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arXiv:2212.09529 · Nano Letters

Beyond the Four-Level Model: Dark and Hot States in Quantum Dots Degrade Photonic Entanglement

Barbara Lehner, Tim Seidelmann, Gabriel Undeutsch, Christian Schimpf, Santanu Manna, Michał Gawełczyk, Saimon Filipe Covre da Silva, Xueyong Yuan, Sandra Stroj, Doris E. Reiter, V. M. Axt, Armando Rastelli

Published Feb 6, 2023• 16 citations
arXivHTMLPDF

Abstract

Entangled photon pairs are essential for a multitude of quantum photonic applications. To date, the best performing solid-state quantum emitters of entangled photons are semiconductor quantum dots operated around liquid-helium temperatures. To favor the widespread deployment of these sources, it is important to explore and understand their behavior at temperatures accessible with compact Stirling coolers. Here we study the polarization entanglement among photon pairs from the biexciton-exciton cascade in GaAs quantum dots at temperatures up to ∼65 K. We observe entanglement degradation accompanied by changes in decay dynamics, which we ascribe to thermal population and depopulation of hot and dark states in addition to the four levels relevant for photon pair generation. Detailed calculations considering the presence and characteristics of the additional states and phonon-assisted transitions support the interpretation. We expect these results to guide the optimization of quantum dots as sources of highly entangled photons at elevated temperatures.

DOI
10.1021/acs.nanolett.2c04734

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Entangled photon pairs are essential for a multitude of quantum photonic applications. To date, the best performing solid-state quantum emitters of entangled photons are semiconductor quantum dots operated around liquid-helium temperatures. To favor the widespread deployment of these sources, it is important to explore and understand their behavior at temperatures accessible with compact Stirling coolers. Here we study the polarization entanglement among photon pairs from the biexciton-exciton cascade in GaAs quantum dots at temperatures up to ∼65 K. We observe entanglement degradation accompanied by changes in decay dynamics, which we ascribe to thermal population and depopulation of hot and dark states in addition to the four levels relevant for photon pair generation. Detailed calculations considering the presence and characteristics of the additional states and phonon-assisted transitions support the interpretation. We expect these results to guide the optimization of quantum dots as sources of highly entangled photons at elevated temperatures.
We theoretically study the polarization entanglement of photons generated by the biexciton cascade in a GaAs/InAs semiconductor quantum dot (QD) located in a nanocavity. A detailed analysis of the complex interplay between photon and carrier coherences and phonons which occurs during the cascade allows us to clearly identify the conditions under which entanglement is generated and destroyed. A quantum state tomography is evaluated for varying exciton fine-structure splittings. Also, by constructing an effective multiphonon Hamiltonian which couples the continuum of the QD-embedding wetting layer states to the quantum confined states, we investigate the relaxation of the biexciton and exciton states. This consistently introduces a temperature dependence to the cascade. Considering typical Stranski-Krastanov grown QDs for temperatures around 80 K the degree of entanglement starts to be affected by the dephasing of the exciton states and is ultimately lost above 100 K.
Entangled photon pairs are essential for quantum communication technology. They can be generated on-demand by semiconductor quantum dots, but several mechanisms are known to reduce the degree of entanglement. While some obstacles like the finite fine-structure splitting of the exciton states can currently be overcome, the excitation scheme itself can impair the entanglement fidelity. Here, we demonstrate that the swing-up of quantum emitter population (SUPER) scheme, using two red-detuned laser pulses applied to a quantum dot in a cavity, yields almost perfectly entangled photons. The entanglement remains robust against phonon influences even at elevated temperatures, due to decoupling of the excitation and emission process. With this achievement, quantum dots are ready to be used as entangled photon pair sources in applications requiring high degrees of entanglement up to temperatures of approximately 80 K.
Entangled photon pairs are essential for many applications in quantum technologies. Recent theoretical studies demonstrated that different types of entangled Bell states can be created in a constantly driven four-level quantum emitter-cavity system. Unlike other candidates for the realization of the four-level emitter, semiconductor quantum dots unavoidably interact with their environment, resulting in carrier-phonon interactions. Surprisingly, phonons change the entanglement of emitted photon pairs in a qualitative way, already at low temperatures on the order of 4 K. While one type of Bell state can still be generated using small driving strengths, the other type is suppressed due to phonon interactions in strongly confined quantum dots. The degree of entanglement decreases with rising temperature and driving strength until it vanishes at a certain parameter value. Because it remains zero afterward, we encounter a phonon-induced transition between entangled and nonentangled photon emission that resembles a phase transition. The transition occurs at temperatures below 30 K and, independent of the driving strength, the concurrence as a function of the reduced temperature is found to obey a power law with exponent one near the transition point.
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.
The generation of entangled photons from radiative cascades has enabled milestone experiments in quantum information science with several applications in photonic quantum technologies. Significant efforts are being devoted to pushing the performances of near-deterministic entangled-photon sources based on single quantum emitters often embedded in photonic cavities, so to boost the flux of photon pairs. The general postulate is that the emitter generates photons in a nearly maximally entangled state of polarization, ready for application purposes. Here, we demonstrate that this assumption is unjustified. We show that in radiative cascades there exists an interplay between photon polarization and emission wavevector, which can be further amplified by embedding the emitters in micro-cavities. We discuss how the polarization entanglement of photon pairs from a biexciton-exciton cascade in quantum dots strongly depends on their propagation wavevector and we even observe entanglement vanishing for large emission angles. Our experimental results, backed by theoretical modeling, yield a brand-new understanding of cascaded emission for various quantum emitters. In addition, our model provides quantitative guidelines for designing optical microcavities that retain both a high degree of entanglement and collection efficiency, moving the community one step further towards an ideal source of entangled photons for quantum technologies. The assumption that light sources based on radiative cascades provide maximally polarization-entangled photons is not always correct. Here the authors show experimentally in cavity-embedded quantum dots that photon polarization correlates with its emission mode, impacting the degree of entanglement for emitted photon pairs.
Abstract Photon pairs emitted from the biexciton‐exciton cascade of a single self‐assembled InGaAs/GaAs quantum dot can be polarization‐entangled. The degree of entanglement is reduced by the fine structure splitting of the involved exciton level. We measure this splitting in high resolution using a scanning Fabry‐Pérot interferometer. By quantum state tomographywe can determine the twophoton polarization state.We are able to verify the conditions of entangled or classically correlated photon pairs in full consistence with the observed fine structure splittings. The entanglement remains relatively unaffected for elevated sample temperatures where we observe reliable entanglement up to 30 K. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)