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arXiv:0811.3329 · Physical Review B

Entangled photons from a strongly coupled quantum dot-cavity system

R. Johne, Николай Алексеевич Гиппиус, G. Malpuech

Published Apr 23, 2009• 20 citations
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Abstract

A quantum dot strongly coupled to a photonic crystal has been recently proposed as a source of entangled photon pairs [R. Johne et al., Phys. Rev. Lett. 100, 240404 (2008)]. The biexction decay via intermediate polariton states can be used to overcome the natural splitting between the exciton states coupled to the horizontally and vertically polarized light modes so that high degrees of entanglement can be expected. We investigate theoretically the features of realistic dot-cavity systems, including the effect of the different oscillator strength of excitons resonances coupled to the different polarizations of light. We show that in this case, an independent adjustment of the cavity resonances is needed in order to keep a high entanglement degree. We also consider the case when the biexciton-exciton transition is also strongly coupled to a cavity mode. We show that a very fast emission rate can be achieved allowing the repetition rates close to the terahertz range. Such fast emission should however be paid for by a very complex tuning of the many strongly coupled resonances involved and by a loss of quantum efficiency. Altogether a strongly coupled dot-cavity system seems to be very promising as a source of entangled photon pairs.

DOI
10.1103/physrevb.79.155317

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A quantum dot strongly coupled to a photonic crystal has been recently proposed as a source of entangled photon pairs [R. Johne et al., Phys. Rev. Lett. 100, 240404 (2008)]. The biexction decay via intermediate polariton states can be used to overcome the natural splitting between the exciton states coupled to the horizontally and vertically polarized light modes so that high degrees of entanglement can be expected. We investigate theoretically the features of realistic dot-cavity systems, including the effect of the different oscillator strength of excitons resonances coupled to the different polarizations of light. We show that in this case, an independent adjustment of the cavity resonances is needed in order to keep a high entanglement degree. We also consider the case when the biexciton-exciton transition is also strongly coupled to a cavity mode. We show that a very fast emission rate can be achieved allowing the repetition rates close to the terahertz range. Such fast emission should however be paid for by a very complex tuning of the many strongly coupled resonances involved and by a loss of quantum efficiency. Altogether a strongly coupled dot-cavity system seems to be very promising as a source of entangled photon pairs.
We show theoretically that entangled photon pairs can be produced on demand through the biexciton decay of a quantum dot strongly coupled to the modes of a photonic crystal. The strong coupling allows us to tune the energy of the mixed exciton-photon (polariton) eigenmodes and to overcome the natural splitting existing between the exciton states coupled with different linear polarizations of light. Polariton states are moreover well protected against dephasing due to their lifetime of ten to a hundred times shorter than that of a bare exciton. Our analysis shows that the scheme proposed is achievable with the present technology.
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.
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.
We present a formal theory of single quantum dot coupling to a planar photonic crystal that supports quasidegenerate cavity modes and use this theory to describe and optimize entangled-photon pair generation via the biexciton-exciton cascade. In the generated photon pairs, either both photons are spontaneously emitted from the dot or one photon is emitted from the biexciton spontaneously while the other is emitted via the leaky cavity mode. In the strong-coupling regime, the generated photon pairs can be maximally entangled in qualitative agreement with the dressed-state predictions of Johne et al. [Phys. Rev. Lett. 100, 240404 (2008)]. We derive useful analytical formulas for the spectrum of the emitted photon pairs in the presence of exciton and biexciton broadening, which is necessary to connect to realistic experiments and demonstrate the important differences with the approximate dressed-state approach. We also present a method for calculating and optimizing the entanglement between the emitted photons, which can account for postsample spectral filtering. Pronounced entanglement values of greater than 80% are demonstrated using experimentally achievable parameters even without spectral filtering.
We compute the concurrence of the polarization-entangled photon pairs generated by the biexciton cascade decay of a semiconductor quantum dot. We show how a cavity-induced increase of the photon emission rate reduces the effect of dot dephasing and excitonic fine structure on the concurrence. However, strong dot-cavity couplings, as well as low detection efficiencies, increase the detrimental effect of multiple cascades. This affects the merits of the entangled photon-pair source, beyond what is estimated by quantum tomography.