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arXiv:1101.2540 · International Journal of Theoretical Physics

Spin Correlations in e + e − Pair Creation by Two-Photons and Entanglement in QED

N. Yongram

Published Dec 15, 2010• 4 citations
arXivHTMLPDF
DOI
10.1007/s10773-010-0621-x

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Spin correlations of e + e − pair productions of two colliding photons are investigated and explicit expressions for their corresponding probabilities are derived and found to be energy (speed) dependent, for initially linearly and circularly polarized photons, different from those obtained by simply combining the spins of the relevant particles, for initially polarized photons. These expressions also depend on the angles of spin of e + (and/or of e −), for initially linearly polarized photons, but not for circularly polarized photons, as a function of the energy. It is remarkable that these explicit results obtained from quantum field theory show a clear violation of Bell's inequality of Local Hidden Variables theories at all energies beyond that of the threshold one for particle production, in support of quantum field theory in the relativistic regime. We hope that our explicit expression will lead to experiments, of the type described in the bulk of this paper, which can monitor energy (and speed) in polarization correlation experiments.
We consider the nonequilibrium dynamics of an interacting spin- fermion gas in a one-dimensional optical lattice after switching off the confining potential. In particular, we study the creation and the time evolution of spatially separated, spin-entangled fermionic pairs. The time-dependent density-matrix renormalization group is used to simulate the time evolution and evaluate the two-site spin correlation functions, from which the concurrence is calculated. We find that the typical distance between entangled fermions depends crucially on the onsite interaction strength, and that a time-dependent modulation of the tunnelling amplitude can enhance the production of spin entanglement. Moreover, we discuss the prospects of experimentally observing these phenomena using spin-dependent single-site detection.
Abstract Via the hierarchy of correlations, we study doublon–holon pair creation in the Mott state of the Fermi–Hubbard model (in higher dimensions) induced by a time-dependent electric field. Special emphasis is placed on the analogy to electron–positron pair creation from the vacuum in quantum electrodynamics. We find that the accuracy and applicability of this analogy depends on the spin structure of the Mott background. For Ising type anti-ferromagnetic order, we derive an effective Dirac equation. A Mott state without any spin order or spin polarized states do not explicitly display the same quasi-relativistic behavior.