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Frontiers in Optics

Open system quantum optics in photonic crystal chips with embedded quantum dots

Stephen Hughes

Published Jan 1, 2012• 0 citations
Publisher

Abstract

We present a formalism to study open-system quantum optics for photonic crystal chips with embedded quantum dots. We study resonance fluorescence (Mollow triplets), nonlinear photon transport and phonon-mediated population inversion using a continuous-wave drive.
DOI
10.1364/ls.2012.lth1i.4

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A single semiconductor quantum dot that is strongly coupled to a photonic crystal nanocavity yields optical nonlinearities at the single photon level. The promise of quantum information processing is driving developments in several different physical implementations. Photons are attractive as carriers of quantum information be-cause they can travel long distances without losing their infor-mation through interactions with their environment. However, their passive nature can be a problem in applications such as the construction of logic gates, where it is necessary for two or more photons to interact. This interaction requires a nonlinear optical medium. Particularly strong nonlinearities are achieved when photons drive an emitter near its resonance frequency, and this nonlinearity is even greater if the photon is confined near the emitter in an optical cavity.
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.