III studies two-photon Rabi oscillations, establishing which systems can sustain such dynamics. We find that a two-photon Rabi oscillating system can induce giant counter-rotating oscillations in the population dynamics, enabling investigations of physical effects beyond the rotating-wave approximation.Paper IV studies ionisation from an atom strongly coupled by a dichromatic field, where interference between the two frequency components shapes the temporal symmetry of the atomic dynamics, allowing for coherent control of the photoelectron distribution.Paper V considers an experiment performed at a Free-Electron Laser facility where a helium atom is ionised and the resulting ion is subsequently strongly coupled. The photoelectron spectra are theoretically reproduced and the entanglement between the ion and photoelectron is studied. Paper VI investigates how the entanglement in the ion--electron pair, generated via photoionisation followed by strong coupling, can be coherently controlled by harnessing the time symmetry of the pulse. We find that the observable manifestation of the entanglement can be altered in such a way that the electron energy becomes associated with the ionic state, allowing the entanglement to be detected via coincidence measurements. Paper VII investigates how quantum correlations between the ion and the electron can be coherently controlled by sequential strong coupling of the ion. We find that both the build-up of entanglement and its manifestation can be controlled, and we establish a quantitative measure of the amplitude entanglement that explains the dynamics in an intuitive way. Paper VIII studies the process of entanglement transfer induced by the spontaneous decay of the ion. We find that the ion--electron entanglement generated during the ultrashort interaction with the laser field is transferred to the electron--photon system over the much longer timescale of fluorescence.
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.
In this paper, we shed new light on the molecular photoionization of a diatomic molecule. We will elaborate the differences and analogy between a quantum optical and light–matter interaction approach in a study of K-shell photoionization of N 2 in which the photoelectron and the subsequently emitted Auger electron are both measured in coincidence in the body fixed frame of the molecule. The two electrons form an entangled state inside a double slit. By changing the photon energy we create different types of interference in the photoelectron and the Auger electron wave.
A tenet of time-resolved spectroscopy is "faster laser pulses for shorter timescales". Here, we suggest turning this paradigm around, and slowing down the system dynamics via repeated measurements, to do spectroscopy on longer timescales. This is the principle of the quantum Zeno effect. We exemplify our approach with the Auger process, and find that repeated measurements increase the core-hole lifetime, redistribute the kinetic energy of Auger electrons, and alter entanglement formation. We further provide an explicit experimental protocol for atomic Li, to make our proposal concrete.