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arXiv:cond-mat/0211689 · Physical review. B, Condensed matter

Entangled two-photon source using biexciton emission of an asymmetric quantum dot in a cavity

Thomas M. Stace, Gerard J Milburn, C. H. W. Barnes

Published Feb 28, 2003• 124 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.67.085317

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Tomographic analysis demonstrates that the polarization state of pairs of photons emitted from a biexciton decay cascade becomes entangled when spectral filtering is applied. The measured density matrix of the photon pair satisfies the Peres criterion for entanglement by more than 3 standard deviations of the experimental uncertainty and violates Bell's inequality. We show that the spectral filtering erases the "which path" information contained in the photons' color and that the remanent information in the quantum dot degrees of freedom is negligible.
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.
Abstract We theoretically investigate the production of polarization‐entangled photons through the biexciton cascade decay in a single semiconductor quantum dot. A biexciton radiatively decays through two intermediate exciton states, where polarization‐entangled photons are emitted if the two decay paths differ in polarization but are indistinguishable otherwise. This ideal performance is usually spoiled by the electron–hole exchange interaction splitting the intermediate exciton states by a small amount and consequently attaching a which‐path information to the photon frequencies. We discuss post‐selection schemes to mask this which‐path information to an outside observer. We show how spectral filtering and time shifts at a single photon level affect the photon state. Here the solid state environment plays a crucial role in the effective measurement of intermediate exciton states. Evaluating our analytical results with realistic quantum dot parameters we quantify the applicability of suggested protocols for solid‐state based quantum cryptography. Our results indicate, that a high degree of entanglement is only reached by spectral alignment of the exciton states. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Semiconductor quantum dots are promising sources for polarization-entangled photons. As an alternative to the usual cascaded biexciton-exciton emission, direct two-photon emission from the biexciton can be used. With a high-quality optical resonator tuned to half the biexciton energy, a large proportion of the photons can be steered into the two-photon emission channel. In this case the degree of polarization entanglement is inherently insensitive to the exciton fine-structure splitting. In the present work we analyze the biexciton emission with particular emphasis on the influence of coupling of the quantum-dot cavity system to its environment. Especially for a high-quality cavity, the coupling to the surrounding semiconductor material can open up additional phonon-assisted decay channels. Our analysis demonstrates that with the cavity tuned to half the biexciton energy, the potentially detrimental influence of the phonons on the polarization entanglement is strongly suppressed---high degrees of entanglement can still be achieved. We further discuss spectral properties and statistics of the emitted twin photons.
Polarization correlation in a linear basis, but not entanglement, is observed between the biexciton and single-exciton photons emitted by a single InAs quantum dot in a two-photon cascade. The results are well described quantitatively by a probabilistic model that includes two decay paths for a biexciton through a nondegenerate pair of one-exciton states, with the polarization of the emitted photons depending on the decay path. The results show that spin nondegeneracy due to quantum-dot asymmetry is a significant obstacle to the realization of an entangled-photon generation device.
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.