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Physical Review B

Violation of Bell’s inequality for two coupled quantum dots confined in a cavity

Amitabh Joshi, Blake Anderson, Min Xiao

Published Mar 5, 2007• 6 citations
Publisher

Abstract

A system of two coupled quantum dots entangled through their interaction with a cavity mode, including F\"orster and exciton-phonon interactions, exhibits violation of Bell's inequality at certain interaction times of these dots with the field mode. The effects of relative positions of these dots in the cavity and exciton-phonon and F\"orster interaction strengths on the violation of Bell's inequality are discussed.

DOI
10.1103/physrevb.75.125304

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A system of two coupled quantum dots entangled through their interaction with a cavity mode, including F"orster and exciton-phonon interactions, exhibits violation of Bell's inequality at certain interaction times of these dots with the field mode. The effects of relative positions of these dots in the cavity and exciton-phonon and F"orster interaction strengths on the violation of Bell's inequality are discussed.
Quantum correlations, such as quantum entanglement (QE), measurement-induced non-locality (MIN) and Bell non-locality, are investigated in a system of two coupled quantum dots (QDs) entangled through their interaction with a cavity mode, including F?rster and exciton?phonon interactions. When the two QDs are situated very close to and symmetrically about the antinode of the sustained longitudinal mode, the violation of Bell?s inequality only occurs with strong MIN and QE. If one of the QDs is located very near to the node while the other one is located slightly far away from the node, the violation does not occur even with strong MIN and QE. When both QDs are located in the cavity in such a way that they see different cavity field amplitudes, the violation occurs with weak or strong MIN and QE. The generalized Rabi frequency acts as a control for the occurrence of these different types of the quantum correlation in the system, with MIN more general than the conventionally mentioned quantum non-locality related to the QE or violation of Bell?s inequalities.
We present and apply a medium-dependent quantum optics formalism for describing the exciton dynamics of two spatially-separated quantum dots on-chip, in the regime of coupled-cavity quantum electrodynamics. With each dot placed in a spatially-separated cavity and coupled through a periodic waveguide channel, the quantum dot excitons behave as a composite entangled pair, exhibiting pronounced entanglement over distances of 300 microm and more. The computed light spectra above the two cavities show clear signatures of pronounced photon coupling including increased vacuum Rabi splitting and cavity-induced transmission and absorption. The macroscopic entanglement is confirmed by investigating the Bell inequality, which is shown to be violated for hundreds of picoseconds.
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.
The dynamical behavior of entanglement for excitons in two quantum dots placed in a cavity driven by a broadband squeezed vacuum is studied in the low exciton density regime. It is found that the excitons in two quantum dots can evolve into a pure entangled state only when the dissipation of the cavity and exciton modes is negligible. When the injected field into the cavity is a squeezed vacuum, the excitons will be in a two-mode Gaussian entangled mixed state even in the long time limit. Analytical expressions are derived, showing the dependence of the entanglement property of the excitons in two quantum dots on the squeezing properties of the initial state prepared in the cavity and the strength of two-photon correlations of the squeezed vacuum injected into the cavity.