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Physical Review A

Twofold decoherence brought on by the phonon bath in a quantum-dot two-state system

Zhide Chen

Published Oct 12, 2015• 1 citation
Publisher

Abstract

Because of the inherent coupling, the influence from the phonon bath on the coherent energy exchange between a quantum-dot (QD) two-state system (TSS) and a resonant optical mode is a twofold action. One action is the influence on the construction of the coherence, and the other is on the constructed coherence. The latter has been extensively studied by the master-equation approach, whereas the former has been ignored so far. In the present paper, the influence from the phonon bath on the construction of the coherence is studied by using the small-polaron theory. It is found that in the presence of phonon coupling, the construction of the coherence depends on the state evolution of the phonon bath during the energy exchange. The coherence construction probability is calculated and found to be a decreasing function of both temperature and coupling strength. The spectrum including the twofold decoherence effect is calculated and the obtained result can help one to understand some peculiar observations in the photoluminescence spectrum of a QD TSS system, including the additional cavity line in the strong-coupling regime and the additional coherent scattering in the case of the Mollow triplet.

DOI
10.1103/physreva.92.043811

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Because of the inherent coupling, the influence from the phonon bath on the coherent energy exchange between a quantum-dot (QD) two-state system (TSS) and a resonant optical mode is a twofold action. One action is the influence on the construction of the coherence, and the other is on the constructed coherence. The latter has been extensively studied by the master-equation approach, whereas the former has been ignored so far. In the present paper, the influence from the phonon bath on the construction of the coherence is studied by using the small-polaron theory. It is found that in the presence of phonon coupling, the construction of the coherence depends on the state evolution of the phonon bath during the energy exchange. The coherence construction probability is calculated and found to be a decreasing function of both temperature and coupling strength. The spectrum including the twofold decoherence effect is calculated and the obtained result can help one to understand some peculiar observations in the photoluminescence spectrum of a QD TSS system, including the additional cavity line in the strong-coupling regime and the additional coherent scattering in the case of the Mollow triplet.
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.
We present a systematic analysis on the role of the quantum dot (QD) shape in the influence of the phonon bath on the dynamics of a QD cavity QED system. The spectral functions of the phonon bath in three representative QD shapes: spherical, ellipsoidal, and disk, are calculated from the carrier wave functions subjected to the confinement potential provided by the corresponding shape. The obtained spectral functions are used to calculate three main effects brought by the phonon bath, i.e., the coupling renormalization, the off-resonance assisted feeding rate and the pure dephasing rate. It is found that the spectral function of a disk QD has the widest distribution, hence the phonon bath in a disk QD can lead to the smallest renormalization factor, the largest dephasing rate in the short time domains(≤ 2 ps), and the off-resonance assisted feeding can support the widest detuning. Except for the pure dephasing rate in the long time domains, all the influences brought by the phonon bath show serious shape dependence.
We present a systematic analysis on the role of the quantum dot(QD) shape in the influence of the phonon bath on the dynamics of a QD cavity QED system. The spectral functions of the phonon bath in three representative QD shapes: spherical, ellipsoidal, and disk, are calculated from the carrier wave functions subjected to the confinement potential provided by the corresponding shape. The obtained spectral functions are used to calculate three main effects brought by the phonon bath, i.e., the coupling renormalization, the off-resonance assisted feeding rate and the pure dephasing rate. It is found that the spectral function of a disk QD has the widest distribution, hence the phonon bath in a disk QD can lead to the smallest renormalization factor, the largest dephasing rate in the short time domains(≤ 2 ps), and the off-resonance assisted feeding can support the widest detuning. Except for the pure dephasing rate in the long time domains, all the influences brought by the phonon bath show serious shape dependence.更多还原
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.
A semiconductor quantum dot (QD) embedded within an optical microcavity is a system of fundamental importance within quantum information processing. The optimization of quantum coherence is crucial in such applications, requiring an in-depth understanding of the relevant decoherence mechanisms. We provide herein a critical review of prevalent theoretical treatments of the QD-cavity system coupled to longitudinal acoustic phonons, comparing predictions against a recently obtained exact solution. Within this review we consider a range of temperatures and exciton-cavity coupling strengths. Predictions of the polaron Nakajima-Zwanzig (NZ) and time-convolutionless (TCL) master equations, as well as a variation of the former adapted for adiabatic continuous wave excitation (CWE), are compared against an asymptotically exact solution based upon Trotter's decomposition (TD) theorem. The NZ and TCL implementations, which apply a polaron transformation to the Hamiltonian and subsequently treat the exciton-cavity coupling to second order, do not offer a significant improvement accuracy relative to the polaron transformation alone. The CWE adaptation provides a marked improvement, capturing the broadband features of the absorption spectrum (not present in NZ and TCL implementations). We attribute this difference to the effect of the Markov approximation, and particularly its unsuitability in pulsed excitation regime. Even the CWE adaptation, however, breaks down in the regime of high temperature (50K50K50K) and strong exciton-cavity coupling (g≳0.2g \gtrsim 0.2g≳0.2 meV). The TD solution is of comparable computational complexity to the above-mentioned master equation approaches, yet remains accurate at higher temperatures and across a broad range of exciton-cavity coupling strengths (at least up to g=1.5g=1.5g=1.5 meV).