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Journal of Physics B Atomic Molecular and Optical Physics

Angular correlation and entanglement between a spin-polarization-resolved photoelectron and a polarization-resolved fluorescent photon

K. Jänkälä

Published Aug 6, 2014• 1 citation
Publisher

Abstract

A theoretical study of the angular correlation and angular variation of entanglement between a photoelectron and a fluorescent photon in photoionization of atoms is provided. The formulation is developed for experiments where spin polarization of a photoelectron and polarization of the subsequent fluorescent photon are detected in a coincidence measurement. The applied formalism of parameterization of all polarization sensitivities of the detectors using Stokes parameters and of the use of statistical and efficiency tensors provides straightforward implementation for any experimental geometry. The framework is demonstrated in the case of calcium photoionization followed by radiative decay.

DOI
10.1088/0953-4075/47/16/165201

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A theoretical study of the angular correlation and angular variation of entanglement between a photoelectron and a fluorescent photon in photoionization of atoms is provided. The formulation is developed for experiments where spin polarization of a photoelectron and polarization of the subsequent fluorescent photon are detected in a coincidence measurement. The applied formalism of parameterization of all polarization sensitivities of the detectors using Stokes parameters and of the use of statistical and efficiency tensors provides straightforward implementation for any experimental geometry. The framework is demonstrated in the case of calcium photoionization followed by radiative decay.
The angular correlation between the photoelectron and subsequent polarized fluorescent radiation measured in coincidence is analysed theoretically for atomic photoionization. Using the density matrix and statistical tensor formalism the general expression for the correlation function is obtained for an arbitrary polarized incident photon beam. The particular geometry of a recent experiment (Beyer et al., 1995) is considered and the parameters which determine the angular correlation are expressed in terms of photoionization amplitudes. It is demonstrated that the photoelectron- (polarized) fluorescence coincidence measurements reveal strong circular and linear dichroism. As an example the photoionization of Ca atoms near the 4p 2P3/2 threshold is calculated within the framework of multichannel quantum defect theory.
A method alternative to the density matrix formalism is applied to derive a general expression for the radiative decay probability following the photoionization of polarized atoms in two-step approximation. The graphical technique of the angular momentum theory is used for the integration over angular and spin variables. The general expression joining both steps of photoionization and fluorescence contains the possibility to investigate the polarization of all particles in the initial and final states and the angular distributions as well as angular correlations of photoelectrons and radiation. A simple way to get the expressions for special cases of the angular distribution and polarization of fluorescence radiation in the photoionization of randomly orientated and polarized atoms is given as an example of the practical application of the general formula.
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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.
Circular dichroism has been detected in the polarization of the fluorescence resulting from the decay of excited calcium ions. Synchrotron radiation was used to both ionize and excite calcium atoms from their ground state, and the photoejected electron was detected in coincidence with the polarized fluorescent photon. By introducing a degree of left, then right circularly polarized light into the incident photon beam the circular dichroism could be measured. The analysis of the results was carried out using recent developments of the statistical tensor method, and it was possible to determine the sign of the phase difference between the outgoing waves.