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arXiv:0707.3556 · Physical Review Letters

Coherence of an Entangled Exciton-Photon State

A. J. Hudson, R. M. Stevenson, Anthony J. Bennett, Robert James Young, Christine A. Nicoll, P. Atkinson, K. Cooper, D. A. Ritchie, Andrew J. Shields

Published Dec 28, 2007• 171 citations
arXivHTMLPDF

Abstract

We study the effect of the exciton fine-structure splitting on the polarization entanglement of photon pairs produced by the biexciton cascade in a quantum dot. Entanglement persists despite separations between the intermediate energy levels of up to 4 microeV. Measurements show that entanglement of the photon pair is robust to the dephasing of the intermediate exciton state responsible for the first-order coherence time of either single photon. We present a theoretical framework incorporating the effects of spin scattering, background light, and dephasing. We distinguish between the first-order coherence time, and a parameter which we measure for the first time and define as the cross-coherence time.

DOI
10.1103/physrevlett.99.266802

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We study the effect of the exciton fine-structure splitting on the polarization entanglement of photon pairs produced by the biexciton cascade in a quantum dot. Entanglement persists despite separations between the intermediate energy levels of up to 4 microeV. Measurements show that entanglement of the photon pair is robust to the dephasing of the intermediate exciton state responsible for the first-order coherence time of either single photon. We present a theoretical framework incorporating the effects of spin scattering, background light, and dephasing. We distinguish between the first-order coherence time, and a parameter which we measure for the first time and define as the cross-coherence time.
A well controlled, triggered source of entangled photons is desirable for many applications in quantum information processing. The two-photon cascade from a biexciton state, two electrons and holes, confined in a quantum dot can be such a source of polarisation-entangled photons provided the two decay paths from the biexciton carry no “which-path” information. In recent years many techniques have been employed to make the two optical decay paths from the biexciton state indistinguishable. We will demonstrate the effect of the exciton fine-structure splitting on a single-dot based entangled photon source. Surprisingly the entanglement is found to persist despite relatively large separations between the intermediate energy levels of up to 4µeV. Measurements demonstrate that entanglement of the photon pair is robust to the dephasing of the intermediate exciton state responsible for the first order coherence time of either of the single photons. We distinguish between the first-order coherence time (2*), and a parameter defined as the cross-coherence time (HV) which is illustrated in the figure. The cross-coherence time is found to be at least an order of magnitude greater than the first-order coherence time. We will also report on recent progress towards an ideal source of triggered polarisation-entangled photons with a single quantum dot.
A well controlled, triggered source of entangled photons is desirable for many applications in quantum information processing. The two-photon cascade from a biexciton state, two electrons and holes, confined in a quantum dot can be such a source of polarisation-entangled photons provided the two decay paths from the biexciton carry no “which-path” information. In recent years many techniques have been employed to make the two optical decay paths from the biexciton state indistinguishable. A number of these techniques will be discussed and entangled-photon emission from a single quantum dot with a high fidelity in the expected Bell-state from the cascade will be demonstrated. This source of entangled photons allows optical interferometry beyond the limits imposed by the photon wavelength. Interference fringes of the entangled biphoton state reveals a periodicity half of that obtained with the single photon, and much less than that of the pump laser. High fringe visibility indicates that biphoton interference is less sensitive to decoherence than interference of two sequential single photons. The effect of the exciton fine-structure splitting on our entangled photon source will be shown. Surprisingly the entanglement is found to persist despite relatively large separations between the intermediate energy levels of up to 4µeV. Measurements demonstrate that entanglement of the photon pair is robust to the dephasing of the intermediate exciton state responsible for the first order coherence time of either single photon. We distinguish between the first-order coherence time, and a parameter defined as the cross-coherence time, this is illustrated in the figure.
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.
A semiconductor quantum dot (QD) is an attractive resource to generate polarization-entangled photon pairs. We study the excitonic spin precession (flip-flop) in a family of QDs with different excitonic fine-structure splitting (FSS) and its impact on the entanglement of photons generated from the excitonic-biexcitonic radiative cascade. Our results reveal that coherent processes leave the time postselected entanglement of QDs with finite FSS unaffected while changing the eigenstates of the system. The flip-flop's precession is observed via quantum tomography through anomalous oscillations of the coincidences in the rectilinear basis. A theoretical model is constructed with the inclusion of an excitonic flip-flop rate and is compared with a two-photon quantum tomography measurement on a QD exhibiting the spin flip-flop mechanism. A generalization of the theoretical model allows estimating the degree of entanglement as a function of the FSS and the spin precession rate. For a finite temporal resolution, the negativity is found to be oscillating with respect to both the FSS and the spin precession rate. This oscillatory behavior disappears for perfect temporal resolution and maximal entanglement is retrieved despite the flip-flop process.
We employ the quantum-jump approach to study single scatterings in single semiconductor quantum dots. Two prototypical situations are investigated. First, we analyze two-photon emissions from the cascade biexciton decay of a dot where the single-exciton states exhibit a fine-structure splitting. We show that this splitting results for appropriately chosen polarization filters in an oscillatory behavior of two-photon correlations, and carefully examine the proper theoretical description of the underlying scattering processes. Second, we analyze the decay of a single-electron charged exciton in a quantum dot embedded in a field-effect structure. We show how the quantum properties of the charged exciton are transferred through tunneling and relaxation to the spin entanglement between electrons in the dot and contact, and identify the pertinent disentanglement mechanisms.
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.