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arXiv:1902.04933 · Physical Review Letters

Phonon-Induced Enhancement of Photon Entanglement in Quantum Dot-Cavity Systems

Tim Seidelmann, F. Ungar, A. M. Barth, Alexei Vagov, V. M. Axt, Moritz Cygorek, T. Kühn

Published Sep 24, 2019• 35 citations
arXivHTMLPDF

Abstract

We report on simulations of the degree of polarization entanglement of photon pairs simultaneously emitted from a quantum dot-cavity system that demand revisiting the role of phonons. Since coherence is a fundamental precondition for entanglement and phonons are known to be a major source of decoherence, it seems unavoidable that phonons can only degrade entanglement. In contrast, we demonstrate that phonons can cause a degree of entanglement that even surpasses the corresponding value for the phonon-free case. In particular, we consider the situation of comparatively small biexciton binding energies and either finite exciton or cavity mode splitting. In both cases, combinations of the splitting and the dot-cavity coupling strength are found where the entanglement exhibits a nonmonotonic temperature dependence which enables entanglement above the phonon-free level in a finite parameter range. This unusual behavior can be explained by phonon-induced renormalizations of the dot-cavity coupling g in combination with a nonmonotonic dependence of the entanglement on g that is present already without phonons.

DOI
10.1103/physrevlett.123.137401

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We report on simulations of the degree of polarization entanglement of photon pairs simultaneously emitted from a quantum dot-cavity system that demand revisiting the role of phonons. Since coherence is a fundamental precondition for entanglement and phonons are known to be a major source of decoherence, it seems unavoidable that phonons can only degrade entanglement. In contrast, we demonstrate that phonons can cause a degree of entanglement that even surpasses the corresponding value for the phonon-free case. In particular, we consider the situation of comparatively small biexciton binding energies and either finite exciton or cavity mode splitting. In both cases, combinations of the splitting and the dot-cavity coupling strength are found where the entanglement exhibits a nonmonotonic temperature dependence which enables entanglement above the phonon-free level in a finite parameter range. This unusual behavior can be explained by phonon-induced renormalizations of the dot-cavity coupling g in combination with a nonmonotonic dependence of the entanglement on g that is present already without phonons.
Cascaded emission from the biexciton state of a quantum dot results in polarization entangled photon pairs. Cavity-enhancement of the direct two-photon emission channel bypasses the dominant source of decoherence in this system - that due to fine-structure splitting of the exciton levels. Here, we investigate the remaining non-Markovian phonon-induced decoherence using the numerically exact uniTEMPO algorithm. We compute the degree of entanglement of photon pairs generated by pulsed two-photon resonant excitation and find surprisingly good agreement between the numerically exact results and those calculated using the approximate polaron master equation method, permitting an efficient exploration of trends across system parameters.
Polarization-entangled photons are key resources for a wide range of protocols in quantum computation and quantum key distribution. Achieving a near-unity degree of polarization entanglement is essential for minimizing qubit error rates in secure key distribution. In this work, we theoretically investigate polarization-entangled photon pairs generated via a quantum-dot radiative cascade embedded in a micropillar cavity. To account for the unavoidable exciton–phonon interactions in the quantum dot–cavity system, we develop a polaron master-equation framework and examine its impact on the degree of entanglement and the resulting qubit error rate. We derive analytical expressions for phonon-induced incoherent scattering rates and show that one-photon incoherent processes dominate, leading to a substantial reduction of entanglement. We further demonstrate that at elevated phonon-bath temperatures, cavity-mediated effects—such as cross-coupling between exciton states, ac-Stark shifts, and multiphoton emission—are significantly suppressed due to phonon-induced renormalization of the cavity coupling strength and the Rabi frequency. Finally, we analyze a BBM92 quantum key distribution protocol and study the evolution of the qubit error rate as a function of the phonon-bath temperature.
We investigate the degree of entanglement quantified by the concurrence of photon pairs that are simultaneously emitted in the biexciton-exciton cascade from a quantum dot in a cavity. Four dot-cavity configurations are compared that differ with respect to the detuning between the cavity modes and the quantum dot transitions, corresponding to different relative weights of direct two-photon and sequential single-photon processes. The dependence of the entanglement on the exciton fine-structure splitting $\ensuremath{\delta}$ is found to be significantly different for each of the four configurations. For a finite splitting and low temperatures, the highest entanglement is found when the cavity modes are in resonance with the two-photon transition between the biexciton and the ground state and, in addition, the biexciton has a finite binding energy of a few meV. However, this widely used configuration is rather strongly affected by phonons such that other dot-cavity configurations, that are commonly regarded as less suited for obtaining high degrees of entanglement, become more favorable already at temperatures on the order of 10K10\phantom{\rule{0.28em}{0ex}}\mathrm{K}10K and above. If the cavity modes are kept in resonance with one of the exciton-to-ground-state transitions and the biexciton binding energy is finite, the entanglement drastically drops for positive $\ensuremath{\delta}$ with rising temperatures when TTT is below $\ensuremath{\simeq}4\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, but is virtually independent of the temperature for higher TTT.
Semiconductor quantum dots have emerged as an especially promising platform for the generation of polarization-entangled photon pairs. However, it was demonstrated recently that the two-photon excitation scheme employed in state-of-the-art experiments limits the achievable degree of entanglement by introducing which-path information. In this work, the combined impact of two-photon excitation and longitudinal acoustic phonons on photon pairs emitted by strongly-confining quantum dots is investigated. It is found that phonons further reduce the achievable degree of entanglement even in the limit of vanishing temperature due to phonon-induced pure dephasing and phonon-assisted one-photon processes, which increase the reexcitation probability. In addition, the degree of entanglement, as measured by the concurrence, decreases with rising temperature and/or pulse duration, even if the excitonic fine-structure splitting is absent and when higher electronic states are out of reach. Furthermore, in the case of finite fine-structure splittings, phonons enlarge the discrepancy in concurrence for different laser polarizations.
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.
Semiconductor quantum dots are among the best sources of on-demand entangled photon pairs. The degree of entanglement, however, is generally limited by the fine structure splitting of exciton states. In this paper, we theoretically investigate the generation of polarization-entangled photon pairs under two-photon excitation and cavity-assisted two-photon emission, both in the weak and strong cavity coupling regimes. We demonstrate and clarify that cavity coupling together with an excitation pulse reduces the degree of entanglement in three different ways. First, in a strong coupling regime, the cavity introduces the unequal ac-Stark shift of horizontally and vertically polarized exciton states, which results in the effective splitting of exciton states. Second, it induces the cross-coupling between the exciton states even in the weak coupling regime, causing the creation of unfavorable two-photon states. Finally, higher excited states of the cavity modes also contribute to the reduction of entanglement. Therefore, in the setting considered here, cavity coupling, which is generally required for the efficient collection of emitted photons, degrades the entanglement both in weak and strong coupling regimes.