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arXiv:0801.3574 · Physical Review A

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

Matthieu Larqué, Isabelle Robert-Philip, A. Beveratos

Published Apr 28, 2008• 22 citations
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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.

DOI
10.1103/physreva.77.042118

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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.
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.
The dynamics of the population density matrix and polarization density matrix of the biexciton system of single semiconductor quantum dots with pulse excitation were analyzed by using master equations and quantum regression theorem. A model based on the spectral distributions of the cascade photon emissions was proposed to calculate the polarization entanglement of the photon pairs emitted from the non-degenerate biexciton system with spectral filters. The influences of the spectral filter width and the exciton energy splitting between the two orthogonally polarized eigenstates on the entanglement were theoretically analyzed. The dependence of the polarization entanglement on the input pulse area was also discussed.
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.
A semiconductor based scheme has been proposed for generating entangled photon pairs from the radiative decay of an electrically pumped biexciton in a quantum dot. Symmetric dots produce polarization entanglement, but experimentally realized asymmetric dots produce photons entangled in both polarization and frequency. In this work, we investigate the possibility of erasing the ``which-path'' information contained in the frequencies of the photons produced by asymmetric quantum dots to recover polarization-entangled photons. We consider a biexciton with nondegenerate intermediate excitonic states in a leaky optical cavity with pairs of degenerate cavity modes close to the nondegenerate exciton transition frequencies. An open quantum system approach is used to compute the polarization entanglement of the two-photon state after it escapes from the cavity, measured by the visibility of two-photon interference fringes. We explicitly relate the two-photon visibility to the degree of the Bell-inequality violation, deriving a threshold at which Bell-inequality violations will be observed. Our results show that an ideal cavity will produce maximally polarization-entangled photon pairs, and even a nonideal cavity will produce partially entangled photon pairs capable of violating a Bell-inequality.
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.