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Variational master equation for a driven quantum dot embedded in an optical resonator

Oscar J. Gómez-Sánchez, Hanz Y. Ramírez

Published Nov 17, 2016• 0 citations
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Abstract

In this work, we study the dynamics of a quantum dot embedded in a QED cavity and driven by a coherent electromagnetic field, while interacting with a bath of acoustic phonons. We address the phonon dissipative effects on the resonance fluorescence of the system by deriving a variational master equation, valid for a broader range of temperatures, pumping rates, and quantum dot-cavity coupling intensities, than previously reported approaches.

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In this work, we study the dynamics of a quantum dot embedded in a QED cavity and driven by a coherent electromagnetic field, while interacting with a bath of acoustic phonons. We address the phonon dissipative effects on the resonance fluorescence of the system by deriving a variational master equation, valid for a broader range of temperatures, pumping rates, and quantum dot-cavity coupling intensities, than previously reported approaches.
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.
In this work, dissipative effects from a phonon bath on the resonance fluorescence of a solid-state two-level system embedded in a high-quality semiconductor microcavity and driven by an intense laser are investigated. Within the density operator formalism, we derive a variational master equation valid for broader ranges of temperatures, pumping rates, and radiation-matter couplings than previous studies. From the obtained master equation, fluorescence spectra for various thermal and exciting conditions are numerically calculated and compared to those computed from weak coupling and polaronic master equations, respectively. Our results evidence the breakdown of those rougher approaches under increased temperature and strong pumping.
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 investigate a quantum-dot-based cavity system via the master-equation approach. The dynamics of the system is greatly affected by dissipation and dephasing processes. We include these phenomena to the theory through the master equation. The dissipation effects such as cavity loss, spontaneous recombination of excitons, and incoherent pumping are considered. The dephasing process is included as an electron--acoustic-phonon interaction. An intrinsic feature of solid-state cavity systems is the presence of electron-phonon interaction, which distinguishes this system from atomic cavity quantum electrodynamics. Due to the temperature dependence of phonons we use the complete form of the master equation (temperature dependence of dissipation rates) in this paper. We study the emission spectrum and photon statistics of the system. We show that cavity mode emission depends on temperature, and temperature strongly affects the photon statistics.
We theoretically propose a scheme for the quadrature squeezing of the cavity field via dissipative processes. The effects of the electron-phonon interaction (EPI) on the squeezing are investigated, where the cavity is off-resonantly coupled with a coherently driven quantum dot (QD) which is allowed to interact with an acoustic-phonon reservoir. Under certain conditions, the participation of the phonon induced by both the EPI and the off-resonant coupling of the cavity with the QD enables some dissipative processes to occur resonantly in the dressed-state basis of the QD. The cavity-mode photons emitted or absorbed during the phonon-mediated dissipative processes are correlated, thus leading to the squeezing of the cavity field. A squeezed vacuum reservoir for the cavity field is built up due to the EPI plus the off-resonant coupling between the cavity and the QD. The numerical results obtained with an effective polaron master equation derived using second-order perturbation theory indicate that, in low temperature limit, the degree of squeezing is maximal but the increasing temperature of the phonon reservoir could hinder the squeezing and degrade the degree of the squeezing of the cavity field. In addition, the presence of the photonic crystal could enhance the quadrature squeezing of the cavity field.
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.