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arXiv:1102.0254 · Physical Review Letters

Phonon-Dressed Mollow Triplet in the Regime of Cavity Quantum Electrodynamics: Excitation-Induced Dephasing and Nonperturbative Cavity Feeding Effects

C. Roy, Stephen Hughes

Published Jun 16, 2011• 165 citations
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Abstract

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.

DOI
10.1103/physrevlett.106.247403

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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 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.
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.
Detailed properties of resonance fluorescence from a single quantum dot in a micropillar cavity are investigated, with particular focus on emission coherence in the dependence on optical driving field power and detuning. A power-dependent series over a wide range reveals characteristic Mollow triplet spectra with large Rabi splittings of |Ω|≤15 GHz. In particular, the effect of dephasing in terms of systematic spectral broadening ∝Ω(2) of the Mollow sidebands is observed as a strong fingerprint of excitation-induced dephasing. Our results are in excellent agreement with predictions of a recently presented model on phonon-dressed quantum dot Mollow triplet emission in the cavity-QED regime.
We present both experimental and theoretical investigations of a laser-driven quantum dot (QD) in the dressed-state regime of resonance fluorescence. We explore the role of phonon scattering and pure dephasing on the detuning-dependence of the Mollow triplet and show that the triplet sidebands may spectrally broaden or narrow with increasing detuning. Based on a polaron master equation approach, which includes electron-phonon interaction nonperturbatively, we derive a fully analytical expression for the spectrum. With respect to detuning dependence, we identify a crossover between the regimes of spectral sideband narrowing or broadening. We also predict regimes of phonon-induced squeezing and anti-squeezing of the spectral resonances. A comparison of the theoretical predictions to detailed experimental studies on the laser detuning-dependence of Mollow triplet resonance emission from single In(Ga)As QDs reveals excellent agreement.
We investigate temperature-dependent resonance fluorescence spectra obtained from a single self-assembled quantum dot. A decrease of the Mollow triplet sideband splitting is observed with increasing temperature, an effect we attribute to a phonon-induced renormalization of the driven dot Rabi frequency. We also present first evidence for a nonperturbative regime of phonon coupling, in which the expected linear increase in sideband linewidth as a function of temperature is canceled by the corresponding reduction in Rabi frequency. These results indicate that dephasing in semiconductor quantum dots may be less sensitive to changes in temperature than expected from a standard weak-coupling analysis of phonon effects.
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.