1111.4415 (C. Roy et al.)
C. Roy, S. Hughes
We present a comprehensive theoretical study of the resonance fluorescence
spectra of an exciton-driven quantum dot (QD) placed inside a high-$Q$
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 issue of {\em Physical Review Letters} (C. Roy and S.
Hughes 2011: Phys. Rev. Lett. {\bf 106} 247403) to describe the QD Mollow
triplet in the regime of semiconductor cavity-QED. Here we introduce two ME
forms, Nakajima-Zwanzig (NZ) 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 Markovian 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.
View original:
http://arxiv.org/abs/1111.4415
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