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arXiv:2312.12054 · Physical Review A

Effects of cavity-mediated processes on the polarization entanglement of photon pairs emitted from quantum dots

Mukesh Kumar Samal, Divya Mishra, Parvendra Kumar

Published Jan 16, 2024• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.109.013708

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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.
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.
Entangled photon pairs are a crucial resource in quantum information processing. However, common sources of entangled photon pairs, such as generation by spontaneous parametric down-conversion, impose a Poisson distribution on the pairs, limiting their applicability to quantum information processing. Therefore, generating entangled photon pairs exhibiting a sub-Poisson distribution (i.e., entangled photon bundle) would be crucial/an important advancement in the current research context. Recently, it has been proposed that antibunched photon pairs can be generated using pulsed excitation of quantum dots based on photon blockade. In this work we propose a scheme to generate entangled photon pairs with strong antibunching properties via continuous driving. Under two-photon resonant continuous pumping, a quantum dot is first excited to a biexciton state and then emits a pair of entangled photons into a two-mode cavity. Owing to the strong coupling between the quantum dot and optical modes of the cavity, at most one pair of left-/right-polarized photons exists at a time in the cavity. Specifically, the antibunching effect, average photon number, and entanglement of the left- or right-polarized photons can be resonantly enhanced when the coupling strengths between the exciton (biexciton) transition and cavity modes are equal. Moreover, our results show that the binding energy of the biexciton substantially affects the antibunching effect, average photon number, and entanglement of the left-/right-polarized photons. With suitable parameters, we can realize photon pairs with strong antibunching, a large average photon number, and deep entanglement. Hence, the studied quantum dot-cavity system is a promising source of antibunched entangled photon pairs.
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.
Entangled photon pairs are key to many novel applications in quantum technologies. Semiconductor quantum dots can be used as sources of on-demand, highly entangled photons. The fidelity to a fixed maximally entangled state is limited by the excitonic fine-structure splitting. This work demonstrates that, even if this splitting is absent, the degree of entanglement cannot reach unity when the excitation pulse in a two-photon resonance scheme has a finite duration. The degradation of the entanglement has its origin in a dynamically induced splitting of the exciton states caused by the laser pulse itself. Hence, in the setting explored here, the excitation process limits the achievable concurrence for entangled photons generated in an optically excited four-level quantum emitter.
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.
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.