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Physical Review A

Influence of electron-phonon interaction on the optical spectrum and quantum statistics in a quantum-dot–cavity system: Master-equation approach

Zeynab Harsij, M. Bagheri Harouni, R. Roknizadeh, M. H. Naderi

Published Dec 4, 2012• 17 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.86.063803

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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.
Semiconductor quantum dots (QDs) in photonic nanocavities provide monolithic, robust platforms for both quantum information processing and cavity quantum electrodynamics (QED). An inherent feature of such solid-state cavity QED systems is the presence of electron-phonon interactions, which distinguishes these systems from conventional atomic cavity QED. Understanding the effects of electron-phonon interactions on these systems is indispensable for controlling and exploiting the rich physics that they exhibit. Here we investigate the effects of electron-phonon interactions on a QD-based cavity QED system. When the QD and the cavity are off-resonance, we observe phonon-assisted cavity mode emission that strongly depends on the temperature and cavity-detuning. When they are on-resonance, we observe an asymmetric vacuum Rabi doublet, the splitting of which narrows with increasing temperature. These experimental observations can be well reproduced using a cavity QED model that includes electron-acoustic-phonon interactions. Our work provides significant insight into the important but hitherto poorly understood mechanism of non-resonant QD-cavity coupling and into the physics of various cavity QED systems utilizing emitters coupled to phonons, such as nitrogen-vacancy centres in diamond and colloidal nanocrystals.
Electron-phonon coupling in semiconductor quantum dots plays a significant role in determining the optical properties of excited excitons, especially the spectral nature of emitted photons. This paper presents a comprehensive theory and analysis of emission spectra from artificial atoms or quantum dots coupled to structured photon reservoirs and acoustic phonons, when excited with incoherent pump fields. As specific examples of structured reservoirs, we chose a Lorentzian cavity and a slow-light coupled-cavity waveguide, which have both been explored experimentally. For the case of optical cavities, we directly compare and contrast the spectra from three well-known and distinct theoretical approaches to treat electron-phonon coupling, including a Markovian polaron master equation, a non-Markovian phonon correlation expansion technique, and a semiclassical linear susceptibility approach, and we point out the limitations of these models. For the cavity-QED polaron master equation, which treats the cavity-mode operator at the level of a system operator, we give closed form analytical solutions to the phonon-assisted scattering rates in the weak excitation approximation, fully accounting for temperature, cavity-exciton detuning, and cavity-dot coupling. We also show explicitly why the semiclassical linear susceptibility approach fails to correctly account for phonon-mediated cavity feeding. For weakly coupled cavities, we calculate the optical spectra using a more general photon reservoir polaron master-equation approach, and explain its differences from the above approaches in the low-QQQ limit of a Lorentzian cavity. We subsequently use this general reservoir approach to calculate the emission spectra from quantum dots coupled to slow-light photonic crystal waveguides, which demonstrate a number of striking photon-phonon coupling effects.
A microscopic theory to study the combined dynamics of a quantum dot exciton coupled to a single cavity mode as well as acoustic phonons is presented. By considering the phonon subsystem in the coherent state representation, the phonon’s impact on the emitted photons is investigated. The single photon emission probability and phonon effects on this quantity are studied. On the other hand, we illustrate that while a quantum dot interacts with a single cavity mode, the collapse and revival phenomenon will occur. It is demonstrated that acoustic phonons have a pronounced impact on the collapse and revival of the quantum dot exciton. Our finding reveals that at elevated temperatures the phonon interaction decreases the Rabi frequency. Moreover, the cavity mode possesses non-classical features such as sub-Poissonian statistics.
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Theoretical derivation and numerical calculation achieve the quantum dot numerically exact multi-photon emission spectra starting from the interaction of quantum dot and cavity,using the master equation that includes incoherent pumping and pure dephasing and combines with the quantum regression theorem, and considering the relevant initial conditions.Then comparing the multi-photon(fermion statistics) spectra with the one-thoton(boson system) correlation level, our analysis shows that according to the fermion statistics the pure dephasing, and the thermal bath model, an excellent fitting to the data is obtained with the recent experimental of Ref[22] results in a quantum dot-micropiller cavity system. The theory and the recent experiments both show pump-induced stimulated emission and anharmonic cavity-QED in quantum dot-cavity systems.