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Bell inequalities for polarization entangled photons out of a two-photon cascade in a single quantum dot

Matthieu Larqué, Isabelle Robert-Philip, A. Beveratos

Published Jan 23, 2008• 0 citations
OpenAlex

Abstract

We theoretically investigate the joint photodetection probabilities of the biexciton-exciton cascade in single semiconductor quantum dots and analytically derive the density matrix and the Bell's inequalities of the entangled state. Our model includes different mechanisms that may spoil or even destroy entanglement such as dephasing, energy splitting of the relay excitonic states and incoherent population exchange between these relay levels. We explicitly relate the fidelity of entanglement to the dynamics of these processes and derive a threshold for violation of Bell's inequalities. Applied to standard InAs/GaAs self-assembled quantum dots, our model indicates that spontaneous emission enhancement of the excitonic states by cavity effects increases the fidelity of entanglement to a value allowing for violation of Bell's inequalities.

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We theoretically investigate the joint photodetection probabilities of the biexciton-exciton cascade in single semiconductor quantum dots and analytically derive the density matrix and the Bell's inequalities of the entangled state. Our model includes different mechanisms that may spoil or even destroy entanglement such as dephasing, energy splitting of the relay excitonic states and incoherent population exchange between these relay levels. We explicitly relate the fidelity of entanglement to the dynamics of these processes and derive a threshold for violation of Bell's inequalities. Applied to standard InAs/GaAs self-assembled quantum dots, our model indicates that spontaneous emission enhancement of the excitonic states by cavity effects increases the fidelity of entanglement to a value allowing for violation of Bell's inequalities.
We theoretically investigate the joint photodetection probabilities of the biexciton-exciton cascade in single semiconductor quantum dots and analytically derive the density matrix and the Bell's inequalities of the entangled state. Our model includes different mechanisms that may spoil or even destroy entanglement such as dephasing, energy splitting of the relay excitonic states, and incoherent population exchange between these relay levels. We explicitly relate the fidelity of entanglement to the dynamics of these processes and derive a threshold for violation of Bell's inequalities. Applied to standard InAs/GaAs self-assembled quantum dots, our model indicates that spontaneous emission enhancement of the excitonic states by cavity effects increases the fidelity of entanglement to a value allowing for violation of Bell's inequalities.
Abstract. We develop a theoretical model to study the Intensity-Intensity correlation of polarization entangled photons emitted in a biexciton-exciton cascade. We calculate the degree of correlation and show how polarization correlation are affected by the presence of dephasing and energy level splitting of the excitonic states. Our theoretical calculations are in agreement with the recent observation of polarization dependent Intensity-Intensity correlations from a single semiconductor quantum dot [R. M. Stevenson et. al. Nature 439, 179 (2006)]. Our model can be extended to study polarization entangled photon emission in coupled quantum dot systems. PACS numbers: 03.67.bg,42.50.Ar,42.50.CtNonclassical Correlation of Polarization Entangled Photons in a Biexciton-Exciton Cascade2 1.
We theoretically study the polarization entanglement of photons generated by the biexciton cascade in a GaAs/InAs semiconductor quantum dot (QD) located in a nanocavity. A detailed analysis of the complex interplay between photon and carrier coherences and phonons which occurs during the cascade allows us to clearly identify the conditions under which entanglement is generated and destroyed. A quantum state tomography is evaluated for varying exciton fine-structure splittings. Also, by constructing an effective multiphonon Hamiltonian which couples the continuum of the QD-embedding wetting layer states to the quantum confined states, we investigate the relaxation of the biexciton and exciton states. This consistently introduces a temperature dependence to the cascade. Considering typical Stranski-Krastanov grown QDs for temperatures around 80 K the degree of entanglement starts to be affected by the dephasing of the exciton states and is ultimately lost above 100 K.
We develop a theoretical model to study the intensity–intensity correlation of polarization-entangled photons emitted in a biexciton–exciton cascade. We calculate the degree of correlation and show how polarization correlations are affected by the presence of dephasing and energy-level splitting of the excitonic states. Our theoretical calculations are in agreement with the recent observation of polarization-dependent intensity–intensity correlations from a single semiconductor quantum dot (Stevenson et al 2006 Nature 439 179). Our model can be extended to study polarization-entangled photon emission in coupled quantum dot systems.
We study the quantum properties and statistics of photons emitted by a quantum-dot biexciton inside a cavity. In the biexciton-exciton cascade, fine-structure splitting between exciton levels degrades polarization-entanglement for the emitted pair of photons. However, here we show that the polarization-entanglement can be preserved in such a system through simultaneous emission of two degenerate photons into cavity modes tuned to half the biexciton energy. Based on detailed theoretical calculations for realistic quantum-dot and cavity parameters, we quantify the degree of achievable entanglement.
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.