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Frontiers in Optics

Strong-Field Pair Production: a Structure of Wave Packets and the Electron-Positron Entanglement (Correlations)

Mikhail Vladimirovich Fedorov

Published Jan 1, 2006• 0 citations
Publisher

Abstract

We investigate a structure of the bipartite electron-positron wave function arising in the process of multiphoton pair production. To evaluate the degree of electron-positron correlations (entanglement) we calculate and analyze the Schmidt number K.
DOI
10.1364/fio.2006.jwe4

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A structure of wave packets arising in the process of a bipartite system decay is investigated and its connection with entanglement of quantum states is discussed. As long as the effect of wave packet spreading can be ignored, the ratio R of the single-particle to coincidence wave packet widths is shown to coincide with the degree of entanglement determined by the Schmidt correlation number K. Mathematically single-particle and coincidence schemes correspond to absolute and conditional probability densities. Coordinate and momentum wave-packets for each particle are compared. A series of reciprocity and identity relations between the corresponding wave packet widths is found to occur. Uncertainty relations following from these relations are found. The coordinate and momentum uncertainty products for each particle are shown to be related directly to the degree of entanglement K: the single-particle and coincidence uncertainty products are shown to be, correspondingly, ∼ K ≥ 1 and ∼ 1/K ≤ 1. A series of specific examples are considered.
We analyse the degree of two-particle entanglement between an electron and a positron that are created in vacuum in the presence of a supercritical field. This degree of entanglement is determined from the spatially and temporally resolved two-particle wave function calculated from relativistic quantum field theory. Some spin components of the two particles are fully correlated with respect to a simultaneous measurement. However, the positions where the two particles are created by the field can be apart from each other by as much as the Compton wavelength for an extended supercritical field. We calculate the K parameter from the two-particle wave function as a quantitative measure for the degree of entanglement.
We use a simplified essential state model to compare two quantum field theoretical approaches to study the creation of electron-positron pairs from the vacuum. In the unitary approach the system is characterized by a state with different numbers of particles that is described by occupation numbers and evolves with conserved norm. The nonunitary approach can predict the evolution of wave functions and density operators with a fixed number of particles but time-dependent norms. As an example to illustrate the differences between both approaches, we examine the degree of entanglement for the Klein paradox, which describes the creation of an electron-positron pair from vacuum in the presence of an initial electron. We demonstrate how the Pauli blocking by the initial electron comes at the expense of a gain in entanglement of this electron with the created electron as well as with the created positron.