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Physical Review B

Microscopic equation-of-motion approach to the multiphonon assisted quantum emission of a semiconductor quantum dot

Julia Kabuß, Alexander Carmele, Marten Richter, Andreas Knorr

Published Sep 30, 2011• 22 citations
Publisher

Abstract

We present a microscopical model for the multiphonon assisted quantum emission from an externally excited semiconductor quantum dot. In the high driving field limit, our model predicts several strong coupling features, in particular, a phonon-assisted Mollow-triplet splitting and anticrossings between the Mollow sidebands and the phonon satellite peaks. The observed anticrossing scales with the effective LO-phonon coupling and can be used as a measure for the phonon coupling strength. Further, we investigate the non-Markovian temporal emission dynamics of the main and multiphonon assisted triplet structures.

DOI
10.1103/physrevb.84.125324

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We present a microscopical model for the multiphonon assisted quantum emission from an externally excited semiconductor quantum dot. In the high driving field limit, our model predicts several strong coupling features, in particular, a phonon-assisted Mollow-triplet splitting and anticrossings between the Mollow sidebands and the phonon satellite peaks. The observed anticrossing scales with the effective LO-phonon coupling and can be used as a measure for the phonon coupling strength. Further, we investigate the non-Markovian temporal emission dynamics of the main and multiphonon assisted triplet structures.
We study the resonance fluorescence spectra of a driven quantum dot placed inside a high-Q semiconductor cavity and interacting with an acoustic phonon bath. The dynamics is calculated using a time-convolutionless master equation in the polaron frame. We predict pronounced spectral broadening of the Mollow sidebands through off-resonant cavity emission which, for small cavity-coupling rates, increases quadratically with the Rabi frequency in direct agreement with recent experiments using semiconductor micropillars [S. M. Ulrich et al., preceding Letter, Phys. Rev. Lett. 106, 247402 (2011)]. We also demonstrate that, surprisingly, phonon coupling actually helps resolve signatures of the elusive second rungs of the Jaynes-Cummings ladder states via off-resonant cavity feeding. Both multiphonon and multiphoton effects are shown to play a qualitatively important role on the fluorescence spectra.
We present a semiconductor quantum optics formalism to study the dynamics of a coherently-driven semiconductor quantum dot interacting with an acoustic phonon bath and a high Q microcavity. A quantum master equation is derived in the polaron frame, where multiphoton and multiphoton effects are included to all orders. As applications of the theory, we study the Mollow triplet of a driven quantum dot in the regime of semiconductor cavity-QED. Pronounced signatures of electron-phonon-photon scattering are observed through excitation-induced dephasing and off-resonant cavity coupling. We also present an effective phonon master in Lindblad form and show example quantum trajectory simulations that help one to understand the features in the Mollow triplet spectra.
We present a comprehensive theoretical study of the resonance fluorescence spectra of an coherently-driven quantum dot (QD) placed inside a high-QQQ semiconductor cavity and interacting with an acoustic-phonon bath. We derive a quantum master equation (ME) in the polaron frame, which includes exciton-phonon and exciton-cavity coupling to all orders. This work details and extends the theory used in a recent paper [C. Roy and S. Hughes, Phys. Rev. Lett. 106, 247403 (2011)] to describe the QD Mollow triplet in the regime of semiconductor cavity QED. Here, we introduce two ME forms, Nakajima-Zwanzig and time convolutionless (TC), both to second order in the system--phonon-reservoir perturbation. In the polaron frame, these two ME forms are shown to yield equivalent population dynamics and fluorescence spectra for a continuous wave (cw) driving field. We also demonstrate that a Markov approximation is valid for computing the incoherent scattering processes, and we subsequently exploit the TC ME to explore the resonance fluorescence spectra of an exciton-driven QD. Both cavity-emitted and exciton-emitted spectra are studied, and these are found to have qualitatively different spectral features. Using a coherent driving field, the well-known characteristics of the atomic Mollow triplet are shown to be considerably modified with electron--acoustic-phonon scattering, and we highlight the key effects arising from both cavity coupling and electron-phonon coupling. Regimes of pronounced cavity feeding and anharmonic cavity QED are exemplified, and we find that the cavity coupling depends sensitively on the exciton-cavity detuning and the temperature of the phonon bath. We show how the full width at half maximum (linewidth) of the Mollow-triplet sidebands varies as a function of the square of the Rabi frequency of the cw pump. Phonon-mediated cavity coupling also contributes to the spectral broadening of the Mollow triplet, depending upon the exciton-cavity detuning and the strength of the exciton-cavity coupling rate. Finally, we calculate the fluorescence spectra for off-resonance cw driving and investigate the resulting Mollow-triplet linewidths.
The thesis presents the investigations of the emission properties of the Mollow triplet (resonance fluorescence above emitter saturation) and dephasing effects in semiconductor quantum dots. The investigations of the Mollow triplet emission properties focus on the detuning dependent Mollow triplet emission especially the relative areas and width of the individual Mollow peaks. If both fine-structure components of the exciton are excited a Mollow quintuplet is experimentally observed, which is found to be in agreement with a theoretical model. In addition the indistinguishable photon emission from the individual Mollow sidebands is verified. The investigations on dephasing effects focus on the phonon-assisted incoherent excitation of a quantum dot and a comprehensive study of the emission properties under these excitation conditions. A second study focuses on the non-resonant emitter mode coupling of a quantum dot coupeld to two modes of the micro pillar cavity together with the corresponding emission properties.
We study the crucial role played by the solid-state environment in determining the photon emission characteristics of a driven quantum dot. For resonant driving, we predict a phonon enhancement of the coherently emitted radiation field with increasing driving strength, in stark contrast to the conventional expectation of a rapidly decreasing fraction of coherent emission with stronger driving. This surprising behavior results from thermalization of the dot with respect to the phonon bath and leads to a nonstandard regime of resonance fluorescence in which significant coherent scattering and the Mollow triplet coexist. Off resonance, we show that despite the phonon influence, narrowing of dot spectral sideband widths can occur in certain regimes, consistent with an experimental trend.
We present a microscopic description of the photon statistics and phonon signatures in the quantum light emission from semiconductor quantum dots. Using higher-order Born approximation, time-resolved optical emission and scattering spectra are calculated in the weak coupling regime. In the strong coupling regime, a mathematical induction method is presented to calculate the longitudinal optical (LO) phonon-assisted quantum dot cavity-QED. The phonon interaction at room temperature has a strong impact on the quantum correlation of the cavity field and enhances the non-classicality of the cavity field, initially prepared in a thermal state.