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Chinese Physics B

Two-photon emission in coupled biexciton quantum dot—cavity system: Phonon-assisted model

Yiwei Peng, Zhongyuan Yu, Yumin Liu, Tiesheng Wu, Wen Zhang

Published Nov 28, 2014• 3 citations
Publisher

Abstract

We theoretically analyze the steady state emission spectrum and transient temporal dynamics in a coupled biexciton quantum dot (QD)—cavity system. For steady state, a phonon-assisted biexciton—exciton cascade model under continuous wave (CW) excitation is presented to explain the asymmetric QD—cavity emission spectrum intensities (intensities of cavity, exciton, and biexciton emission peak) in off-resonance condition. Results demonstrate that the electron—phonon process is crucial to the asymmetry of emission spectrum intensity. Moreover the transient characteristics of the biexciton—exciton cascade system under pulse excitation show abundant nonlinear temporal dynamic behaviors, including complicated oscillations which are caused by the four-level structure of QD model. We also reveal that under off-resonance condition the cavity outputs are slightly reduced due to the electron—phonon interaction.

DOI
10.1088/1674-1056/23/12/124204

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We theoretically analyze the steady state emission spectrum and transient temporal dynamics in a coupled biexciton quantum dot (QD)—cavity system. For steady state, a phonon-assisted biexciton—exciton cascade model under continuous wave (CW) excitation is presented to explain the asymmetric QD—cavity emission spectrum intensities (intensities of cavity, exciton, and biexciton emission peak) in off-resonance condition. Results demonstrate that the electron—phonon process is crucial to the asymmetry of emission spectrum intensity. Moreover the transient characteristics of the biexciton—exciton cascade system under pulse excitation show abundant nonlinear temporal dynamic behaviors, including complicated oscillations which are caused by the four-level structure of QD model. We also reveal that under off-resonance condition the cavity outputs are slightly reduced due to the electron—phonon interaction.
In this work, we experimentally and theoretically study the dressed-state emission of the biexciton-exciton cascade in a semiconductor quantum dot under pulsed, resonant, two-photon excitation. Building on the well-characterized steady-state dressed emission of the four-level system, we examine its dynamic counterpart under pulsed, resonant excitation, addressing both experimental observations and theoretical modeling. Here we report several sidebands emerging from the biexciton-to-exciton transition, whose number and spectral width depend on the excitation pulse duration and the effective pulse area, while no sidebands emerge from the exciton-to-ground-state transition. Since the biexciton state population follows a nonlinear pulse area function, sidebands with a small spectral nonlinearity result. Detuning- and time-dependent measurements provide deeper insight into the emission properties of the dressed states. They show that side peak emission only occurs in the presence of the excitation pulse. Moreover, when the system is excited by a Gaussian-shaped laser pulse, side peak emission takes place sequentially.
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.
We demonstrate the simultaneous dressing of both vacuum-to-exciton and exciton-to-biexciton transitions of a single semiconductor quantum dot in a high-Q micropillar cavity, using photoluminescence spectroscopy. Resonant two-photon excitation of the biexciton is achieved by spectrally tuning the quantum dot emission with respect to the cavity mode. The cavity couples to both transitions and amplifies the Rabi frequency of the likewise resonant continuous wave laser, driving the transitions. We observe strong-field splitting of the emission lines, which depend on the driving Rabi field amplitude and the cavity-laser detuning. A dressed state theory of a driven 4-level atom correctly predicts the distinct spectral transitions observed in the emission spectrum, and a detailed description of the emission spectra is further provided through a polaron master equation approach which accounts for cavity coupling and acoustic phonon interactions of the semiconductor medium.
We investigate the influence of multiple excitons on the photon emission properties of a quantum dot (QD)-cavity system via the master equation for the density matrix. We show that in the intermediate to strong coupling regimes, the multiple excitons lead to the suppressed QD emissions as well as the absence of anti-crossing near zero detuning, arising from the interaction between the multiple excitons and cavity. Furthermore, we analyze the role of the cavity-biexciton detuning in the photon emission properties of cavity and exciton through the second-order correlation function. The small cavity-biexciton detuning yields the significant Purcell effect and the high probability of single photon emissions. The proposed model offers the fundamental approach in developing efficient single-photon emitting devices.
Electron-phonon coupling in semiconductor quantum dots plays a significant role in determining the optical properties of excited excitons, especially the spectral nature of emitted photons. This paper presents a comprehensive theory and analysis of emission spectra from artificial atoms or quantum dots coupled to structured photon reservoirs and acoustic phonons, when excited with incoherent pump fields. As specific examples of structured reservoirs, we chose a Lorentzian cavity and a slow-light coupled-cavity waveguide, which have both been explored experimentally. For the case of optical cavities, we directly compare and contrast the spectra from three well-known and distinct theoretical approaches to treat electron-phonon coupling, including a Markovian polaron master equation, a non-Markovian phonon correlation expansion technique, and a semiclassical linear susceptibility approach, and we point out the limitations of these models. For the cavity-QED polaron master equation, which treats the cavity-mode operator at the level of a system operator, we give closed form analytical solutions to the phonon-assisted scattering rates in the weak excitation approximation, fully accounting for temperature, cavity-exciton detuning, and cavity-dot coupling. We also show explicitly why the semiclassical linear susceptibility approach fails to correctly account for phonon-mediated cavity feeding. For weakly coupled cavities, we calculate the optical spectra using a more general photon reservoir polaron master-equation approach, and explain its differences from the above approaches in the low-QQQ limit of a Lorentzian cavity. We subsequently use this general reservoir approach to calculate the emission spectra from quantum dots coupled to slow-light photonic crystal waveguides, which demonstrate a number of striking photon-phonon coupling effects.
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.