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Physica Scripta

Entanglement Change in Atomic Photoionization

Young Soon Kim, Yi Jin Kim, Richard H. Pratt

Published Jan 1, 2004• 7 citations
Publisher

Abstract

Photoionization is one of the basic processes of light-matter interaction, which may be used to transfer at least part of quantum information from photons to electrons in the continuum in such a way that the final state electron carries composite information of the initial electron and of the incident photon. We examine how photoionization may change entanglement of electrons. Our result shows that entanglement in one degree of freedom is affected by a transition in another degree of freedom through the coupling of the two degrees of freedom.

DOI
10.1238/physica.topical.110a00079

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Photoionization is one of the basic processes of light-matter interaction, which may be used to transfer at least part of quantum information from photons to electrons in the continuum in such a way that the final state electron carries composite information of the initial electron and of the incident photon. We examine how photoionization may change entanglement of electrons. Our result shows that entanglement in one degree of freedom is affected by a transition in another degree of freedom through the coupling of the two degrees of freedom.
The density-matrix theory, based on Dirac's relativistic equation, is applied for studying the entanglement between the photoelectron and residual ion in the course of the photoionization of atoms and ions. In particular, emphasis is placed on deriving the final-state density matrix of the overall system ``photoion+electron\text{photoion}+\text{electron}photoion+electron,'' including interelectronic effects and the higher multipoles of the radiation field. This final-state density matrix enables one immediately to analyze the change of entanglement as a function of the energy, angle and the polarization of the incoming light. Detailed computations have been carried out for the 5s5s5s photoionization of neutral strontium, leading to a photoion in a 5s2S5s\phantom{\rule{0.2em}{0ex}}^{2}S5s2S Jf=1∕2{J}_{f}=1∕2Jf​=1∕2 level. It is found that the photoion-electron entanglement decreases significantly near the ionization threshold and that, in general, it depends on both the photon energy and angle. The possibility to extract photoion-electron pairs with a well-defined degree of entanglement may have far-reaching consequences for quantum information and elsewhere.
This paper investigates the relationship, if any, which may exist between the electron-electron correlation and spin entanglement of two electrons ejected simultaneously from a linear molecule following the absorption of a single photon. In order to properly learn about the influence of the molecular dynamics on this relationship and also to take into account the parity of the molecular states, double photoionization has been studied by including rotational degrees of freedom in the Hund's coupling schemes (a) and (b). Entanglement properties of the ejected pair of electrons with respect to their spins have been investigated in each of these coupling schemes without or with taking spin dependent interactions into account. The existence, or otherwise, of the entanglement is predicted on the basis of the negativity of the partial transpose of the density matrix calculated for each case considered in this paper.
Objectives: To study of entanglement between two electronic qubits,without observing spin orbit interaction (SOI), produced by double photo ionization from Xeon atom following the absorption of a photon. Methods: In absence of SOI, Russel-Salunders coupling (L-S coupling) is applicable. As the estimations of entanglement we have considered PeresHorodecki condition and negativity. In case of L-Scoupling, all the properties of electronic qubits are predicted merely with the knowledge of the spins of the target atom, the residual photoion, emitted electrons and the state of polarization of the absorbed photon. Findings: We have found that the electronic qubits may be totally entangled, partially entangled or separable depending on spin states of target Xe, residualdication Xe2+,emitted electrons and the state of polarization of incident photon as well as of the direction sspin quantization and ejection of the photoelectrons. Applications/ Improvements: Studies of quantumen tanglement and its paradoxical properties hold the key to various Quantum information (QI) tasks such as quantum teleportation, quantum cryptography and quantum computer technology. Keywords: Density Operator PACS No. 32.30, L-S Coupling, Negativity, Peres-Horodecki Condition
In this paper, we study the entanglement properties of a pair of electrons ejected simultaneously from an atom following the absorption of a single photon. We show that, in the absence of spin-orbit interaction (SOI), the non-separability of the state of two photoelectrons in a pair depends upon the spins of the atom and of its residual dication. The two electrons produced in a double photoionization experiment may always be entangled, on the other hand, if the SOI is taken into account. In the latter case, entanglement will be affected by, among other things, the photoionization dynamics and the state of polarization of the absorbed radiation.
Quantum entanglement is a unique phenomenon of quantum mechanics that explains how two subatomic particles are correlated even if they are separated by a vast distance. The phenomena of quantum entanglement are useful resources for quantum information. In this chapter, we will study the entanglement properties of bipartite states of two electronic qubits, without observing spin-orbit interaction (SOI), produced by single-step double photoionization in helium atom following the absorption of a single photon. In absence of SOI, Russell-Saunders coupling (L-S coupling) is applicable. We observe that the entanglement depends significantly on the direction of the ejection, as well as the spin quantization of photoelectrons.