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arXiv:0905.4420

Comment on "Entanglement on Demand through Time Reordering"

Pradyumna K. Pathak, Stephen Hughes

Published May 27, 2009• 0 citations
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Abstract

In a recent Letter [Phys. Rev. Lett. {\bf 100}, 120501 (2008)], Avron {\em et al.} discuss a time reordering scheme to achieve efficient "across-generation" of entangled photon pairs in a semiconductor quantum dot with a suppressed biexciton binding energy. They demonstrate that the scheme can be implemented using time delay between the generated photons. In this Comment, we derive an exact expression for the concurrence of the time delayed photons, and show that the predicted values by Avron {\em et al.} are not achievable, which stems from an approximation used in their approximate theoretical analysis.

DOI
10.48550/arxiv.0905.4420

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In a recent Letter [Phys. Rev. Lett. {\bf 100}, 120501 (2008)], Avron {\em et al.} discuss a time reordering scheme to achieve efficient "across-generation" of entangled photon pairs in a semiconductor quantum dot with a suppressed biexciton binding energy. They demonstrate that the scheme can be implemented using time delay between the generated photons. In this Comment, we derive an exact expression for the concurrence of the time delayed photons, and show that the predicted values by Avron {\em et al.} are not achievable, which stems from an approximation used in their approximate theoretical analysis.
Entangled photons can be generated "on demand" in a novel scheme involving unitary time reordering of the photons emitted in a radiative decay cascade. The scheme yields polarization entangled photon pairs, even though prior to reordering the emitted photons carry significant "which path information" and their polarizations are unentangled. This shows that quantum chronology can be manipulated in a way that is lossless and deterministic (unitary). The theory can, in principle, be tested and applied to the biexciton cascade in semiconductor quantum dots.
Coulomb interactions between confined carriers remove degeneracies in the excitation spectra of quantum dots. This provides a which-path information in the cascade decay of biexcitons, thus spoiling the energy-polarization entanglement of the emitted photon pairs. We theoretically analyze a strategy of color coincidence across generation (AG), recently proposed as an alternative to the previous within generation approach. We simulate the system dynamics and compute the correlation functions within the density-matrix formalism. This allows estimations of quantities that are accessible by a polarization-tomography experiment and that enter the expression of the two-photon concurrence. We identify the optimum parameters within the AG approach and the corresponding maximum values of the concurrence.
We theoretically investigate the production of polarization-entangled photons through the biexciton cascade decay in a single semiconductor quantum dot. To accomplish a high degree of entanglement, despite the exciton fine-structure splitting, one must either energetically align the two exciton states by means of external fields or erase the which-path information by postselection or time reordering of photons. Here we show that in the latter schemes the photon state becomes deteriorated through dephasing processes in the solid, and the degree of entanglement remains low.